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Universita degli studi di PerugiaPhD course: Scienza e tecnologia per la fisica e la geologia
Phenomenology andexperimental search of excitedcomposite fermions at Run II
of the LHC
Candidate: Supervisor:Roberto Leonardi Orlando Panella
Assistant supervisors: Coordinator:Livio Fano Paola Comodi
Francesco Romeo
Abstract
This thesis concerns the beyond the Standard Model physics, in particular ittakes into account the hypothesis of the composition of leptons and quarks(Composite models).
We perform a phenomenological study on the production and decay atLHC of quarks of charge Q = 5/3e and Q = 4/3e predicted in compositemodels of higer isospin multiplets (IW = 1 or IW = 3/2). We compute decaywidths and rates for production of the exotic quarks at the LHC. Focusingon pp→ U+j → `+pT/ jj process, we perform a fast simulation of the detectorreconstruction based on DELPHES. We then scan the parameter space of themodel (m∗ = Λ) and study the statistical significance of the signal againstthe relevant standard model background providing the luminosity curves asfunction of m∗ for discovery at 3- and 5-σ level.
We perform a phenomenological study also on the production af a heavycomposite Majorana neutrino. While previous studies of the composite Majo-rana neutrino were focused on gauge interactions via magnetic type couplingbetween ordinary and excited fermions, here we complement the compositemodel with contact interaction. We find that the production cross sectionare dominated by such contact interaction. We study the same-sign di-leptonand di-jet signature (pp→ ``jj) and perform a fast detector simulation basedon DELPHES. We compute the 3- and 5-σ contour plots of the statisticalsignificance in the parameter space (Λ,m∗).
We perform also an experimental search for the heavy composite Majo-rana neutrino in the two same-flavour leptons (electrons or muons) and twoquarks final state. The analysis is performed using proton-proton collisions at√s = 13TeV collected by the CMS experiment at the CERN LHC in 2015,
the datad correspond to an integrated luminosity of 2.3 fb−1. The observeddata are in good agreement with the Standard Model prediction and Exclu-sion limits are set on the mass of the heavy composite Majorana neutrino(MN`
) and the compositness scale (Λ). For the case MN`= Λ the existence
of Ne and Nµ is excluded up to masses of 4.60 and 4.70 TeV , respectively,at 95% confidence level.
Contents
1 The Standard Model and its extensions 31.1 Introduction to the Standard Model . . . . . . . . . . . . . . . 31.2 The Standard Model lagrangian . . . . . . . . . . . . . . . . . 41.3 Shortcoming of the Standard Model . . . . . . . . . . . . . . . 71.4 Models beyond the Standard Model . . . . . . . . . . . . . . . 81.5 Composite models . . . . . . . . . . . . . . . . . . . . . . . . . 101.6 Extended weak isospin model (IW = 1, 3
2) . . . . . . . . . . . . 12
2 Phenomenology of excited quarks of charge 5/3e and 4/3e 142.1 The U+ and D− states in the extended weak isospin model . . 162.2 Production and decay of the exoticly charged quarks . . . . . 172.3 Signal and background . . . . . . . . . . . . . . . . . . . . . . 202.4 Fast detector simulation and reconstructed object . . . . . . . 242.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 Phenomenology of the heavy composite Majorana neutrino 303.1 The heavy Majorana neutrino in composite models with gauge
and contact interactions . . . . . . . . . . . . . . . . . . . . . 313.2 Cross section and decay width of the composite Majorana neu-
trino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.3 Topology of the signal . . . . . . . . . . . . . . . . . . . . . . 383.4 Signal and background . . . . . . . . . . . . . . . . . . . . . . 403.5 Fast detector simulation and reconstructed objects . . . . . . . 423.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Relations between theory and experiments 47
5 The LHC and the CMS experiment 505.1 LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.2 The CMS experiment . . . . . . . . . . . . . . . . . . . . . . . 51
5.2.1 Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . 53
1
5.2.2 Inner tracker . . . . . . . . . . . . . . . . . . . . . . . 535.2.3 Electromagnetic calorimeter . . . . . . . . . . . . . . . 545.2.4 Hadronic calorimeter . . . . . . . . . . . . . . . . . . . 555.2.5 Muon system . . . . . . . . . . . . . . . . . . . . . . . 555.2.6 Trigger and data acquisition . . . . . . . . . . . . . . . 56
6 Experimental search for heavy composite Majorana neutrino 586.1 Data and Monte Carlo samples . . . . . . . . . . . . . . . . . 586.2 Object reconstruction and identification . . . . . . . . . . . . 61
6.2.1 Primary vertex . . . . . . . . . . . . . . . . . . . . . . 616.2.2 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . 626.2.3 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.2.4 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.3 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . 666.3.1 Particle selection . . . . . . . . . . . . . . . . . . . . . 676.3.2 High mass region definition . . . . . . . . . . . . . . . 686.3.3 Request on number of jets or large-radius jets . . . . . 686.3.4 Summary of signal region selection . . . . . . . . . . . 72
6.4 Choice of the variable for the signal extraction . . . . . . . . . 746.5 Background estimation . . . . . . . . . . . . . . . . . . . . . . 74
6.5.1 Estimation of DY background . . . . . . . . . . . . . . 756.5.2 Estimation of QCD multijet background . . . . . . . . 766.5.3 Estimation of the tt and tW backgrounds . . . . . . . . 78
6.6 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . 806.7 Unblinded results . . . . . . . . . . . . . . . . . . . . . . . . . 836.8 Statistical interpretation of the results . . . . . . . . . . . . . 84
6.8.1 Upper limit extraction . . . . . . . . . . . . . . . . . . 846.8.2 Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7 Conclusions 90
A The parton model 91
B Plots of systematic uncertainties 93B.1 eejj channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93B.2 µµjj channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Bibliography 109
2
Chapter 1
The Standard Model and itsextensions
1.1 Introduction to the Standard Model
The Standard Model (SM) of particle physics is the theory describing thepresent vision of the fundamental particles and their interactions. The fun-damental blocks of matter are the fermions, particles of spin 1/2, organisedin families. Each family contains two leptons and two flavour of quarks. Inthe first family we find the electron, the electronic neutrino, the up quarkand the down quark; in the second family the muon, the muonic neutrino,the charm quark and strange quark; in the third family the tau, the tauneutrino, the top quark and the bottom quark.
The forces between these particles, which are included in the model, arethe electromagnetic, the weak and the strong interactions. So far all attemptsto encompass the last type of known interaction, the gravity, has been un-successful. In the Standard Model forces are mediated by particles calledgauge bosons. Electromagnetic interaction is mediated by photons (γ), weakinteraction by weak bosons (W±, Z) and strong interaction by gluons (G).
The important aspect of the model is related to the concept of symmetry.According to Noether’s theorem every symmetry is associated with a con-servation law. The requirement of charge (electrical or color) conservationfollows from invariance under a global phase (gauge) transformation. Therequirement of local gauge invariance is accomplished by introducing newvector boson fields, the so called gauge fields. The number of introducedvector fields corresponds to the number of independent generators of a cho-sen symmetry group. Therefore by a proper specification of the symmetrygroup one can describe the particle system with the number of vector field
3
which is expected from experiments.The gauge symmetry group of the Standard Model is SU(3) × SU(2) ×
U(1). There is no particular reasons for this choice, except that it successfullydescribes the experimental data. The SU(2)×U(1) group was introduced byGlashow to unify electromagnetic and weak interactions [1]. This formulationwas not able to introduce masses for the gauge bosons. Later, independently,Weinberg [2] and Salam [3] extended and completed the theory, integratingin it the Higgs proposal of spontaneous symmetry breaking [4], that allowsto originate the masses of all particles described in the model as long aswe introduce in the theory a neutral scalar particle, the Higgs boson. TheSU(3) group, on the other hand, is associated with the local color symmetryof quarks. It underlies the theory of Quantum Chromo Dynamics (QCD)which describes the interactions of quarks.It has been introduced in differentmoments, also thanks to a work of Glashow, Iliopoulos and Maiani [5], thathave introduced a fourth quark, called “charm”, and to a work of Kobayashiand Maskawa [6] that have introduced the third generation quarks.
1.2 The Standard Model lagrangian
Within the Standard Model the quarks and leptons are represented by fermionsfields. Since the electroweak interactions are chiral, the left- and the right-handed components are assigned to different representations of the SU(2)group: the left-handed fields transform as SU(2) doublets and the right-handed fields transform as singlets. The fundamental fermions can thereforebe grouped as:(
νee−
)L
(νµµ−
)L
(νττ−
)L(
ud′
)L
(cs′
)L
(tb′
)L
Left-handed fermions SU(2) doublets
e−R µ−R τ−RuR cR tRdR sR bR
Right-handed fermions SU(2) singlets
and they transform as:
ΨL =1
2(1− γ5)Ψ→ eiY β(x)+iIjα
j(x)ΨL (1.1)
ΨR =1
3(1 + γ5)Ψ→ eiY β(x)ΨR (1.2)
4
where Ij, j = 1, 2, 3 are the three generators of the SU(2) group and Yis the generator of the U(1) group, often referred to as the weak isospinand the weak hypercharge, respectively. The respective charges of the weakisospin and weak hypercharge need to be conserved due to gauge invariance.Unification of weak and electromagnetic interactions yields the Gell-Mann-Nishijima relation for the electric charge: Q = Y
2+ I3 with I3 being the third
component of the weak isospin.The fundamental Standard Model lagrangian can be written as:
L = L0 + LEW + LQCD + LH + LY (1.3)
The L0 is the kinetic term, corresponding to the lagrangian of a freefermion:
L0 = Ψ(iγµ∂µ −m)Ψ (1.4)
The LEW is the term describing the electroweak interaction. The weakforce acts only on left-handed particles, leaving the right-handed particlesuntouched, therefore we have
LEW = ΨLγµ
(−g′Y
2Bµ − gIiW i
µ
)ΨL + ΨR
(−g′Y
2Bµ
)ΨR+
− 1
4BµνB
µν − 1
4W iµνW
µνi (1.5)
where W iµ with i = 1, 2, 3 and Bµ are respectively the SU(2) and U(1) gauge
fields. The W iµν and Bµν are the field strength tensors and they are given by
W iµν = ∂µW
iν − ∂νW i
µ + gεijkW jµW
kν (1.6)
Bµν = ∂µBν − ∂νBµ (1.7)
The SU(2) coupling costant g and the weak hypercharge coupling costant g′
are related to the electromagnetic coupling costant e through the Weinbergangle θW as g = e/ sin θW and g′ = e/ cos θW . The first two terms of Eq.1.5describe the interaction of the gauge fields with the left- and right-handedfermions. The remaining terms are the kinetic energy of the Bµ field and thekinetic energy and self coupling of the Wµ fields. The bilinear term in Wµν
generates quadratic and cubic self interactions which are characteristic fornon-Abelian gauge theories.
The LQCD is the term describing the strong interaction. It affects onlythe quarks, that carry a color charge, but it does not affect the leptons, thatdo not carry a color charge. Its expression is
LQCD = Ψγµ(gsG
aµT
a)
Ψ− 1
4GaµνG
aµν (1.8)
5
where Gaµ with a = 1, ..., 8 are the gluon fields, the T a are the eight generators
of SU(3) group and the Gaµν are the field strength tensors, given by
Gaµν = ∂µG
aν − ∂νGa
µ − gsεabcGbµG
cν (1.9)
gs is the strong coupling constant. The first term of Eq.1.8 describes theinteraction of the gluons with the quarks, while the second term is the kineticenergy and self coupling of the gluons. The bilinear term in Ga
µν generatesquadratic and cubic self interactions.
The LH has the form
LH = H
(∂µ − ig′Y
2Bµ − igIiW iµ
)(∂µ + ig′
Y
2Bµ + igIiW
iµ
)+
− V (H,H†) (1.10)
Here four scalar fields, H, are introduced. They are arranged in a complexSU(2)L isospin doublet with weak hypercharge Y = 1. The self-interactionterm between the Higgs, V (H), is given by
V (H) = −µ2H†H + λ2(H†H)2, λ2 > 0 (1.11)
Provided that µ2 is positive, the potential is at its minimum when H†H =µ2
2λ= v2
2.
Since electric charge is a conserved quantity, the gauge group associatedwith electromagnetic interaction, U(1)em, needs to remain a true symmetryof the vacuum. This is accomplished by letting the neutral component of theHiggs doublet have the vacuum expectation value (VEV):
〈H〉 =1√2
(0v
)(1.12)
After a suitable gauge transformation, we can parametrise H around itsminimum as
H =1√2
(0
v + h
)(1.13)
The neutral field h is usually referred to as the Higgs field. The StandardModel symmetry group, SU(3)c × SU(2)L × U(1)Y , is spontaneusly brokenand the remaining symmetry is SU(3)c × U(1)Y .
This mechanism, called the Higgs mechanism, gives rise to masses for thegauge fields, W±
µ and Zµ, and leaves the photon field, Aµ, massless. Thephysical gauge fields are defined as
W±µ =
W 1µ ∓W 2
µ√2
, Zµ =gW 3
µ − g′Bµ√(g′2g2)
, Aµ =g′W 3
µ + gBµ√(g′2g2)
(1.14)
6
of which the first two acquire masses
M2W =
g2v2
4, M2
Z =M2
W (g2 + g′2)
g2=
M2W
cos2 θW(1.15)
The value for the sin2 θW is 0.23 and the masses for the W and the Z bosonsare 80.4 and 90.2 GeV respectively. The measured values for the couplingsthen yield v = 246GeV .
The last term in the Standard Model lagrangian, LY describes the inter-action between fermions and the Higgs doublet. It has the form
−∑f
gf (ΨfLH)Ψf
R + h.c. (1.16)
The Youkawa couplings, gf , are arbitrary values, determined from experi-ments. To generate masses one substitutes Eq.1.12 for H and we can expressthe fermionic masses as
mf =v√2gf . (1.17)
The Standard Model had a great success in explaining the experimentalobservation, the last of which is the discovery of the Higgs boson in 2012[8][9].
1.3 Shortcoming of the Standard Model
Although the Standard Model is a very successful theory, it is believed notto be an ultimate theory of nature. The reasons for that are twofold. On theone hand, there are a number of phenomena which are not explained withinthe Standard Model:
Neutrino masses. Within the Standard Model the neutrinos are con-sidered massless. However experiments with solar and atmospheric neutrinoshave shown that the three generations of neutrinos mix with each other [10].This would not be possible if their mass were zero.
Dark matter and dark energy. Cosmological observation, such as thecosmic microwave background and the structure and movements of galaxies,show that the energy content of the universe consists of roughly 5% baryonicmatter, 25% dark matter and 70% dark energy [11]. The Standard Modeldescribes only the baryonic matter.
Gravity. The fourth type of interaction, gravity, is not incorporatedin the Standard Model. At the electroweak scale gravity is so weak to be
7
negligible. The scale at which effects of quantum gravity are expected tobecome important is of order of 1019 GeV and it is referred to as the Planckscale.
Baryogenesis. The baryon-antibaryion asymmetry observed in the uni-verse is not explained by the Standard Model.
On the other hand, there is a number of problems which either remainunsolved or the solutions incorporated in the Standard Model do not haveany fundamental justification:
The hierarchy problem. It arises from the fact that the weak scale(mweak ≈ 100GeV ) and the Planck scale (Mp ≈ 1019GeV ) differ by 17 ordersof magnitude. The Higgs mass is quadratically divergent when one loop ofself-interactions of the Higgs boson is considered. For these divergences to becancelled an additional mass counterterm, δm2
H , needs to be introduced. Atthe lowest order in perturbation theory, the Higgs mass is m2
H = m20 +δm2
H ≈m2
0−g2λ2 where m20 is the “ground” Higgs mass, g is a dimensionless coupling
constant and λ is the energy scale. Taking into account the Higgs mass(≈ 125GeV ) and assuming that g ≈ 1 and λ is around the Planck scale,then m0 must be adjusted so that m2
0 − g2λ2 ≈ m2H . This requires a precise
adjustment of the Standard Model parameters. This fine-tuning is not a verysatisfying solution.
The unification problem. The Standard Model gauge group SU(3)c×SU(2)L×U(1)Y consists of three different subgroups each having its couplingconstant. The couplings run with the scale and it would be natural if theyconverge toward a common value at some scale. This scale is referred to asthe unification scale. However, precision measurement have shown that thethree coupling constants do not exactly meet in a single point [12]
The masses and the flavour problem. The Standard Model does notexplain why there are exactly three generations of quarks and leptons, thelast two being heavier version of the first. Furthermore, the masses of thefermions span over many order of magnitude. The reason for this is unknown.
1.4 Models beyond the Standard Model
Several extensions of the Standard Model have been proposed to address theproblems outlined in section 1.3. General concepts involve:
Grand Unification Theories. The grand unification theories (GUT)[13] hypothesize that the SU(3)c × SU(2)L ×U(1)Y symmetry, consisting of
8
three different subgroups each having its own coupling constant, originatesfrom a larger symmetry group with only one coupling constant.
One of the most popular GUT scenarios is the Left-Right symmetricmodel (LRM). It is based on a SO(10) group, that breaks down via thefollowing chain:
SO(10)→ SU(3)c × SU(2)L × SU(2)R × U(1)B−L (1.18)
The U(1)B−L is a global gauge symmetry associated to the conservation ofbaryon minus lepton number. The LRM predicts the existence of new gaugebosons, Z ′ and W ′±, that couple to right handed fermions. It predicts also aright-handed neutrino.
Supersymmetry. Supersymmetry (SUSY) [14] is a theory which postu-lates the existence of a symmetry between fermions and bosons. It predictsthat for every Standard Model particle, there exist a supersymmetric partnerwith the same mass, but with the spin differing by 1/2. Since the particleshave not yet been discovered, the symmetry must be broken at some scale.Supersymmetry can offer a solution to the hierarchy problem. In fact thefermion and boson loops that make the Higgs boson very heavy are cancelledby the SUSY partners. In R-parity conserving models the lightest SUSYparticle is stable and it can therefore account for the dark matter. The mostpopular model is the minimal supersymmetric standard model (MSSM) [15].
Extra-dimensions. The idea is that the four-dimensional world, we livein, is embedded in a higher dimensional space. Since the extra dimensionshave not been detected so far, they have to be either compactified as in theN.Arkani-Hamed, S.Dimopoulos and G.Divali (ADD) [16] and universal ex-tra dimension (UED) models or they have a strong curvature, which makesit hard to escape into them as in the Randall-Sundrum (RS) model [17].In these models gravity can propagate in the extra dimensions and there-fore the Standard model particles experience only a small fraction of totalgravitational force. In this way the hierarchy problem is solved because thefundamental scale of gravity (and therefore the ultimate limit up to whichthe SM is valid) lies around the TeV region. In scenarios where the StandardModel particles are allowed to propagate in the extra dimensions (such as inthe UED) for every Standard Model particle there is a series os particles, theso called Kaluza-Klein excitations. The lightest of these Kaluza-Klein modesis stable and it may be a good candidate for dark matter [11].
Dynamical symmetry breaking. The idea is motivated by the premisethat every fundamental energy scale should have a dynamical origin and thusthe weak scale should reflect the characteristic energy of a new strong interac-tion called technicolor. Thechnicolor (TC) and extended technicolor (ETC)
9
models are asymptotically free gauge theories of fermions with no elementaryscalars. The electroweak symmetry is dynamically broken through the new,technicolor interaction [18][19].
String theory. The string theory [20] tries to combine the quantisticmechanics with the general relativity. It is based on the principle that theparticles are the manifestations of primal physical entity, called strings. Eachstring presents many modes of vibration, each of which corresponds to adifferent kind of fundamental particle.
Leptoquark models. The leptoquarks are hypotetical particles thatcarry both lepton and baryon number. They are predicted in many extensionsof the Standard Model described in this chapter, such as GUT, compositemodels, extended technicolor models. They are SU(3) color triplet bosonswith properties depending on the structure of each specific model. For thisreason direct searches for leptoquarks at collider experiments are typicallyperformed in the context of an effective leptoquark model: the Buchmuller-Ruckl-Wyler (BRW) model [21].
This model provides a general effective lagrangian describing interactionsof leptoquarks with Standard Model fermions, through a Yukawa coupling.Specific properties are required: leptoquarks need to have dimensionless cou-plings to Standard Model lepton-quark pairs in order for their interactionsto be renormalizable; leptoquarks interactions are required to be invariantunder the Standard Model SU(3)c × SU(2)L × U(1)Y gauge groups; lepto-quark interaction with lepton-quark pairs are required to preserve baryonand lepton number separately; leptoquarks couple to a single chirality andgeneration of Standard Model fermions at a time. From the previous prop-erties three generation of leptoquarks arise in accordance with the StandardModel nomenclature.
Composite models. These models consider quarks and leptons com-posed by more fundamental constituents generically called “preons”. Thesemodels will be described more in detail in the following.
1.5 Composite models
The particles considered as the fundamental constituents of the matter havechanged during the time. In the eighteenth and the nineteenth century manykinds of atoms were known. These seemed to be different from each other,until common characteristics were discovered and they were sorted in theperiodic table. At this point the question rose if this multiplicity could beexplained trough a minor number of constituents. Different atomic models
10
were proposed and experiments led to the discovery of electrons and nuclei.They were assumed play the role of fundamental constituents of the mattertaking the place of the atoms.
Later it was found that also the nuclei have a multiplicity, like for theatoms, and the nucleus of an element can also have different isotopes. There-fore, in an analogous way, the constituents of the nuclei, protons and neu-trons, were discovered. The fundamental constituents of the matter werethus identified in protons, neutrons and electrons.
Subsequentially experiments on cosmic rays and accelerated beams led tothe discovery of many particles that could be considered as fundamental forthe knowledge of that time. With the discovery of the π, ρ and κ mesonsand of their excited states the number of the particles that were consideredfundamental grew up. Furthermore theoretical considerations predicted aset of hadrons that were effectively observed, so the number of fundamentalparticles increased more. With the strengthening of the accelerators, finally,the internal structure of the hadrons was revealed. The hadrons resultedto be constituted by the quarks, that, together with the leptons, assumetoday the role of fundamental particles. Despite there are not experimentalobservations that require the introduction of a composite model for quark andleptons, following this historical evolution, it is natural to speculate aboutthe compositeness of the current assumed fundametal particles [23][43].
In general there are two important facts that lead to consider compositemodels:
• The proliferation of the particles considred as fundamental
• The observation of excited states of the particles considered as funda-mental
During the years new leptons and quarks have been discovered and a highnumber of particles considered as fundamental can be a clue of a furthercomposition.
In the lepton sector the electron has been joined by the muon, the tau,the electron neutrino, the muonic neutrino and the tau neutrino; in the quarksector the up and down quark, that have been the first to be discovered, havebeen joined by the charm, the strange, the bottom and finally the top.
The current scheme of the fundamental particles includes twenty-fourfermions divided in eighteen quarks (six flavours each of which can havethree colors) and six leptons. They are sorted in three generations thatpresents the same characteristics except the mass. In addition there is thepossibility of decay from one particle to another, for example the tau candecay in a muon and a muon in an electron; in the quark sector too there
11
are transitions, both in the same generation and, with a lower probability,between different generations. Therefore we have to deal with fundamentalparticles that decay in each other and this is not an ideal feature for particlesconsidered fundamental.
However an important fact that would allow to consider seriously thehypothesis of compositness of quark and leptons is the observation of theirexcited states. In the past excited atoms, nuclei and hadrons were observedand later all of these systems revealed to be composite. In the same way ifquarks and leptons have a substructure we expect to observe some excitedstate.
In this approach quarks and leptons are assumed to have an internalsubstructure which should become manifest at some sufficiently high energyscale, the compositness scale Λ. Ordinary fermions are then tought to bebound states of some yet unobserved fundamental constituents, genericallycalled preons.
1.6 Extended weak isospin model (IW = 1, 32)
When a physical system is studied, we usually have not enough informationsto give a complete description of some properties, therefore the correspondenteffects have to be parametrised. The experimental measure of the parameterswill provide the information needed for a more complete description.
A common procedure usually adopted to this purpose is to determine thedegrees of freedom and the symmetries of the system and then to build upan effective lagrangian.
This method is useful in the description of the compositness, in fact wehave not information about the potential constituents of quarks and leptons.These constituents interact at higher energies than the experimental limits,so it is not yet possible to observe their dynamics. However the consequencesof this dynamics could arise at lower energies, with the production of boundstates or transitions among standard model fermions and their excited states.We can therefore try to study these effects.
The weak isospin model proposed by Pancheri and Srivastava in [22] usesthe effective lagrangian formalism. The authors propose to use the weakisospin symmetry to reveal the excited leptons and quarks, without refer-ring to the internal dynamics, in analogy with the strong isospin symmetry,by means of which the hadronic resonances have been predicted before thediscovery of quarks and gluons.
The innovation of this work with respect to the previous ones like [23] isthe introduction of the weak isospin multiplets with IW = 1 and IW = 3/2 for
12
the excited fermions. In fact the standard fermions belong to weak isospindoublets or singlets, IW = 0 and IW = 1/2, while the electroweak bosonshave IW = 0 and IW = 1, therefore for the excited fermions we can considermultiplets with IW ≤ 3/2. The excited fermions with the respective quantumnumber are shown in the tables 1.1. In the tables we can see that the highermultiplets, IW = 1, 3
2, contain states with exotic charge: quark with charge
5/3e and 4/3e and leptons with charge 2e. Phenomenological studies on thismodel have been done considering the doubly charged excited lepton [27][28]. In the work described in the following chapters we will concentrate onthe phenomenology of the excited quarks with charge 5/3e and 4/3e, and onthe phenomenology and experimental search of heavy composite neutrinos.
IW Multiplet Q Y0 L− −1 −2
12
L =
(L0
L−
)0−1
-1
1 L =
L0
L−
L−−
0−1−2
-2
32
L =
L+
L0
L−
L−−
10−1−2
-1
IW Multiplet Q Y0 U 2/3 4/30 D −1/3 −2/3
12
Ψ =
(UD
)2/3−1/3
1/3
1 U =
U+
UD
5/32/3−1/3
4/3
1 D =
UDD−
2/31/3−4/3
−2/3
32
Ψ =
U+
UDD−
5/32/3−1/3−4/3
1/3
Table 1.1: The excited leptons multiplets with IW ≤ 3/2 and their quantumnumbers on the left and the excited quark multiplets with IW ≤ 3/2 andtheir quantum numbers on the right.
13
Chapter 2
Phenomenology of excitedquarks of charge 5/3e and 4/3e
In this chapter we will consider the phenomenology at the LHC of the exoticcomposite quarks of charge 5/3e and 4/3e, predicted by the extended weakisospin model as stated in the section 1.6.
The majority of the phenomenological studies about the production atcolliders of excited composite fermions has been concentrated on the mul-tiplets of isospin IW = 0, 1/2 [23][24][25]. Recently ATLAS [29] and CMS[30] have put bounds on the mass of excited quarks related to multiplets ofisospin IW = 0, 1/2. The phenomenology at colliders of the excited fermionbelonging to multiplets of weak isospin IW = 1, 3/2 has received only re-cently some attention with respect to the lepton sector, with some worksstudying the production at the LHC of the doubly charged leptons [27][28].The possibility of high-charge, high-mass quarks has been proposed [31], butin view of a different scenario. The work presented in this chapter is the firstthat consider exoticly charged quarks arising from a composite scenario withmultiplets of weak isospin IW = 1, 3/2.
The U+ exotic state of charge 5/3e couples only to the W gauge boson,so it can be resonantly produced and than decay to Wu. Within the firstgeneration we have the production subprocesses
uu→ U+(5/3)d (2.1a)
ud→ U+(5/3)u (2.1b)
and the decay processU+
(5/3) → W+u (2.2)
For the D− exotic state of charge −4/3e the same statements are valid and,
14
WU+(5/3)
u
u
d
b)
U+(5/3)u
d u
W
a)
U+(5/3)u
u d
W
U+(5/3)u
u d
W
Figure 2.1: Example processes of U+ resonant production in pp collisions. a)the Feynman diagrams for the process in the Eq.2.1a showing theW exchangein the t-channel (left) and u-channel (right); b) the Feynman diagrams forthe process in the Eq.2.1b showing the s-channel annihilation (left) and thet-channel W exchange (right).
within the first generation, we have the production subprocesses:
dd→ D−(4/3)u (2.3a)
du→ D−(4/3)d (2.3b)
and the decay processD−(4/3) → W−d (2.4)
In a pp collider the production cross section of the U+ state is higher thanthe one of D− state, due to the availability of two valence u quarks from eachof the colliding particles.
In Fig.2.1 we show the Feynman diagrams contributing to the partonsub-processes in Eq.2.1. We have t-channel and u-channel W exchange forthe subprocess in Eq.2.1a and a s-channel annihilation and a t-channel W
15
exchange for the subprocess in Eq.2.1b. The subprocesses in Eq.2.3 havesimilar diagrams. In this work we discuss the phenomenology of the U+
and D− excited quarks at the LHC, considering the leptonic decay of the Wboson (W → `ν`), therefore our signature is `pT/ jj and the processes are:
pp→ U+j → `+pT/ jj (2.5)
pp→ D−j → `−pT/ jj (2.6)
2.1 The U+ and D− states in the extended
weak isospin model
In order to compute the production cross section and decays of the excitedfermions we need to define their couplings to light fermions and gauge bosons.The rules are easily derived [22] referring to the weak isospin and hypercharge(Y). Since all the the gauge fields have Y = 0, excited fermions can onlycouple to light fermions with the same Y value. Moreover to satisfy gaugeinvariance, we need transition current containing a σµν term and not a singleγµ i.e. an anomalous magnetic moment type coupling. This automaticallyensures current conservation.
As stated in Section 1.6, the U+ and D− states belong to weak isospinmultiplets with IW = 1 and IW = 3/2 shown in Table 1.1. While referringto work [22] for a detailed discussion of all couplings and interactions, wediscuss here only the main features of these higher multiplets. We recall thatthese multiplets (IW = 1, 3/2) contribute only to the isovector current anddo not contribute to the hypercharge current. Therefore the particles of thesemultiplets interact with standard model fermions only trough the W gaugefield. The effective lagrangians for the two multiplets are :
L(IW =3/2) = g∑
M,m,m′
C(3
2,M |1,m;
1
2,m′)×
(f3q
m∗
)(ΨMσµνqLm′)∂
ν(Wm)µ+h.c.
(2.7)
L(IW =1) = g∑
m=−1,0,1
[(f1u
m∗
)(UmσµνuR) +
(f1d
m∗
)(DmσµνdR)
]∂ν(Wm)µ+h.c.
(2.8)In the above equations g is the SU(2) coupling, f1u, f1d, f3q are unknowndimensionless couplings expected to be of order one, for which a value 1 isassumed. The C are the Clebsch-Gordan coefficients. The compositness scaleΛ, i.e. the energy scale at which the compositness should become manifest,has been assumed equal to the mass of the excited fermions, m∗.
16
For the U+ quark of charge 5/3e belonging to the IW = 1 triplet andthe one belonging to the IW = 3/2 quadruplet the relevant interaction la-grangians are:
L(1)
U+ = igf1u
m∗(U+σµνPRu)∂νW µ + h.c. (2.9)
L(3/2)
U+ = igf3u
m∗(U+σµνPLu)∂νW µ + h.c. (2.10)
where PL = (1− γ5)/2 and PR = (1 + γ5)/2 are the chiral projectors, σµν =i[γµ, γν ]/2. The correspondent relevant interaction lagrangian for the D−
quark of charge −4/3e are:
L(1)
D− = igf1d
m∗(D−σµνPRd)∂νW µ + h.c. (2.11)
L(3/2)
D− = igf3d
m∗(D−σµνPLd)∂νW µ + h.c. (2.12)
In order to perform the needed numerical calculations of the productioncross section and kinematical distributions, we need to implement our modelin a parton level generator, so we implemented the interactions of the exoticquarks within the CalcHEP software [32]. This has been done with the helpof Feynrules [34], a Mathematica package that generates the Feynman rules ofany given quantum field theory model as specified by a particular lagrangianand it produces the output in several formats suitable for different Feynmandiagram calculators.
2.2 Production and decay of the exoticly char-
ged quarks
The U+ quark interacts with the light fermions only via the W gauge boson,therefore the only available decay channel is U+ → W+u. Considering theinteraction lagrangians discussed above, it is possible to compute the totaldecay width of this exotic state:
ΓU+ = Γ(U+ → W+u) = αf 2
sin2 θw
m∗
8
(2 +
M2W
m∗2
)(1− M2
W
m∗2
)2
(2.13)
where f is the dimensionless coupling, which depends on the choice of themultiplets: f = f1u for IW = 1 and f = f3u for IW = 3/2, see Eqs. 2.9 and2.10.
For the D− quark analogous considerations are valid and its only decaychannel is D− → W−d. The expression of the total decay width is the same
17
Figure 2.2: The width of the exotic quark U+ as a function of its mass. Thesolid blue line is the analytical result in Eq.2.13 which is compared with theCalcHEP output, that is represented by the yellow dots, as obtained fromthe implementation of our model. The agreement is excellent.
than the previous one, but for f we have f = f1d for IW = 1 and f = f3d forIW = 3/2 according to Eqs. 2.11 and 2.12.
From Fig.2.2 we can see that the decay width increases linearly with themass, as we can infer from Eq.2.13, since we expect the mass of excitedquarks to be much larger than the W boson’s one (m∗ �MW ). In the samefigure we compare the analytical result with the CalcHEP output and wefind a very good agreement.
The U+ quark interacts with the ordinary quarks through a typical mag-netic type interaction only via the W gauge boson and in pp collision it canbe produced via the subprocesses uu → U+d and ud → U+u, in which, forsimplicity, only the first generation has been explicitly wrote down. As shownin Fig.2.1, the first subprocess has a t-channel and a u-channel W exchange,while the latter has a s-channel annihilation and a t-channel W exchange.Similar considerations can be made for the production of the D− quark.
We now give the cross sections of the partonic subprocesses for IW = 1 andIW = 3/2 in terms of the Mandelstam variables. For the IW = 1 multiplet,that is characterized by the absence of interference between t- and u-channel
18
or s- and t-channel, the cross sections are:(dσ
dt
)uu→U+d
=1
4s2m∗2g4f 2
16π
t
(t−M2W )2
[m∗2(t−m∗2) + 2su+m∗2(s− u)
]+
+1
4s2m∗2g4f 2
16π
u
(u−M2W )2
[m∗2(u−m∗2) + 2st+m∗2(s− t)
](2.14a)(
dσ
dt
)ud→U+u
=1
4s2m∗2g4f 2
16π
s
(s−M2W )2
[m∗2(s−m∗2) + 2tu+m∗2(t− u)
]+
+1
4s2m∗2g4f 2
16π
t
(t−M2W )2
[m∗2(t−m∗2) + 2su+m∗2(s− u)
](2.14b)
For the IW = 3/2 multiplet the interference plays a role and its cross sectionsare:(dσ
dt
)uu→U+d
=1
4s2m∗2g4f 2
16π
t
(t−M2W )2
[m∗2(t−m∗2) + 2su−m∗2(s− u)
]+
+1
4s2m∗2g4f 2
16π
u
(u−M2W )2
[m∗2(u−m∗2) + 2st−m∗2(s− t)
]+
+1
8s2m∗2g4f 2
16π
1
(u−M2W )
1
(t−M2W )
(2stu+
3
4utm∗2
)(2.15a)(
dσ
dt
)ud→U+u
=1
4s2m∗2g4f 2
16π
s
(s−M2W )2
[m∗2(s−m∗2) + 2tu−m∗2(t− u)
]+
+1
4s2m∗2g4f 2
16π
t
(t−M2W )2
[m∗2(t−m∗2) + 2su−m∗2(s− u)
]+
1
8s2m∗2g4f 2
16π
1
(s−M2W )
1
(t−M2W )
(2stu+
3
4stm∗2
)(2.15b)
So far we have considered the partonic subprocesses assuming the quarks tobe free particles. Actually the quarks are bound inside the protons, so theFeynman’s parton model, described in Appendix A, allows us to obtain thehadronic cross section at the LHC in terms of convolution of the partoniccross sections σ(τs,m∗), where the symbol “ˆ” means that they are evaluatedat the partons center of mass energy
√s =√τs, and the parton distribution
functions fa which depend on the parton longitudinal momentum fractions,x, and on the factorization scale Q:
σ =∑a,b
∫ 1
m∗2s
dτ
∫ 1
τ
dx
xfa(x, Q)fb(
τ
x, Q)σ(τs,m∗) (2.16)
In the calculation of the production cross section we have considered all thegenerations, but we have to take into account that the U+ exotic quark couple
19
only to the u quark (or u anti-quark). In both the two diagrams of the firstline of Fig.2.1 the U+ exotic quark couples to one of the ingoing quarks,therefore they have the same subprocesses involved:
• uu→ U+d
• uu→ U+s
• uu→ U+b
• uc→ U+d
• uc→ U+s
• uc→ U+b
• ut→ U+d
• ut→ U+s
• ut→ U+b
On the contrary for the second line the U+ quark couples to the outgoinglight quark in the s-channel and to an ingoing light quark in the t-channel,therefore they have different subprocesses involved.The s-channel has:
• ud→ U+u
• us→ U+u
• ub→ U+u
• cd→ U+u
• cs→ U+u
• cb→ U+u
• td→ U+u
• ts→ U+u
• tb→ U+u
The t-channel has:
• ud→ U+u
• ud→ U+c
• ud→ U+t
• us→ U+u
• us→ U+c
• us→ U+t
• ub→ U+u
• ub→ U+c
• ub→ U+t
Similar considerations are valid also for theD− exotic quark that couple tod quark (or d anti-quark). The results of the integration for U+ andD− exoticquarks are presented in Fig.2.3 for two different values of the LHC energy,√s = 8, 13 TeV and for both the multiplets, IW = 1 and IW = 3/2. The
bands correspond to running the factorization and renormalization scale fromQ = MW to Q = m∗. As expected the production of U+ has a larger crosssection, this is due to the fact that producing U+ quark involves processeswith u quarks in the initial state that is the quark with the highest availabilityin the proton, infact it has two valence u quarks.
2.3 Signal and background
The Standard Model background for the final state given in in Eq.2.5 andEq.2.6, as discussed in [35][36][37][38], are the following: pp → Wjj, both
20
10-2
10-1
100
101
102
103
104
105
1000 2000 3000 4000 5000
pp → U +
j
pp → D -
j
LHC-8 TeV
IW=1
σ(f
b)
10-2
10-1
100
101
102
103
104
105
1000 2000 3000 4000 5000
pp → U +
j
pp → D -
j
LHC-8 TeV
IW=3/2
10-2
10-1
100
101
102
103
104
105
1000 2000 3000 4000 5000
pp → U +
j
pp → D -
j
LHC-13 TeV
IW=1
m*(GeV)
σ(f
b)
10-2
10-1
100
101
102
103
104
105
1000 2000 3000 4000 5000
pp → U +j
pp → D -
j
LHC-13 TeV
IW=3/2
m*(GeV)
Figure 2.3: The total integrated cross sections at the LHC energies of√s =
8, 13 TeV for the production of the U+ and D− exotic quarks. The bandscorrespond to running the factorization and renormalization scale from Q =MW to Q = m∗.
21
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 100 200 300 400 500 600 700 800
1/N
(dN
/dP
tj1)(
bin
wid
th 1
0 G
eV
)
PT(j1) (GeV)
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 200 400 600 800 1000
1/N
(dN
/dP
tW)(
bin
wid
th 1
0 G
eV
)
Pt(W) (GeV)
Figure 2.4: The pT distributions of the decay products of the exotic quark,on the left the jet pT and on the right the W boson pT . In red the signal andin blue the background.
gluonic ααs order, when the W boson decay leptonically, and electroweak α2
order, when the W boson decay leptonically and a second boson (W or Z)decay hadronically; pp→ tt pair top production, when one of the top decayshadronically and another one leptonically; and the multijet QCD processes,when a jet imitates a lepton. The most important background is given bythe Wqq production followed by the leptonic decay of the W gauge boson,W → `ν:
pp→ Wjj → `+pT/ jj (2.17)
In this section we will study the main kinematic differences between thesignal and the background in order to find suitable requirements for opti-mizing the statistical significance. The main kinematic feature of our signalprocess is the production of an excited quark with a high mass. It will thenbe a good approximation to assume the exotic quark to be produced almostat rest. It will decay in a high pT jet and in a high pT W gauge boson,that are produced almost back to back. The pT distributions of these twoparticles are expected to be peaked at pT ≈ m∗/2 and to be similar in shape.This qualitative features are confirmed by our simulations whose result areshown in Fig. 2.4: for the simulations we used m∗ = 1000GeV and the peakof the distribution is around 500 GeV = m∗/2.
In order to find a selection cut for optimizing the statistical significance wehave studied the kinematical distribution of the final state particles, which isshown in Fig.2.5. The angular distributions are quite similar between signaland background; for the azimuthal angle (φ) only the one for the leadingjet is shown as example, because all the φ distribution are similar. On thecontrary the signal and background are very well separated in the leading andsub-leading quark jet pT distributions. From these distributions we can see
22
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 100 200 300 400 500 600 700 800
1/N
(dN
/dP
tj1)(
bin
wid
th 1
0 G
eV
)
PT(j1) (GeV)
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
-8 -6 -4 -2 0 2 4 6 8
1/N
(dN
/dη
j1)(
bin
wid
th 0
.1)
η(j1)
0
0.05
0.1
0.15
0.2
0.25
0.3
0 100 200 300 400 500 600 700 800
1/N
(dN
/dP
tj2)(
bin
wid
th 1
0 G
eV
)
Pt(j2) (GeV)
0
0.005
0.01
0.015
0.02
0.025
0.03
-8 -6 -4 -2 0 2 4 6 8
1/N
(dN
/dη
j2)(
bin
wid
th 0
.1)
η(j2)
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 100 200 300 400 500 600 700 800
1/N
(dN
/dP
tl)(
bin
wid
th 1
0 G
eV
)
Pt(l) (GeV)
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
-8 -6 -4 -2 0 2 4 6 8
1/N
(dN
/dη
l)(b
in w
idth
0.1
)
η(l)
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 100 200 300 400 500 600 700 800
1/N
(dN
/dM
ET
)(bin
wid
th 1
0 G
eV
)
MET (GeV)
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
-8 -6 -4 -2 0 2 4 6 8
1/N
(dN
/dφ(j1)(
bin
wid
th 0
.1)
φ(j1)
Figure 2.5: The ideal kinematical distributions of the final state particles forthe signal in red and the background in blue. On the first three lines there arethe pT and pseudorapidity (η) distributions of the leading jet (j1), the sub-leading jet (j2) and the lepton, in the last line the MET and the azimuthalangle (φ) of the leading jet, the other φ distribution are very similar.
23
that a very efficient way to reduce drastically the background while keepingmost of the signal is the use of the requirements:
pT (j1) ≥ 180 GeV, pT (j2) ≥ 100 GeV (2.18)
2.4 Fast detector simulation and reconstructed
object
The kinematical distributions described in the previous section are relatedto numerical CalcHEP outputs, therefore they refer to ideal particles, not toreconstructed objects. To give a more realistic description of our signatureat LHC, it is necessary to take into account the effects of the detectors thatare characterized by a certain efficiency in reconstructing the kinematicalvariables. This causes a smearing of the distributions, due to detector res-olution effects, and a lost in the number of events, due to inefficiencies inthe selection. To examine these axpects, CalcHEP has been interfaced withDELPHES [39], a software for the simulation of a generic detector. In factCalcHEP can do a parton level Montecarlo (MC) simulation, giving as outputa LHE (Les Houches Events) file. This file contains the particles in the initialand final states with their four-momenta and it can be read by DELPHESthat simulates the reconstruction of particles in the final state, introducingthe detector efficiency, the tracker and calorimeter resolutions, and the geo-metrical acceptance according to a parameterization of the detector response.We use a CMS-like parameterization. In Fig.2.6 are shown the kinematicaldistributions after the detector simulation by means of DELPHES.
We use the DELPHES simulations also to estimate the statistical signifi-cance in a potential experimental search at LHC, only for the case of the U+
exotic quark. To this purpose we have generated signal samples with massesbetween 500 and 5000 GeV in steps of 250 GeV. For each signal point and forthe background we have generated 100000 events, in order to have enoughstatistic to evaluate the reconstruction efficiencies for signal (εs) and back-ground (εb). We require that the event has two quark jets and one lepton andwe introduce the requirements described in Eq.2.18. We then count the num-ber of events detected so that the efficiency is given by the ratio between thenumber of detected events and the total events (100000). Once we have theefiiciency, the expected number of events of the signal (Ns) and background(Nb) for a given luminosity, L, is given by:
Ns = Lσsεs, Nb = Lσbεb (2.19)
24
0
0.05
0.1
0.15
0.2
0.25
0 100 200 300 400 500 600 700 800
1/N
(dN
/dP
tj1)(
bin
wid
th 1
0 G
eV
)
PT(j1) (GeV)
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
-8 -6 -4 -2 0 2 4 6 8
1/N
(dN
/dη
j1)(
bin
wid
th 0
.1)
η(j1)
0
0.05
0.1
0.15
0.2
0.25
0.3
0 100 200 300 400 500 600 700 800
1/N
(dN
/dP
tj2)(
bin
wid
th 1
0 G
eV
)
Pt(j2) (GeV)
0
0.005
0.01
0.015
0.02
0.025
0.03
-8 -6 -4 -2 0 2 4 6 8
1/N
(dN
/dη
j2)(
bin
wid
th 0
.1)
η(j2)
0
0.05
0.1
0.15
0.2
0.25
0 100 200 300 400 500 600 700 800
1/N
(dN
/dP
tl)(
bin
wid
th 1
0 G
eV
)
Pt(l) (GeV)
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
-8 -6 -4 -2 0 2 4 6 8
1/N
(dN
/dη
l)(b
in w
idth
0.1
)
η(l)
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 100 200 300 400 500 600 700 800
1/N
(dN
/dM
ET
)(bin
wid
th 1
0 G
eV
)
MET (GeV)
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
-8 -6 -4 -2 0 2 4 6 8
1/N
(dN
/dφ(j1)(
bin
wid
th 0
.1)
φ(j1) (GeV)
Figure 2.6: The kinematical distributions of the final state particles afterthe detector simulation. For the signal in red and the background in blue.On the first three lines there are the pT and pseudorapidity (η) distributionsof the leading jet (j1), the sub-leading jet (j2) and the lepton, in the lastline the MET and the azimuthal angle (φ) of the leading jet, the other φdistribution are very similar.
25
10-3
10-2
10-1
100
101
102
103
104
105
106
107
108
1000 2000 3000 4000 5000
L(f
b-1
)
m*(GeV)
IW=1
10-3
10-2
10-1
100
101
102
103
104
105
106
1000 2000 3000 4000 5000
L(f
b-1
)
m*(GeV)
IW=3/2
Figure 2.7: Luminosity curves at 5-σ level in blue and 3-σ level in green asa function of the mass of exotic quark. On the left the case IW = 1, on theright IW = 3/2.
and the statistical significance, S, is evaluated as:
S =Ns√
Ns +Nb
(2.20)
Combining Eq. 2.19 and Eq. 2.20, it is possible to obtain the luminosityneeded to have a given statistical significance as:
L =S2
σsεs
[1 +
σbεbσsεs
](2.21)
Therefore luminosity curves at 5- and 3-σ level (i.e. fixing S = 3 or S = 5) canbe straightforwardly given as a function of the mass m∗ of the exotic quark.Fig.2.7 shows such luminosity curves which can be used to get indications onthe potential for discovery or exclusion at a given luminosity reached by theexperiments at Run II of the LHC.
Finally we want to point out that experimentally we can’t exactly re-construct the mass of the exotic quark, because among its final decay prod-ucts there is a neutrino for which it is possible to reconstruct the transversecomponent of the momentum, but not the longitudinal one. However it ispossible to define a transverse mass variable (MT ) and also try to reconstructthe invariant mass of the exotic quark to some degree of accuracy.
The transverse mass is defined in terms of the reconstructed transversemomentum of the W gauge boson (pTW = pT` + pTν) and the transversemomentum of the leading jet:
M2T =
(√p2TW +M2
W + pTj1
)2
− (pTW + pTj1)2 (2.22)
26
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 200 400 600 800 1000 1200 1400
1/N
(dN
/dM
t)(b
in w
idth
30 G
eV
)
Mt (GeV)
0
0.05
0.1
0.15
0.2
0.25
0 500 1000 1500 2000 2500 3000
1/N
(dN
/dM
lνj)(b
in w
idth
30 G
eV
)
M(l,ν,j) (GeV)
Figure 2.8: on the left the transverse mass distribution and on the right Thedistribution in the invariant mass of lepton, jet and neutrino. The red lineis for the signal (Λ = 10 TeV, m∗ = 1000 GeV) and the blue line for thebackground.
The transverse mass distribution is strongly correlated with the exotic quarkmass m∗, this is shown in Fig.2.8 left, where the transverse mass, obtainedfor mass value of 1000 GeV, has a clear peak for MT = m∗.
In order to still reconstruct the invariant mass of the exotic quark to somedegree of accuracy, we can follow the method described in [54] modified toadapt it to our case. We use the conservation of four-momentum to solvefor the longitudinal momentum of the neutrino (pzν). Conservation of four-momentum gives the following equation
M2W = (p` + pν)
2 (2.23)
Now the only unknown quantity on the eq. 2.23 is the longitudinal momen-tum of the neutrino. Expanding the right-hand side of eq. 2.23 we obtain asecond-order equation for pzν :
(1−B2)(pzν)2 − 2ABpTν p
zν + (1− A2)(pTν )2 = 0 (2.24)
where pTν = |~p tν | while pzν and pz` are the true components (with sign) of theneutrino and lepton momentum along the longitudinal direction and A andB are defined in the following equations:
A =M2
W + 2~pT` · ~pTν2E`pTν
B =pz`E`
It has the solutions
pzν =1
1−B2
[AB ±
√A2 +B2 − 1
]pTν (2.25)
27
For convenience we denote the quantity in the square root as
D = A2 +B2 − 1. (2.26)
We have three distinct cases:
• D > 0: two real solutions
• D = 0: one real solution
• D < 0: two complex solutions
If the discriminant is positive, there are two possible pzν solutions. Usingboth of them, the two possible neutrino momentum vectors are constructedand, combining them with the lepton momentum, the two W candidate areconstructed. We then select the pzν solution that gives the more central W ,i.e. with the smaller pseudo-rapidity. We then construct the correspondentinvariant mass M`νj. If the discriminant is zero there is one only solutionfor pzν and it is used to construct the invariant mass. If the discriminantis negative, the event is rejected. Fig.2.8 right shows the distribution inthe invariant mass of the lepton, jet and neutrino. There is a clear peak incorrespondence of the exotic quark mass.
2.5 Summary
We have presented the first study of the production at the LHC of new exoticquark states of charge 5/3e and 4/3e which appear in composite models ofquark and leptons when considering higher weak isospin multiplets IW = 1and IW = 3/2. Such states have been discussed previously in [22], but theirphenomenology has been not addressed in detail. Only very recently someattention has been devoted to the phenomenology of the higher multiplets inthe leptonic sector [27][28]. Here we explore the phenomenology of the quarksector with a focus on the Run II of the LHC.
We have implemented the magnetic type gauge interaction in the CalcHEPgenerator and performed a fast simulation of the detector reconstruction ofboth signal and background based on the DELPHES software. Finally wecompute the luminosity curves as function of m∗ for 3- and 5-σ level statis-tical significance including the statistical error. For different values of theintegrated luminosity L=30, 300 and 3000 fb−1 we find, for instance, that forIW = 3/2 we can either observe or exclude at 3-σ level respectively massesup to m∗ =2800, 3500 and 4200 GeV . This is a quite interesting result which
28
in our opinion warrants more detailed studies. For instance the two dimen-sional parameter space (Λ,m∗) could be fully explored. Also the inclusion ofthe effect of expected contact interaction should be taken into account.
29
Chapter 3
Phenomenology of the heavycomposite Majorana neutrino
In this chapter we describe the phenomenology of a heavy composite Majo-rana neutrino within the scenario of compositness of fermions. Differentlywith respect to the previous chapter, in this one we keep the parameters m∗
and Λ separated and we complement the composite model with the intro-duction of the contact interaction, that is an effective approach to considerthe residual interaction of the unknown internal dynamics [23][24][25].
Preliminary studies on a composite Majorana neutrino considering thelike-sign di-lepton and di-jet signature have been performed long ago [40]in the gauge case only. Our aim is to complement that work introducingthe contact interaction. Based on previous studies related to the productionat the LHC of exotic doubly charged leptons [28] we expect this contactinteraction to be the dominant mechanism for the resonant production ofthe composite Majorana neutrino.
The composite Majorana neutrino is resonantly produced in associationwith a lepton (pp → `N). Given the relatively important branching ratiofor the decay N → `qq, we concentrate on the study of the like-sign di-lepton and di-jet final state pp → ``qq to characterise the heavy neutrinophenomenology. In particular we consider the final state with two positiveelectrons:
pp→ e+e+qq (3.1)
30
3.1 The heavy Majorana neutrino in compos-
ite models with gauge and contact inter-
actions
We consider here the various possible composite models with respect to theidea of introducing lepton number violation via a composite Majorana neu-trino.(a) Homo-double model.The homo-doublet model [25][26] contains a left-handed excited doublet alongwith a right-handed doublet:
L∗L =
(ν∗Le∗L
), L∗R =
(ν∗Re∗R
). (3.2)
Typically the left- and right-handed doublet are assumed to have the samemass. It is known that two left and right Majorana fields with the samemass combine to give a Dirac field [41]. The homo-doublet model thereforecannot accommodate Majorana excited neutrinos and hence lepton numberviolation. This become possible if one introduce a mass difference betweenthe left and right doublet (ν∗L− ν∗R) or, in other words, a breaking of the L-Rsymmetry. Such a possibility has been discussed for instance in [42] wherethe ν∗ is possibly a linear combination with mixing coefficients of Majoranamass eigenstates.
On the other hand we can account for lepton number violation advocat-ing different models within the compositeness scenario which naturally canaccommodate a Majorana neutrino [42][43]:(b) Sequential type model.The sequential model contains excited states whose left-handed componentsare accommodated in SU(2) doublets while the right-handed components areSU(2) singlets:
L∗L =
(ν∗Le∗L
), e∗R, [ν∗R]; (3.3)
and the notation [ν∗R] means that ν∗R is necessary if the excited neutrino is aDirac particle, while it could be absent for a Majorana excited neutrino. Themagnetic type interactions in this case can be constructed by coupling theleft-handed excited doublet to the SM fermion singlets via the Higgs doublet[42]. This results in coupling strengths suppressed by a factor v/Λ [43] wherev ≈ 246 GeV is
√2 times the expectation value of the Higgs field.
(c) Mirror type model.
31
The mirror type model contains a right-handed doublet and left-handed sin-glets:
e∗L, [ν∗L]; L∗R =
(ν∗Re∗R
). (3.4)
where we may assume that there is no left-handed excited neutrino (ν∗L)so that we can associate to ν∗R a Majorana mass term and ν∗ is a Majo-rana particle. This model is described by a magnetic type coupling betweenthe left-handed SM doublet and the right-handed excited doublet via theSU(2)L × U(1)Y gauge fields [42][43]:
L =1
2ΛL∗Rσ
µν(gfτ
2Wµν + g′f ′Y Bµν
)LL + h.c., (3.5)
where LL =
(νL`L
)is the ordinary SU(2)L lepton doublet, g and g′ are
the SU(2)L and U(1)Y gauge couplings and Wµν , Bµν are the field strengthfor the SU(2)L and U(1)Y gauge fields; f and f ′ are dimensionless couplingswhich are typically assumed to be of order unity.
The relevant charged current gauge interaction of the excited Majorananeutrino N = ν∗ is then:
LG =gf√2ΛNσµν`L∂
νW µ + h.c. (3.6)
This last kind of model is the one to which we refer our detailed sim-ulations of the like-sign di-lepton and di-jet signature at the Run II of theLHC.
It is also possible to consider the higher multiplets of the extended weakisospin composite models [22].
The IW = 1 triplet, εT = (L0, L−, L−−), can only couples with the right-handed lepton singlet `R [22]. Therefore we may assume a sequential typestructure with a left-handed triplet and right-handed singlets. If the L0
R ismissing we may assume for the L0
L a Majorana mass term and so the excitedneutral L0 of the triplet is a Majorana neutrino (N). The magnetic typeinteraction is:
L =f1
ΛεLσµν`R∂
νW µ + h.c. (3.7)
where f1 is an unknown dimensionless coupling in principle different from fappearing in Eq.3.5 and Eq.3.6. The relevant charged current interaction ofthe neutral component of the triplet is in this case:
L =f1
ΛL0σµν`R∂
νW µ + h.c. (3.8)
32
which differs from Eq.3.6 in the chirality of the projection operator.The IW = 3/2 quadruplet, εT = (L+, L0, L−, L−−), couples instead with
the left-handed SM doublet [22], so that assuming a mirror type model andthat there is no L0
L we can assign to L0R a Majorana mass term and the L0
neutral of the quadruplet can be a Majorana neutrino (N). The magnetictype interaction is:
L = C(3
2,M |1,m;
1
2,m′)
f3/2
ΛεRMσµν`Lm′∂
νW µm + h.c. (3.9)
where f3/2 is an unknown dimensionless coupling in principle different fromf ,f1 and C(3
2,M |1,m; 1
2,m′) are Clebsch-Gordan coefficients. The relevant
neutrino charged current interaction turns out to have the same structure asin Eq.3.6:
L =f3/2√
3ΛL0σµνeL∂
νW µ + h.c. (3.10)
Therefore the interaction in Eq.3.6 describes the charged current interactionof a heavy Majorana neutrino both in the IW = 1/2 mirror type compositemodel and in the IW = 3/2 mirror type composite model, but in this last
case with a factor√
2√3
respect to the Eq.3.6.Contact interaction is an effective approach to take into account the
unknown internal dynamics given by constituent exchange, if the fermionshave common constituents, and/or by exchange of the binding quanta of thenew unknown interaction whenever such binding quanta couple to the con-stituents of both particles [43][44]. This contact interaction is described bythe following lagrangian:
LC =g2∗
Λ2
1
2jµjµ (3.11a)
jµ = ηLfLγµfL + η′Lf∗Lγµf
∗L + η′′Lf
∗LγµfL + h.c.+ (L↔ R) (3.11b)
where g2∗ = 4π and the η factors are usually set equal to unity. The single
production qq′ → N` proceeds through currents like third term in Eq.3.11bwhich couples excited states with ordinary fermions. The relevant interactionis:
LC =g2∗
Λ2qLγ
µq′LNLγµ`L (3.12)
Therefore in the model we are studying the excited fermions couplingto SM fermion trough both magnetic-type gauge interaction and contactinteraction as described by Fig. 3.1, where, as example, the production ofthe heavy Majorana neutrino is shown.
The model for the composite Majorana neutrino with the interactions inEq. 3.6 and Eq. 3.11 has been implemented in CalcHEP with the help of
33
qj
qi
ℓ+
N
=
qj
qi
W
ℓ+
N
+
qj
qi
ℓ+
N
Figure 3.1: The dark grey blob describes the production of on shell heavyMajorana neutrinos in proton-proton collisions at LHC. The production ispossible via both gauge interaction (first diagram in the right-hand side) andfour fermions contact interaction (second diagram in the right-hand side).
Feynrules. The implementation of the gauge interaction is straightforward,while for the contact interaction it is necessary to use a workaround, becauseCalcHEP is not able to directly recognize such type of interaction. Thereforeone has to define an auxiliary particle with a point like propagator thathas the function of interaction mediator [33]. In this way the lagrangian inCalcHEP is:
LcontCH =g2∗2Jµ
ηµν
M2aux
Jν =g2∗
2M2aux
JµJµ (3.13)
Therefore the auxiliary particle’s mass has to be set in such way that LcontCHcorresponds to the real contact interaction lagrangian:
Lcont =g2∗
2Λ2JµJ
µ (3.14)
Equaling the two lagrangians one obtains:
Maux = Λ (3.15)
3.2 Cross section and decay width of the com-
posite Majorana neutrino
From the lagrangian presented in the previous section it is possible to obtainthe partonic cross section, calculated considering the quarks to be free. Weneed to take into account the fact that the quarks are bound in the protonsand to evaluate the hadronic cross sections for the Majorana neutrino inpp collisions at the LHC. This can be done thanks to the Feynman’s partonmodel, explained in Appendix A, according to which a hadronic cross section
34
qk
ℓ+
ℓ+
ql
qj qj
qi ℓ+
N N
ℓ+
qk
ql
qi
Figure 3.2: On the left the process with the virtual heavy composite Majo-rana neutrino (N), on the right the process with resonant production of Nand its subsequent decay. The dark blob includes both gauge and contactinteractions.
is given in terms of the convolution of the partonic cross sections σ(τs,m∗),evaluated at the partons center of mass energy
√s =√τs, and the parton
distribution functions fa which depend on the parton longitudinal momentumfractions, x, and on the factorization scale, Q:
σ =∑a,b
∫ 1
m∗2s
dτ
∫ 1
τ
dx
xfa(x, Q)fb(
τ
x, Q)σ(τs,m∗) (3.16)
In this section we will present this production cross section at the LHC.The like-sign di-lepton plus di-jet signature can be realized by two dis-
tinct classes of Feynman diagrams, a t-channel exchange of a virtual heavyMajorana neutrino, Fig.3.2(left), and the resonant production of the heavyMajorana neutrino and its subsequent decay, Fig.3.2(right). In both dia-grams the interactions can be both gauge interaction and contact interactionand in Fig.3.2, for each grey blob, we have the same situation given in Fig.3.1.
The process in Fig.3.2(left) is the collider analogue of the neutrinolessdouble-β decay (0νββ), the well known lepton number violating (∆L = ±2)nuclear rare decay [45][46] which, if detected, would unambiguously verify theMajorana nature of neutrinos. In a high energy collider the signature underexamination can be obtained also trough the process in Fig.3.2(right), whenthe mass of the Majorana neutrino is kinematically accessible m∗ <
√s. In
this case the cross section for the signature pp→ ``jj is approximated by
σ(pp→ ``qq) ≈ σ(pp→ `N)B(N → `qq). (3.17)
35
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
1 2 3 4 5
σ(p
p →
N e
+)
(fb)
m* (TeV)
contact
gauge
Λ=10TeV
Figure 3.3: The production cross section of the process pp→ Ne+ for guageand contact interactions at
√s = 13 TeV in the case Λ = 10 TeV.
The σ(pp → `N) in Eq.3.17 is the cross section for the resonant pro-duction of the heavy Majorana neutrino in association with a lepton in ppcollision. In Fig.3.3 we show the production cross section against the heavyneutrino mass for Λ = 10 TeV for the LHC center of mass energy
√s = 13
TeV. We show the results for the case ` = e and we consider the positivecharge. The figure clearly shows that the production of the heavy compositeMajorana neutrino is dominated by the contact interactions.
The B(N → `qq) is the branching fraction, which is defined as the ratiobetween the amplitude of a particular decay of the heavy neutrino and thetotal decay amplitude of the heavy neutrino. The possible decays of theheavy Majorana neutrino are:
N → `qq′ N → `+`−ν(ν) N → ν(ν)qq′
In the first we can have a positive lepton, a down-type quark and an up-typeantiquark or a negative lepton, an up-type quark and a down-type antiquark;in the second, owing to Majorana character of N , we can have either aneutrino or an antineutrino of the same flavour of the heavy neutrino andaccordingly two opposite sign leptons belonging to a family that can be thesame or different from the other one, or alternatively a positive (negative)lepton of the same family of the heavy neutrino and a negative (positive)lepton and an antineutrino (neutrino) belonging to a family that can be thesame or different from the other one; in the third we can have a neutrinoor an antineutrino and a quark and an antiquark both of up-type or bothof down-type. Considering also in this case ` = e and a positive charge,we present in Fig.3.4 the decay amplitude and the branching ratio for thedecay N → e+qq′. In the decay the dominat interaction is the gauge one
36
10-3
10-2
10-1
100
101
102
1 2 3 4 5
Γ(N
→ e
+ q
q-’)(G
eV
)
m* (TeV)
contact gauge
Λ=10TeV
0.3
0.32
0.34
0.36
0.38
0.4
0.42
0.44
1 2 3 4 5
B(N
→ e
+ q
q-’)
m* (TeV)
Λ=10TeV
10-3
10-2
10-1
100
101
1 2 3 4 5
Γ(N
→ e
+ q
q-’)(G
eV
)
m* (TeV)
Λ=15TeV
contactgauge
10-4
10-3
10-2
10-1
100
1 2 3 4 5
Γ(N
→ e
+ q
q-’)(G
eV
)
m* (TeV)
Λ=25TeV
contactgauge
Figure 3.4: The gauge and contact contribution to the width of the decay ofthe heavy neutrino in to a positron and two quarks Γ(N → e+qq′) for three Λvalues: 10 TeV (Top-left), 15 TeV (Bottom-left) and 25 TeV (Bottom-right).In the Top-right the branching ratio B(N → e+qq′) in the case of Λ = 10TeV.
37
10-5
10-4
10-3
10-2
10-1
100
101
1 2 3 4 5
σ(p
p →
e+e
+jj)
(fb
)
m* (TeV)
Λ=10TeV
10-4
10-3
10-2
10-1
100
101
1 2 3 4 5
cro
ss s
ection (
fb)
m* (TeV)
Λ=10TeV
pp → e +e +
jjpp → e -e -
jj
Figure 3.5: Left: Comparison between the cross-section of the process pp→e+e+qq with resonant production of heavy Majorana neutrino (solid line)and that with a virtual heavy Majorana neutrino (dashed line). Both gaugeand contact interactions are considered. Right: Comparison between crosssection of the final state with negative di-lepton and the one with positivedi-lepton.
at lower masses and the contact one at higher masses; the interchange pointgoes toward higher values of masses with the growing of the Λ parameter, asit is shown in Fig. 3.4.
Now we can compare the final state cross section, σ(pp → e+e+jj), forthe two diagrams of Fig.3.2. This comparison is shown in Fig.3.5(left). Theresonant production is dominant relative to the virtual neutrino exchangecontribution. This was demonstrated in [47] for the gauge-only case, here weshow it including also the contact interaction.
Finally in Fig.3.5(right) we compare the cross sections of pp → e+e+qqand pp→ e−e−qq. The cross section for the production of positive di-leptonis larger than that for the production of negative dilepton as expected inproton-proton collisions due to larger luminosity of a ud pair, needed toproduce a positive di-lepton, compared to that of a ud pair, needed to producea negative di-lepton. Therefore experimentally we would have more yieldsfor the positive-dilepton, for this reason we refer our results and simulationsto this case.
3.3 Topology of the signal
As stated in the previous sections the heavy Majorana neutrino can decayvia both gauge and contact interactions. When the decay happens troughgauge interaction, since we assume m∗ � MW , we expect the two jets from
38
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 1 2 3 4 5 6
(1/N
)(d
N/d
R)
(bin
wid
th 0
.1)
∆R(jj)
Λ=10 TeVm*=1000 GeVm*=3000 GeVm*=5000 GeV
Figure 3.6: The distribution in the ∆R of the two jets at Λ = 10 TeV anddifferent masses at generator level.
the W decay to be highly boosted and with a small separation in ∆R =√(∆η)2 + (∆φ)2, where η is the pseudorapidity and φ is the azimuthal angle
in the transverse plane. This effect is expected to be more pronounced as themass of the neutrino increases. On the other hand the lepton coming fromthe decay of the heavy neutrino is produced with the W and does not decayfrom it, thus we expect it to be separated from the jets. When the decayhappens trough contact interaction, because this interaction is not mediatedby a gauge particle, all the decay products of the heavy neutrino are producedwithout being constrained to a particular direction and all are separated.
This behavior is clearly described by Fig.3.6, in which the distributionsin the ∆R of the two jets have two peaks: one at low values of ∆R, due tothe gauge interactions, that moves closer to ∆R = 0 with the growing of theneutrino mass; one at ∆R ≈ 3, due to contact interaction. The fraction ofevents around this peak becomes greater with the growing of the neutrinomass, because with the mass the contact width grows respect to the gaugeone (cfg. Fig.3.4).
In the reconstruction process, for the jets with small separation in ∆R,it is possible to have merging, i.e. the two jets can be often reconstructed asa single jet.
The same is not true for the leptons, because in the production processpp→ `N , the lepton and the neutrino are produced in two opposite regionsof the transverse plane and, consequently, the same will be true for the leptonand the second lepton from the decay of the neutrino. This second lepton isseparated from the jets for the reason yet explained.
39
3.4 Signal and background
As it is well known, in the Standard Model the lepton number L is strictlyconserved and thus processes with final state, like the one we are considering,with ∆L± 2 are not allowed. However, within the standard model there areseveral processes that can produce same-sign di-lepton plus di-jet in associa-tion with neutrinos. Even if our process does not have neutrinos in the finalstate, these SM processes may be background for it. In fact the neutrinosdo not interact with detectors and give rise to missing energy and, given thenon-ideality of the detectors also our process will have missing energy in thefinal state. The following processes are considered as main backgrounds [48]
pp→ tt→ `+`+ννjets (3.18a)
pp→ W+W+W− → `+ν`+νjj (3.18b)
Now we discuss the main kinematical differences between the signal and thebackground to choose suitable requirements to optimize the signal/backgroundratio.
Fig.3.7 shows the transverse momentum and pseudorapidity distributionsfor the two positrons with the comparison between signal and background,for the parameters value Λ = 10 TeV and m∗ = 1000 GeV. In the transversemomentum distributions signal and background are very well separated andwe can drastically reduce the background, while keeping a large fractionof the signal, applying the following selection on the transverse momentumdistributions:
pT (e+leading) ≥ 200GeV (3.19a)
pT (e+second−leading) ≥ 100GeV (3.19b)
On the contrary the angular distributions of the leading and second-leadingleptons are quite similar between signal and background and we do not applyselections on them.
The correspondent distributions for the jets are not considered because,given the large fraction of events in which the jets are merged (see section3.3), the theoretical distributions are not reproducible at reconstruction leveland the cuts found here would not be directly utilizable to separate signaland background at reconstruction level.
Information about the mass of the heavy Majorana neutrino can be ob-tained from the invariant mass distribution of the second leading lepton andthe two jets. In Fig.3.8 we show that this distribution has a very sharp peakin correspondence of the heavy Majorana neutrino mass. This is indeed ex-pected since in the resonant production the heavy Majorana neutrino N is
40
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 500 1000 1500 2000
1/N
(dN
/dP
t) (
bin
wid
th 1
0 G
eV
)
Pt(eleading) (GeV)
signal Λ=10TeV, m*=1000GeV
background tt-
background W+W
+W
-
0
0.05
0.1
0.15
0.2
0.25
0 200 400 600 800 1000 1200 1400
1/N
(dN
/dP
t) (
bin
wid
th 1
0 G
eV
)
Pt(esecond leading) (GeV)
signal Λ=10TeV, m*=1000GeV
background tt-
background W+W
+W
-
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
-8 -6 -4 -2 0 2 4 6 8
1/N
(dN
/dη
) (b
in w
idth
0.1
)
η(eleading)
signal
tt-
W+W
+W
-
0
0.005
0.01
0.015
0.02
0.025
0.03
-8 -6 -4 -2 0 2 4 6 8
1/N
(dN
/dη
) (b
in w
idth
0.1
)
η(esecond leading)
signal
tt-
W+W
+W
-
Figure 3.7: Top-left: The leading positron transverse momentum distri-bution. Top-right: The second-leading positron transverse momentum dis-tribution. Bottom-left: The leading positron pseudorapidity distribution.Bottom-right: The second-leading positron pseudorapidity distribution. Thedistributions are at generator level.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0 500 1000 1500 2000
1/N
(dN
/dM
) (b
in w
idth
10
Ge
V)
M(e2jj) (GeV)
signal Λ=10TeV, m*=1000GeV
background tt-
background W+W
+W
-
Figure 3.8: The distribution in the invariant mass of the second-leadingpositron and the two jets at generator level.
41
decaying to `+qq′ and the lepton from N is expected to be the second-leading,while the leading lepton is expected to be the one produced in associationwith N , in pp→ `+N .
It is interesting also the study of the eeqq invariant mass, in fact a CMSsearch for heavy neutrino and W bosons with right-handed couplings [49],which will be better explained in the next chapter, has observed an excess inthis distribution in the interval 1.8 TeV < Meejj < 2.2 TeV. The invariantmass distribution of our eeqq final state, owing to the QCD factorizationtheorem and the well known recursive properties of the multi-particle phase-space [50][51], is easily estabilished to be given by the following relation (notethat the ``jj invariant mass coincides with the energy of the parton centerof mass frame, M2
``jj = s):
sdσ
dM2``jj
=∑ab
∫ 1
M2``jjs
dx
xfa(x,Q
2)fb
(M2
``jj
sx,Q2
)×
×∫ M2
``jj
0
dQπ
√Q2σqaqb→`N(M``jj,Q)ΓN→`jj(Q)
(Q2 −M2N)2 + (MNΓtot(Q))2
(3.20)
where Q is the QCD factorisation scale and Q is the virtual momentum ofthe resonantly produced heavy Majorana neutrino, N . We see that suchinvariant mass distribution is the poroduct of two factors. The first factorin the right-hand side of the Eq.3.20 is a dimensionless parton distributionluminosity factor that vanishes at very large invariant masses M``jj ≈
√s,
while the second factor in the right-hand side of Eq.3.20 is an integral overthe virtuality of the produced neutrino, Q, and vanishes for small valuesof the invariant mass or M``jj � MN . Therefore in general we expect aninvariant mass distribution characterised by a peak for M``jj &MN . Fig.3.9(left panel) shows explicitly the behavior described above for three differentvalues of the heavy neutrino mass, m∗ = 1, 2, 3, TeV, for a fixed Λ value,Λ = 10 TeV. The same behavior is also observed in Fig.3.9 (right panel) fordifferent value of the compositness scale, Λ = 5, 15, 25 TeV, for a given valueof the heavy neutrino mass, m∗ = 1500 GeV.
3.5 Fast detector simulation and reconstructed
objects
In order to take into account the detector effects, such as efficiency andresolution in reconstructing kinematic variables, as explained in Sec.2.4, weinterfaced the LHE output of CalcHEP with the software DELPHES, which
42
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
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0 1000 2000 3000 4000 5000 6000
1/N
(dN
/dM
) (b
in w
idth
10
Ge
V)
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Λ=10 TeV m*=1000 GeVm*=2000 GeVm*=3000 GeV
tt-
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+W
-
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/dM
) (b
in w
idth
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Ge
V)
Meejj (GeV)
m*=1500 GeV Λ=5 TeVΛ=15 TeVΛ=25 TeV
Figure 3.9: Invariant mass distribution, at generator level, of the eejj sys-tem. The left panel shows the distribution for three different mass value ata fixed value of Λ. The right panel shows the shape independence of thedistribution from the values of Λ, giving the distribution for three Λ valuesat a given mass.
simulates the response of a generic detector according to predefined config-urations. We used a CMS-like parameterisation. For the signal we considera scan of the parameter space (Λ, m∗) within the ranges Λ ∈ [8, 40] TeVwith step of 1 TeV and m∗ ∈ [500, 5000] GeV with step of 250 GeV. Foreach signal point and each background we generate 100000 events in orderto have enough statistics to evaluate the reconstruction efficiency (εs, εb) ofthe detector and of the cuts previously fixed in Eq.3.19a, 3.19b.
The leptonic flavour of our signature is determined by the flavour of theexcited heavy Majorana neutrino. We consider for our fast simulation of thedetector reconstruction the electron signature.
We select events with two positive electrons and at least one jet. Thenumber of jets may be just one, in case of merging of the generated twojets, or two, if there is no merging of the generated two jets. This selectionwarrants a very high signal efficiency, regardless of whether there are indeedone or two jets in the reconstructed events.
We can then define the efficiencies as the ratio between the events passingthis selection and the total number of generated events (100000). Once wehave the signal and background efficiencies, we can estimate the expectednumber of events for the signal (Ns) and for the background (Nb):
Ns = Lσsεs, Nb = Lσbεb (3.21)
and finally it is possible to evaluate the statistical significance (S):
S =Ns√Nb
(3.22)
43
10
15
20
25
30
35
40
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Λ (
TeV
)
m* (TeV)
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S<3
L=30 fb-1
10
15
20
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TeV
)
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TeV
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Λ (
TeV
)
m* (TeV)
L=30 fb -1
L=300 fb -1
L=3000 fb -1
Figure 3.10: Contour maps of the statistical significance for S = 5 and S = 3in the parameter space (Λ, m∗) for
√s = 13 TeV and for three values of the
integrated luminosity L=30,300.3000 fb−1. The solid lines are the centralvalues, the dashed colored bands are an estimate of the statistical error. Inthe lower-right panel we compare the 5-σ exclusion plots at the three valuesof integrated luminosity. Regions below the curves are excluded.
In Fig.3.10 we show the contour plots at S = 3 and S = 5 in the parameterspace (Λ, m∗) for three different values of integrated luminosity, L = 30 fb−1
(Top-left), L = 300 fb−1 (Top-right) and L = 3000 fb−1 (Bottom-left). Thesolid lines are the central values and the colored bands are an estimate ofthe statistical uncertainty. In Fig.3.10 (Bottom-right) we compare the 5-σcurves at the three integrated luminosity values.
Finally in Fig.3.11 we compare the 3-σ contour plots of our signaturefrom the heavy composite Majorana neutrino, for three different values ofthe integrated luminosity L=30,300,3000 fb−1 with the 95% confidence levelexclusion bounds from two Run I searches of excited leptons via the processpp → ``∗ → ``γ (` = e): ATLAS with 13 fb−1 [52] and CMS with 19.7fb−1 [53]. Such analyses have investigated signatures of excited electronsand muons, therefore, strictly speaking, they access the parameters spaces(me∗ ,Λ) and (mµ∗ ,Λ), that are in principle different from the one presented
44
Λ (
TeV
)
m* (TeV)
Th. (13 TeV, 3000 fb-1
)
Th. (13 TeV, 300 fb-1
)
Th. (13TeV, 30 fb-1
)
CMS (8 TeV, 19.7 fb-1
)
ATLAS (8 TeV, 13 fb-1
)
m*>Λ
5
10
15
20
25
30
35
40
0.5 1 1.5 2 2.5 3 3.5
Figure 3.11: Current exclusion regions at 95% confidence level on the planeof parameters (Λ, m∗) from CMS [53] and ATLAS [52] searches (Run I) ofpp → ``∗ → ``γ (` = e) versus 3-σ significance curves expected at RunII from the eeqq signature due to a heavy composite Majorana neutrino(pp→ `N → ``qq, ` = e).
here (mN ,Λ). However, all excited states masses can be assumed to beapproximately degenerate, at least at a first order approximation. Underthe hypothesis MN ≈ me∗ ≈ mµ∗ the eeqq signature discussed here providescontour maps that can be considered on the same parameter space of thecited analyses. The blue region below the solid line is the CMS exclusion,the yellow region below the dashed line is the ATLAS exclusion and thegrey region below the dot-dashed line is the region of parameter space wherethe model is not applicable (m∗ > Λ). The dot-dashed green, dashed redand solid magenta lines are the contour plots for S=3 from our signatureat√s = 13 TeV respectively for an integrated luminosity value of 30,300
and 3000 fb−1. We note that while the notion of a discovery reach at 3-σis different from that of an exclusion region at 95% confidence level, it issufficiently close to it that the comparison of the two gives a rough idea ofthe sensitivity achievable at the LHC Run II with the eeqq signature. FromFig.3.10 and Fig.3.11 we can evince that an experimental study of the eeqqsignature at LHC is sensitive to a heavy composite Majorana neutrino upto masses of ≈ few TeV. In the absence of a discovery, it will be possibleto increase the excluded regions of the parameter space for the compositescenario.
45
3.6 Summary
We have presented a study of the phenomenology of an excited Majorananeutrino stemming from the composite scenario. This excited states hadbeen considered in [40], where a model based on gauge interaction only wasconsidered; we have included the contribution of contact interaction in thephenomenology of the composite Majorana neutrino.
The model has been implemented in CalcHEP which allows simulations atgenerator level. The contact interaction mechanism turns out to be dominantin the resonant production of the heavy Majorana neutrino. We have per-formed a fast simulation study of the same sign dilepton plus dijet signature(eeqq) arising from the resonant production of a heavy Majorana neutrinoand its subsequent decay at the LHC, analysing in detail both signal andbackground in order to optimise the statistical significance.
A fast simulation of the detector effects and efficiencies in the reconstruc-tion process has been performed using DELPHES package. We have scannedthe two dimensional parameter space (m∗,Λ) and computed the statisticalsignificance. We have provided the contour plots of the statistical significanceS at 3-σ and 5-σ level. We have found, for instance, that with Λ = 15TeV theLHC can reach a 3-σ sensitivity for masses up to m∗ = 1500, 2500, 3000GeVrespectively for an integrated luminosity of L = 30, 300, 3000 fb−1.
The results presented here are quite encouraging and certainly endorsethe interest and feasibility of a full fledged analysis of the experimental dataof the LHC Run II for a search of the heavy composite Majorana neutrino,within a Mirror type model, in proton-proton collision at
√s = 13TeV . This
analysis has been done by the CMS Collaboration and it will be presentedin chapter 6.
46
Chapter 4
Relations between theory andexperiments
DIfferent experimental searches on composite scenario have been made.Both ATLAS and CMS performed an Analysis of the ``γ signature arising
from `∗ production (pp→ ``∗) via four fermion contact interaction, followedby the decay `∗ → `γ. ATLAS Collaboration reports an analysis [56] at
√s =
8TeV with an integrated luminosity of 13 fb−1 that gives a lower bound onthe mass of the excited leptons of 2.2 TeV , derived with the hypothesism∗ = Λ. The CMS Collaboration in [57] reports the results of data collectedwith 19.7 fb−1 at
√s = 8TeV and, assuming m∗ = Λ, excludes excited
electrons with masses up to 2.45 TeV and excited muons with masses up to2.48 TeV . A correspondent CMS analysis [58] at
√s = 13TeV and with 2.7
fb−1, set the limits to 2.8 TeV for the electrons and 3.0 TeV for the muons.In [59] CMS Collaboration presents an experimental search for narrow
resonances decaying to di-jets which uses 12.9 fb−1 data at√s = 13TeV and
excludes excited quarks with masses below m∗ ≈ 5.4TeV in the hypothesism∗ = Λ. Similar searches performed by ATLAS Collaboration with 3.6 fb−1
of proton-proton collisions at√s = 13TeV report a heavy quark mass limit
of 5.3 TeV in the hypothesis m∗ = Λ) [60].All These searches on composite scenario are based on the assumption
of standard weak isospin assignments (IW = 0, 1/2) and the correspondentlimits apply to this assumption. In chapter 2 and in ref. [28] we studied theweak isospin spectroscopy of excited quarks and leptons showing that thestructure of the standard model symmetries allow to consider higher isospinmultiplets, IW = 1, 3/2. We think that an experimental search based onthese higher multiplets would be very interesting.
Analysis based on heavy neutrinos arising from a composite scenario havenever been made before and the one presented in chapter 6 will be the first.
47
However analysis based on heavy neutrino arising from different models areperformed by both CMS and ATLAS.
In 2014 CMS collaboration made public a measurement looking for heavyneutrino associated to right-handed gauge bosons, WR, [49]. This analysiswas performed using a sample of proton-proton collisions at a center of massenergy of 8 TeV and with a luminosity of 19.7 fb−1. The search reportsa 2.8 σ excess in the eeqq invariant mass distribution in the interval 1.8TeV < M(e, e, j, j) < 2.2 TeV. An excess of 2.4 σ in the same final statetogether with a 2.6 σ excess in the eνeqq final state was observed in a searchfor first generation leptoquarks [65], while no deviation of data respect to theSM expectation is observed in the correspondent muonic final states of thetwo analyses.
The model for the composite Majorana neutrino described in chapter 3can produce an excess in the same electronic channels and can also explainthe absence of the excess in the correspondent muonic channels, assumingthe muonic composite neutrino to be heavier than the electronic compositeneutrino and so it would be observable at higher energies. Motivated bythis, we decided to perform a measurement to look for composite Majorananeutrino with CMS data, considering the eeqq and µµqq final states.
The observed eejj excess consists of 14 events of which 13 are oppositesign and only one is same sign. It must be said that our Mirror type compositemodel with Majorana neutrino will produce the same yield of opposite signand same sign events. This asymmetry between opposite sign and same signcould be explained within composite model assuming the existence of anadditional Majorana state with a slightly different mass. Indeed it has beenshown, albeit within a different model [73][74], that the interference betweenthe contributions of two different Majorana states could depress the same signyield relative to the opposite sign. In view of this it could be worthwile eitherto upgrade the CalcHEP implementation of our mirror model to include otherMajorana states or alternatively to reconsider the homo-doublet model withν∗L − ν∗R mixing. In order to address quantitatively this issue we would needto build a new model, with more than one Majorana neutrino state, in theCalcHEP generator. This goes beyond the scope of the present work and itwill be addressed in a future study.
Also ATLAS made the analyses searching for leptoquarks [66] and heavyneutrino associated to right-handed gauge boson [67]. The ATLAS lepto-quark search uses a data sample of 20 fb−1 collected at a center of massenergy of 8 TeV . It finds a good agreement between data and SM expecta-tions and can exclude first and second generation leptoquarks up to 1050 and1000 GeV respectively. The ATLAS search for heavy neutrinos associated toright-handed gauge bosons is performed at
√s = 7TeV on a data sample of
48
2.1 fb−1, it does not find any relevant disagreement between data and the SMexpectations and can exclude WR bosons with masses below 1.8 or 2.3 TeV ,depending on the hypothesis of the model (mass differences between the WR
and N larger than 0.3 or 0.9 TeV ). A more recent CMS analysis considers adata sample of 2.7 fb−1 at
√s = 13TeV to look for second-generation lepto-
quarks [68] and can exclude them up to masses of 1165 GeV for β = 1 and965 GeV for β = 0.5, where β is the leptoquark branching ratio to a chargedlepton and a quark. A similar ATLAS analysis uses a data sample of 3.2fb−1 at
√s = 13TeV to seacrh for first and second generation leptoquarks
[69] and can exclude them up to masses of 1100 GeV in the eeqq channeland 1050 GeV in the µµqq channel. Both searches in CMS and ATLAS at√s = 13TeV observe agreement between data and SM expectation.
Besides the eejj excess, the composite scenario can interpret also otherLHC excesses.
The yet mentioned eνjj excess [65] can be reproduced by the compositescenario by means of processes like pp → `N → `νjj. The absence of theexcess in the corresponding muonic channel can be explained assuming thatthe excited muon state is heavier than the excited electron state.
In a search for high-mass diboson resonances with boson-tagged jets at√8TeV [61] the ATLAS Collaboration observed an excess around 2 TeV
with a global significance of 2.5 standard deviations (note, however, thatthe same search performed by CMS Collaboration did not observe a similarexcess [62]). Our model contains fermion resonances (excited quarks andleptons) which do not couple directly to a pair of gauge bosons. On generalground our fermion resonances could produce final states with a pair of gaugebosons, but these would be accompanied by other objects such as leptons andjets. As an example one might think to pair produce the excited neutrinospp → Z∗ → ν∗ν∗ with the excited neutrinos decaying leptonically ν∗ →W±e∓. One obtains a final signature W+W−e+e− which is different fromthe one considered in the ATLAS search consisting of only gauge boson pairs(WW , WZ or ZZ). However one might imagine to pair produce the chargedexcited fermions, almost at threshold (if they are very massive). Such pairof heavy fermions could in principle form a 1S bound state (via the knownCoulomb and/or color interactions) which in turn could decay to a pair ofintermediate vector bosons given the high mass of the hypothetical heavyfermions [63][64].
49
Chapter 5
The LHC and the CMSexperiment
In this chapter we describe the LHC accelerator and the CMS experiment.
5.1 LHC
The LHC (large hadron collider) is the world’s largest and most powerfulparticle accelerator. It is at the border between France and Switzerland,near Geneva. It is built inside a ring tunnel with a circumference of 27 km tothe depth of 175 m. It can accelerate proton beam up to energies of 7 TeV perparticle or heavy nuclei up to energies of 574 TeV per nucleus. The tunnelcontains two adjacent pipes crossing each other in four points. The particlesto be accelerated run along the pipes and the two beams travel in oppositedirections. The collisions happen in the intersection points. To maintain thebeam on the curvilinear trajectory, 1232 magnetic dipoles are used, while392 magnetic quadrupoles are used to maintain the beams focused, so thatto increase the interaction probability of the particles in the intersectionpoints. The superconducting magnets are made by niobium and titanium.To maintain them at the operating temperature, equal to 1.9 K, liquid heliumis used.
Before entering in the LHC the particles pass trough a chain of accelera-tors that gradually bring the beam to higher energies. In fact each technologyof particle acceleration has maximum and minimum limits of operating en-ergy. The particle at low energy are produced by two linear accelerators,called LINAC, one for the protons and one for the heavy nuclei. Then theparticles go trough the ring accelerators, first the PS booster, then the Pro-ton Synchrotron, then the Super Proton Synchrotron and finally they enter
50
Figure 5.1: Scheme of the accelerators chain at the CERN.
in the LHC.Along the LHC ring are present six experiments. The two biggest exper-
iments are CMS and ATLAS, that are enormous dimensions detector withadvanced technology. They are realized by international collaborations. TheLHCb experiment is projected to study the physics of the B mesons. ALICEis optimized for the study of the heavy ions collisions.
5.2 The CMS experiment
The CMS (Compact Muon Solenoid) [55] is a general purpose detector whichoperates at the LHC. The overall layout of CMS, shown in Fig.5.2, is typicalfor a general purpose high energy detector: it has a cylindrical shape withseveral layers coaxial to the beam direction, called barrel layers, closed atboth ends by disks, called endcaps. The overall length is 28.7 m, of which21.6 m make the main cylinder which has a diameter of 15 m and the rest ofthe length comes from the forward calorimeter. The total mass is 14000 t.
The central features of the CMS detector are the ≈ 3.8 T superconductingsolenoid in the barrel part, the full-silicon-based inner tracker, the electro-magnetic calorimeter and the hadronic calorimeter. In particular the largebending power, needed to measure precisely the momentum of high-energycharged particles, forced a choice of superconducting technology for the mag-nets. Inside the 6 m diameter bore of the solenoid the silicon tracking system,
51
Figure 5.2: Sectional view of the CMS detector.
the electromagnetic calorimeter and the hadronic calorimeter are located.Outside of the solenoid the muon tracking system is sandwiched between thelayers of the steel return yoke for the magnetic field. The high magnetic fieldnot only provides a large bending power within a compact spectrometer, butalso avoids stringent demands on muon-chambers resolution and alignment.The return field is large enough to saturate 1.5 m of iron, allowing 4 muonstations to be integrated to ensured robustness and full geometric coverage.
The origin of the coordinate system of the detector lies in the center at thenominal collision point. The x-axis points radially inward the center of theLHC ring, the y-axis points vertically upward and the z-axis points horizon-tally in the direction of the Jura mountains. Since the cylindrical symmetryof the CMS design, it makes sense to use a cylindrical coordinates system forthe description. It is based on the azimuthal angle φ, defined as the anglemeasured from the x-axis in the x−y plane, the radial coordinate r, measuredin the x − y plane, the polar angle θ, measured from the z-axis. Instead ofthe polar angle the pseudorapidity η is used. Its definition is η = − ln(tan θ
2).
In hadron collider physics the pseudorapidity is preferred over the polar an-gle, because differences in pseudorapidity are Lorentz invariant under boostsalong the longitudinal axis. This is an important feature for hadron colliderphysics, because the colliding partons carry different longitudinal momentum
52
fractions, which means that the rest frames of the parton-parton collisionswill have different longitudinal boosts. The pseudorapidity is zero in thex − y plane and goes to positive and negative infinity, respectively, towardsthe positive and negative z-axis. The forward regions of the detector meansregions of higher |η|, close to the z-axis or about |η| > 3.
5.2.1 Magnet
The solenoid of the CMS detector produces uniform field in the axial direc-tion, while the flux return is assured by an external iron yoke with threelayers, among which the muon system is installed. The superconductingmagnet has a length of 12.5 m and a diameter of the cold bore of 6.3 m. It ismade from a 4-layer cable of NbTi reinforced with aluminium and it is keptat a temperature of 4.5 K with liquid helium. It was designed to produce afield of 4 T, but it operates at 3.8 T.
The momentum analysis of charged particles is performed by measure-ment of their trajectories inside the solenoid. A particle with unitary charge,crossing a region of length l with a uniform magnetic field B, follow a curvewith sagitta
s ' 0.3Bl2
8pT
where pT is the particle momentum in the transverse plane with respectto the field. Therefore measuring s it is possible to evaluate the pT . Themomentum resolution is related to the accuracy of the sagitta measurementby the relation
∆pTpT
= ∆s8pT
0.3Bl2
5.2.2 Inner tracker
The inner tracker is the detector closest to the beam line, being situated inthe 0.2 < r < 1.2m region. The aim of the inner tracker is to reconstructthe trajectories of charged particles in the region |η| < 2.5 with high effi-ciency and momentum resolution, to measure their impact parameter and toreconstruct secondary vertices. For the tracker is required a detector tech-nology featuring high granularity and fast response, keeping to the minimumthe amount of material in order to limit multiple scattering, bremsstrahlung,photon conversion and nuclear interactions.
The innermost tracker is made of three leyers of silicon pixel detectorsnamed Tracker Pixel Barrel (TPB), ranging from 8.8 cm to 20.4 cm diame-ters, and two wheels of Tracker Pixel Endcap (TPE). TPB and TPE contain
53
48 millions and 18 millions pixels respectively. The pixels have a size of 100× 150 µm2. The measured hit resolution in the TPB is 9.4 µm in the r − φcoordinate, while the longitudinal resolution depends on the angle of trackrelative to the sensor, ranging between 20 and 40 µm.
The silicon strip tracker is placed outside of the pixel tracker. The barrelpart of the strip tracker is divided in the 4 layers of the Tracker Inner Barrel(TIB) and the 6 layers of the Tracker Outer Barrel (TOB). Coverage in theforward region is provided by the 3 Tracker Inner Disks (TID) and the 9 disksof the Tracker Endcap (TEC) on each side. The pitch of the strips variesbetween 80 µm in the innermost layers of the TIB and 183 µm in the outerlayers of the TOB. In the disks the pitch varies between 97 µm and 184 µm.The resolution in the barrel strip detector varies between ∼ 20 µm in TIBand ∼ 30 µm in TOB.
5.2.3 Electromagnetic calorimeter
The electromagnetic calorimeter (ECAL) is situated in the 1.2 < r < 1.8mregion. It has been designed to execute precise measurement on both elec-trons and photons with an expected energy resolution better than 1%. TheCMS detector has a hermetic homogeneus electromagnetic calorimeter com-prising 61200 lead tungstate (PbWO4) crystals in the central barrel part and7324 crystals of the same type in each of the two endcaps. The led tungstatecrystals have a small Moliere radius (Rm = 21.9 mm) and a short radiationlength (X0 = 8.9 mm), that allows good shower containment in the lim-ited space available for the ECAL. The scintillation decay time of the leadtungstate crystal is enough small to have about 85% of the light emittedwithin the 25 ns interval between two pp collisions.
The ECAL in the barrel part covers yhe |η| < 1.48 pseudorapidity region,while the endcap covers the 1.48 < |η| < 3 region.
Crystals are trapezoidal with the minor basis turned toward the beaminteraction vertex. The length of the crystals is 230 mm in the barrel and220 mm in the endcaps, the two basis measure 22×22 mm2 and 26×26 mm2
in the barrel, and 28.62×28.62 mm2 and 30×30 mm2 in the endcaps.The energy resolution of a calorimeter can be parametrised as the quadratic
sum of a stochastic term (σ/√E), a noise term (σn/E) and a costant term
(c):σEE
=σs√E⊕ σnE⊕ c.
For the CMS electromagnetic calorimeter σs ≈ 0.028GeV 1/2, σn ≈ 0.12GeVand c ≈ 0.003.
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5.2.4 Hadronic calorimeter
The hadronic calorimeter (HCAL) is situated in the 1.8 < r < 2.9 m region.It is involved in the identification and measurement of quarks, gluons andneutrinos by measuring the energy and the direction of jets and of missingenergy flow in the event.
The HCAL consist in a barrel (HB) that extends to |η| < 1.4 and twoendcaps (HE) ranging from 1.3 < |η| < 3. Since the absorber depth of theECAL barrel and the HCAL barrel in the solenoid is not sufficient to con-tain the complete particle shower, an additional calorimeter (HO) is placedas a tail catcher outside the cryostat, using it as an additional absorber.The intense magnetic field imposes the usage of non-ferromagnetic materi-als. Stainless stell and copper alloys (brass) have been chosen as constituentof the supporting structure and calorimetric absorbers. HCAL is a samplingcalorimeter: absorber plates are interleaved with tiles of plastic scintillators(active medium). The tiles are piled-up into quasi-projective towers. Thescintillation light coming from each tile of one tower is channeled by opticfibres, added together, and finally translated into an analogical signal byhybrid photodiodes (HPD).
Since the identification of forward jets is very important for the rejectionof many backgrounds, the barrel and the endcap parts are complemented bytwo very forward calorimeters (HF), placed on the endcaps at 11.2 m fromthe interaction point, which extends the pseudorapidity range up to |η| < 5.2.The HF consists of steel absorbers with embedded quartz fibres that channelthe Cerenkov light emitted by the shower to photomultiplier tubes (PMT).
The HCAL single particle energy resolution is
σEE
=65%√E[GeV ]
⊕ 5%
in the barrel,σEE
=83%√E[GeV ]
⊕ 5%
in the endcaps andσEE
=100%√E[GeV ]
⊕ 5%
in the forward calorimeter.
5.2.5 Muon system
The muon chambers are situated in the outer 4.0 < r < 7.4 m region.
55
Together with the tracker they are specifically optimised for muon iden-tification and transverse momentum measurement. The barrel covers the|η| < 1.2 region and the endcaps cover the 1.2 < |η| < 2.4 region. Bothbarrel and endcaps contain four stations of detectors arranged in cylindersintervaled with the iron yoke for the magnetic flux return containment and toserve as an absorber. A precision in the transverse momentum measurement∆pT/pT between 8% and 15% for muons with pT = 10 GeV/c and between20% and 40% for muons with pT = 1 TeV/c is expected.
Three independent subdetectors compose the muon chambers: drift tube(DT) chambers, cathode strip chambers (CSC) and resistive plate chambers(RPC).
Drift tube chambers are installed in the barrel region. These chambersare organized in five wheels and each wheel has twelve sectors; each sector hastwelve relevant surfaces: eight with anodic wires parallel to beam directionto measure the r and φ coordinates and 4 with orthogonal wires to measurethe z coordinate. Anodoc wires have a diameter of 50 µm, they are madeof stainless steel and they are alternated with cathode wires. The innervolume is filled with a gaseous mixing of 85% Ar and 15% CO2. The spatialresolution is 100 µm and the temporal resolution is 4 ns.
Cathode strip chambers are installed in the endcap region. The CSC aremultiwire proportional chambers. They are organized in four stations eachof which has six anodic wire layers. Each layer is interleaved with cathodesheets segmented into strips orthogonal to the wires. The wires are in agaseous mixing of 40% Ar, 50% CO2 and 10% CF4. Many strips pick upthe signal and permits the φ measurement with a resolution of 50 µm. Ther coordinate is determined by anode signals with less resolution. The timeresponse has an error of about 25 ns.
Resistive plate chambers have an excellent timing resolution, less than 3ns, and a good spatial resolution, about 10 µm, both in the barrel and inthe endcap region.
5.2.6 Trigger and data acquisition
The maximum expected LHC bunch crossing rate is 40 MHz. Since eachevent takes about 1 MB of data and the expected total storage capability forCMS is O(102) MB
s, it is clear that a rate reduction down to 100 Hz is needed.
To obtain this reduction the selection is splitted into two main steps.In the first step, the Level-1 trigger (L1), a dedicated hardware is used to
reduce at the minimum the dead time and to take a very quick accept/rejectdecision in order to cut down the data rate from 40 MHz to almost 100KHz. L1 selection is based exclusively on calorimeter and muon chamber
56
information, since they are the fastest. Their signals are processed withhardware logical circuits and the selection is based on a rapid identificationof some physical objects (muons, electrons, photons, jets or missing energy),by fixing the right thresholds.
In case of positive decision, data are temporarily stored and then passed tothe second step, the High Level trigger (HLT) system. It relies on commercialprocessors, organised in a farm of personal computers. Numerous dedicatedsoftware algorithms select events coming from the L1 trigger. Since the L1trigger data occour at 105 Hz and the total storage capability is 102 Hz,a reduction factor of 103 is required. The HLT uses the response of allsubdetectors so that it is possible to get complete information of the eventsfor offline analysis.
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Chapter 6
Experimental search for heavycomposite Majorana neutrino
In this chapter we present a search for a heavy composite Majorana neu-trino based on the theoretical model described in chapter 3. The analysisis performed with 2.3 fb−1 of data collected by the CMS experiment during2015 with pp collisions at
√s = 13TeV . This work is summarised in [75].
In the following we first describe the data and MC simulation samples, thathave been used, section 6.1; we then discuss the reconstruction and identi-fication of the particles in which we are interested, section 6.2; right afterwe discuss the definition of the signal region, section 6.3, and the variablefor the signal extraction, section 6.4; in section 6.5 we detail the estimationof the backgrounds that contaminates the signal region; in section 6.6 wediscuss the systematic uncertainties of the measurement; in section 6.7 weshow the results; finally in section 6.8 we discuss the statistical treatmentsof the results.
6.1 Data and Monte Carlo samples
The measurement uses a data sample of proton-proton collisions at a cen-ter of mass energy of 13 TeV recorded in 2015 with the CMS detector atthe CERN LHC, which corresponds to an integrated luminosity of 2.32 fb−1
[76]. The data were reconstructed using a dedicated software developed bythe CMS collaboration (CMSSW version 7 6 3) and they were skimmed con-sidering only runs in which the detector has performed well (this list of runs isrecorded in the JSON file Cert 13TeV 16Dec2015ReReco Collisions15 25ns JSON.txt).In particular, the samples of data that we consider include runs in which thepresence of at least an electron or a muon has been found. The list of these
58
Data samples Luminosity fb−1
/SingleElectron/Run2015C-16Dec2015-v1/MINIAOD 2.32/SingleMuon/Run2015C-16Dec2015-v1/MINIAOD 2.32
Table 6.1: Data samples used in the analysis and their corresponding inte-grated luminosity.
datasets is reported in Table 6.1.The MC samples for the signal are generated at leading order for Λ =
3 TeV and mass = 500, 1500, 2500, 3000 GeV , Λ = 5TeV and mass =500, 1500, 2500, 3500, 4500 GeV , Λ = 9TeV and mass=500, 1500, 2500,3500, 4500 GeV , Λ = 13TeV and mass = 500, 1500, 2500, 3500, 4500 GeV .The signal generation uses CalcHEP 3.6 [32] and NNPDF3.0 [77] partondistribution functions (PDF). The samples of the signal processes and theircross sections are listed in table 6.2
The MC samples for the SM background are produced with differentgenerators. The tt, tW , and tW samples are produced with POWHEG2.0 [78] and are calculated at NNLO. The Drell-Yann and W + Jets aregenerated with MADGRAPH 5 [79], we consider two sets for those samples:the inclusive sample and the samples enriched with events where the sum ofthe pT of the partons at generator level, gen HT, is constrained in specificranges (binned samples). The formers are calculated at NNLO, while thelatters are calculated at LO and their cross sections are multiplied for a k-factor, that is defined as the ratio NLO/LO. All these background samplesuse the NNPDF3.0 parton distribution function and they are interfaced withPYTHIA 8 [80] for the simulation of the parton shower and hadronisation.The WW , WZ and ZZ are produced with PYTHIA 8 and the CTEQ5 [81]PDF, the WW is calculated at NNLO, the WZ and ZZ are calculated atNLO. The samples for the background processes and their cross sections arelisted in table 6.3.
In order to improve the simulations with respect to the data, the MCsamples are adjusted according to the following corrections:
• For the inclusive samples of the Drell-Yann and W + Jets only eventswith gen HT< 100GeV are considered.
• Events are normalised to the integrated luminosity of the data.
• Events are corrected in order to account for differences between thedistributions of the number of pileup interaction compared to the data.
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Signal MC samples σ (pb)eejj L3000 M500 CalcHEP 3.730eejj L3000 M1500 CalcHEP 0.8825eejj L3000 M2500 CalcHEP 0.1725eejj L3000 M3000 CalcHEP 8.02e-02eejj L5000 M500 CalcHEP 331.7e-03eejj L5000 M1500 CalcHEP 114.4e-03eejj L5000 M2500 CalcHEP 22.36e-03eejj L5000 M3500 CalcHEP 5.029e-03eejj L5000 M4500 CalcHEP 1.282e-03eejj L9000 M500 CalcHEP 2.605e-02eejj L9000 M1500 CalcHEP 8.731e-03eejj L9000 M2500 CalcHEP 2.131e-03eejj L9000 M3500 CalcHEP 4.793e-04eejj L9000 M4500 CalcHEP 1.223e-04eejj L13000 M500 CalcHEP 5.714e-03eejj L13000 M1500 CalcHEP 1.488e-03eejj L13000 M2500 CalcHEP 4.659e-04eejj L13000 M3500 CalcHEP 1.101e-04eejj L13000 M4500 CalcHEP 2.809e-05
µµjj L3000 M500 CalcHEP 3.730µµjj L3000 M1500 CalcHEP 0.8825µµjj L3000 M2500 CalcHEP 0.1725µµjj L3000 M3000 CalcHEP 8.02e-02µµjj L5000 M500 CalcHEP 331.7e-03µµjj L5000 M1500 CalcHEP 114.4e-03µµjj L5000 M2500 CalcHEP 22.36e-03µµjj L5000 M3500 CalcHEP 5.029e-03µµjj L5000 M4500 CalcHEP 1.282e-03µµjj L9000 M500 CalcHEP 2.605e-02µµjj L9000 M1500 CalcHEP 8.731e-03µµjj L9000 M2500 CalcHEP 2.131e-03µµjj L9000 M3500 CalcHEP 4.793e-04µµjj L9000 M4500 CalcHEP 1.223e-04µµjj L13000 M500 CalcHEP 5.714e-03µµjj L13000 M1500 CalcHEP 1.488e-03µµjj L13000 M2500 CalcHEP 4.659e-04µµjj L13000 M3500 CalcHEP 1.101e-04µµjj L13000 M4500 CalcHEP 2.809e-05
Table 6.2: Signal MC samples and their cross sections used in the analysis.
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Background MC samples σ (pb)TT TuneCUETP8M1 13TeV-powheg-pythia8 831.76
ST tW top 5f inclusiveDecays 13TeV-powheg-pythia8 TuneCUETP8M1 35.6ST tW antitop 5f inclusiveDecays 13TeV-powheg-pythia8 TuneCUETP8M1 35.6
DYJetsToLL M-50 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 6025.2DYJetsToLL M-50 HT-100to200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 147.40*1.23DYJetsToLL M-50 HT-200to400 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 40.99*1.23DYJetsToLL M-50 HT-400to600 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 5.678*1.23DYJetsToLL M-50 HT-600toInf TuneCUETP8M1 13TeV-madgraphMLM-pythia8 2.198*1.23
WJetsToLNu TuneCUETP8M1 13TeV-madgraphMLM-pythia8 61526.7WJetsToLNu HT-100To200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 1345*1.21WJetsToLNu HT-200To400 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 359.7*1.21WJetsToLNu HT-400To600 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 48.91*1.21WJetsToLNu HT-600To800 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 12.05*1.21WJetsToLNu HT-800To1200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 5.501*1.21WJetsToLNu HT-1200To2500 TuneCUETP8M1 13TeV-madgraphMLM-pythia8 1.329*1.21WJetsToLNu HT-2500ToInf TuneCUETP8M1 13TeV-madgraphMLM-pythia8 0.03216*1.21
WW TuneCUETP8M1 13TeV-pythia8 118.70838WZ TuneCUETP8M1 13TeV-pythia8 47.13ZZ TuneCUETP8M1 13TeV-pythia8 16.523
Table 6.3: Background MC samples and their cross sections used in theanalysis
• Events are weighted considering proper correction factors to resolveresidual differences in data and simulation related to the particle selec-tion.
6.2 Object reconstruction and identification
The reconstruction and identification of the objects employed in the anal-ysis are described in the following. Different definitions of the algorithmsare developed by dedicated group within the CMS collaboration, the POG(“Physics Object Group”), for different value of signal efficiency with thelower possible misidentification rate.
6.2.1 Primary vertex
Primary vertices are reconstructed using the deterministic annealing (DA)algorithm [82]. Only those vertices that pass a set of quality requirements arefurther considered. The distance of their position from the beamspot shouldbe smaller than 2.4 cm in z and 2 cm in the transverse coordinate r. Amongall the reconstructed vertices, the one with the highest sum of squares of the
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transverse momenta of tracks associated to that vertex (∑p2T ) is chosen as
the production vertex of the signal event.
6.2.2 Electrons
The electron selection used in the analysis rely on the HEEPv6.1 algorithm[83] that has been optimised for high pT electrons, that we expect to havein our analysis. The HEEPv6.1 selection contains the following requests:
• ET > 35GeV where ET is the corrected supercluster transverse energy.A supercluster indicates the energy deposit in ECAL constructed bygrouping hot cells found inside a window that is centered around thecell with the maximal energy (seed) and extends over ±0.3 radians inφ and by 0.09 units of η.
• |ηsc| < 1.4442 for electron in the barrel part of the detector and 1.566 <|ηsc| < 2.5 for electrons in the endcap part of the detector. |ηsc| is thesupercluster pseudorapidity.
• IsEcalDriven=1, which means requiring the electron to be reconstructedusing techniques that exploit the energy deposit in the ECAL.
• ∆ηin < 0.004 for a barrel electron and ∆ηin < 0.006 for an endcapelectron. This variable is defined as the difference in η between the trackposition of the electron, as measured in the inner layers, extrapolatedto the interaction vertex and then extrapolated to the calorimeter, andthe position of the supercluster.
• ∆φin < 0.004 for a barrel electron and ∆φin < 0.006 for an endcap elec-tron. This variable is defined as the difference in φ between the trackposition of the electron, as measured in the inner layers, extrapolatedto the interaction vertex and then extrapolated to the calorimeter, andthe position of the supercluster.
• H/E < 1/E + 0.05 for a barrel electron and H/E < 5/E + 0.05 foran endcap electron. This variable is defined as the ratio of the energyin the HCAL towers in a cone of radius 0.15 centerd on the electron’sposition and the electromagnetic energy of the electron’s supercluster.
• Full 5 × 5σiηiη < 0.03 for an endcap electron. This variable gives ameasure of the spread in η in units of crystals of the electron energy inthe 5× 5 block centered on the electron seed crystal.
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• E2×5/E5×5 > 0.94 ||E1×5/E5×5 > 0.83 for a barrel electron. Thesevariables are defined in the (η, φ) plane as the ratio of the energy of themost energetic 1 × 5 (2 × 5) band of ECAL crystals centered in φ tothe most energetic crystal and the energy collected in the 5× 5 matrixof ECAL crystals.
• EcalIso+HadDepth1Isoz < 2+0.03∗ET +0.28ρ for a barrel electrons,< 2.5 + 0.28ρ for an endcap electron with ET < 50GeV , < 2.5 + 0.03 ∗(ET − 50) + 0.28ρ for an endcap electron with ET > 50GeV . EcalIsois the transverse energy of all the rec-hits with ET > 80MeV in thebarrel (ET > 100MeV in the endcap) in a cone of 0.3 radius centeredon the electron’s position in the calorimeter excluding those in an innercone of radius 3 crystals and η strip of a total width of 3 crystals.HadDepth1Iso is the transverse energy of all the towers of the firstlayer of the HCAL in a cone of 0.3 radius centered on the electron’sposition in the calorimeter, excluding the towers in a cone of 0.15 radius.ρ is a variable introduced to correct for energy contamination due topile-up.
• Track pT isolation < 5GeV for a barrel electron with ET < 95GeV ,< 5 + 1.5ρGeV for a barrel electron with ET > 95GeV , < 5GeV foran endcap electron with ET < 100GeV , < 5 + 0.5ρGeV for an endcapelectron with ET > 100GeV . This variable is defined as the sum of pTof all the tracks in a double cone of 0.04-0.3 centered on the electrondirection.
• Number of Lost Hits ≤ 1, which requires that electron tracks must nothave more than one missing hit in the inner layers of the pixel detector,in order to remove electrons coming from conversions.
• |dxy| < 0.02 cm for a barrel electron and |dxy| < 0.05 cm for an endcapelectron. This variable is defined as the transverse impact parameterof the electron track with respect to the primary vertex.
6.2.3 Muons
The muon selection used in the analysis rely on the so called “High-pT”selection [84] and it is complemented with the loose tracker isolation selection.The High-pT selection consists in the following requests:
• IsGlobalMuon, which indicates that the muon must be reconstructedusing information of both tracker and muon chambers subdetectors.
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• Number of valid hits > 0, for which at least one muon chamber hithas to be included in the global muon track fit, to suppress hadronicpunch-through and muons from decays in flight.
• Number of matched stations > 1, for which muon segments in at leasttwo muon stations has to be found, to suppress punch-trough and ac-cidental track-to-segment matches.
• |dxy| < 0.2 cm. This variable is defined as the transverse impact pa-rameter of the muon track with respect to the primary vertex. Thisrequirement suppresses the cosmic muons and muons from decays inflight.
• |dz| < 0.5 cm. This variable is defined as the longitudinal distanceof the muon track with respect to the primary vertex. This requestsuppresses cosmic muons, muons from decay in flight and tracks frompileup.
• Number of pixel hits > 0, for which at least one pixel hit in the track ofthe global muon has to be used, to further suppress muons from decaysin flight.
• Number of tracker layers with means > 5, in which at least five layersare passed trough the tracker, to guarantee a good pT measurement,for which some minimal number of measurement points in the trackeris needed. It also suppresses muons from decays in flight.
• ∆pT/pT < 0.3, which suppresses grossly mis-reconstructed muons.
For the isolation we consider the pT of the tracks in a cone of DR < 0.3around the muon direction, according to the following definition:∑
pT (track)/pT (µ) < 0.1
6.2.4 Jets
Jets are collections of hadrons originating from a common parton. They areconfined to a relatively small cone due to the large momentum magnitude ofthe parent particle and the relatively small transverse momentum associatedwith the fragmentatioin process.
The aim of jet clustering algorithms (JCA) is to identify and clusterthe final state particles belonging to the same jet while ignoring potentialfakes. Two main difficulties arise in identifying jets. The first, known as
64
“collinearity”, arises when two close particles are not resolved: the JCAinterprets them as one single energetic particle, which leads to an incorrectjet seed. The second problem, “infrared sensitivity”, involves soft radiationbetween two seeds from different jets: the JCA produces a single merged jet.
Building infrared and collinear-safe (IRC) algorithms is non-trivial. Theso called ktJCAs, currently among the most used jet algorithms in CMS, areIRC-safe by construction, but computationally demanding. They are builtupon an interactive process using abstract distances d between protojets orpreclusters. Initially each particle is labelled as a protojet. The distance dijis computed for every possible pair of protojets, as well as the distance diBfor each individual protojet, as defined by equations 6.1a and 6.1b,
dij = min(k2pti , k
2ptj )
∆2ij
R2, ,∆2
ij = (yi − yj)2 + (φi − φj)2 (6.1a)
diB = k2pti (6.1b)
in which kt, y and φ refer respectively to the protojet’s transverse momentum,rapidity and φ coordinate; while p andR are algorithm parameters controllingthe relative power of the momentum versus geometrical energy scales andthe characteristic peripheral size respectively. The minimum distance, dmin,among all dij and diB is determined. If dmin is found within the set of dij,which naturally occurs at least in the first iteration since a minimum of twoparticles is needed to form a jet, the two protojets in question are replacedby a protojet built from the merger of their four-momenta. The protojet inquestion is upgraded to the category of jet, only when dmin is not an elementof the dij set.
The process is repeated, starting with the updated list of protojets, untilno protojets remain. The anti-kt JCA, used in parts of the CMS trigger andalmost unanimously in offline analyses, is a particular instance of kt JCA,in which p = −1. Under this construction, the distance dij is dominatedby the momentum of a high-pT particle and the distance to other particles.This results in a tendency for soft, colse particles to group themselves withhard particles (acting indirectly as jet seeds). Perfectly conical jets are henceproduced if no hard particles are found within a radius of 2R; and, in thiscase, the hard particle seeding the jet simply accumulates soft particles.Conversely, two distinct jets are created if two hard particles exist such thatR < ∆ < 2R. Given jets 1 and 2 with kt1 � kt2, jet 1 will be conicaland jet 2 will be partly conical. Neither jet will be conical if kt1 = kt2. Inconclusion, the anti-kt JCA prevents soft particles from altering the shapeof the jet, while allowing hard particles to seed new jets and redefine otherjets’ boundaries when necessary.
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PFjets are built from particle-flow, PF, particles using the anti-kt JCA.The PF algorithm combines information from all CMS subdetectors andreconstructs individual particles in the event (namely electrons, muons, pho-tons, neutral hadrons and charged hadrons). Two predefined R values havebeen validated, 0.4 and 0.8. In the following the jets with R = 0.4 willbe called simply “jets”, while the jets with R = 0.8 will be referred to as“large-radius jets”.
For borh kinds of jet the selection criteria are the following:for |η| ≤ 2.4:
• Neutral hadronic energy fraction < 0.9
• Neutral electromagnetic energy fraction < 0.9
• Number of constituents > 1
• Charged hadronic energy fraction > 0
• Charged multiplicity > 0
• Charged electromagnetic energy fraction < 0.99
for 2.4 < |η| ≤ 2.7
• Neutral hadronic energy fraction < 0.9
• Neutral electromagnetic energy fraction < 0.9
• Number of constituents > 1
for 2.7 < |η| ≤ 3
• Neutral electromagnetic energy fraction < 0.9
• Number of neutral particles > 2
for |η| > 3
• Neutral electromagnetic energy fraction < 0.9
• Number of neutral particles > 10
6.3 Event selection
In this section we describe the final selection of the events that defines oursignal region.
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6.3.1 Particle selection
To perform our analysis, we take the object reconstructed and identified asdescribed in the previous section and we apply some kinematical selectionsto comply with the trigger selection.
Electrons
In the eeqq channel we first consider events that pass the online data tak-ing where at least an electron candidate has a minimum pT of 105 GeV(HLT Ele105 CaloIdVT GsfTrkIdT). The trigger selection is also applied tothe MC samples. This selection constraints the choice of the pT of the leadingelectron in the offline analysis, which is required to be greater than 110 GeV.For the second electron instead a minimum pT value of 35 GeV is sought.The requirement on the peseudorapidity is |η| < 2.4 for both candidates. Inorder to improve the modelling of the simulation, we use specific data/MCcorrection factors according to the measurement reported in [83].
Muons
In the µµqq channel we consider only events triggered according to the pres-ence of a muon candidate with pT higher than 50 GeV(HLT Mu50). Thetrigger selection is required also in the MC samples. Because of this triggerthresholds we require that the leading muon has a minimum pT of 53 GeV inthe main selection, while the subleading muon 30 GeV. The requirement onthe pseudorapidity is |η| < 2.4. We use proper data/MC correction factorsaccording to the measurement in [84].
Jets
Both jets and large-radius jets are preliminary considered when optimisingthe definition of the signal region, but only the latters are used in the mainanalysis. Together the jet selection detailed in section 6.2 We further performa cleaning against electrons and muons requiring ∆R > 0.4 for jets and ∆R >0.8 for large-radius jets. Jets should have pT > 30GeV and large-radius jetspT > 190GeV . For both jet definition the requirement on the pseudorapidityis |η| < 2.4. The jet and large-radius jet candidates are corrected accordingto the JEC and JER, as recommended by CMS collaboration.
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Figure 6.1: In top part of the figure there are the decay amplitudes of thecomposite neutrino for gauge and contact interactions at different Λ value,in the bottom the DR between the two quarks for the same values of Λ.
6.3.2 High mass region definition
The signal in which we are interested is expected to show up in the regionat high dilepton mass. Because of this we require that M(`, `) > 300GeV ,in order to veto Drell-Yan events that would populate the region around theZ-peak and part of its tail.
6.3.3 Request on number of jets or large-radius jets
According to the topology of the signal process described in section 3.3, weexpect that in the ``qq channel the DR distribution of the two quarks pop-ulates two regions: around zero for gauge interaction decays and aroundthree for contact interaction decays, with a relative contribution dependingon the hypothesis of Λ and the composite Majorana neutrino mass of thesignal. This behavior is illustrated in fig. 6.1, where the DR between gener-ated quarks decaying from the composite Majorana neutrino are reported forthree different values of Λ and five mass values. To facilitate the comparisonbetween the DR and the decay widths of the neutrino, the latter are reportedon top of the figure.
As a consequence of this behavior, in case of gauge interaction the two
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Figure 6.2: Multiplicity of large-radius jets with Λ = 5TeV and differentmass values.
Mass (GeV) Fraction of events with gluons close to q1 Fraction of events with gluons close to q2500 0.79111 0.604501500 0.80210 0.662192500 0.81904 0.682873500 0.83536 0.705784500 0.84492 0.72287
Table 6.4: The fraction of events with gluons close (DR < 0.3 to the leadingquark (second column) and to the sub-leading quark (third column).
quarks are reconstructed as a single large-radius jet, due to their small angu-lar distance. At the same time, we find that we can reconstruct a large-radiusjet also at high composite Majorana neutrino mass when contact interactiondominates and the quarks are not spatially constrained, as shown in fig. 6.2.The reason of this is related to the final state radiation. In fact, if this has asufficiently small angular distance from the quark, the ensemble of quark plusradiation can be reconstructed as a large-radius jet. Table 6.4 shows that thefraction of events in which the radiation is found close to a generated quarkby DR < 0.3 is minimum 80% for the leading quark and minimum 60% forthe sub-leading quark.
To summarize, in case of gauge interaction decay the quarks are expectedto be close to each other and, when their distance becomes sufficiently small,they will be reconstructed as a single large-radius jet. In case of contactinteraction decay we expect two separated quarks in the events, but because
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of the overlapping with final state radiation they can also be reconstructedas large-radius jets.
In order to optimise our signal selection we performe a study of sensi-tivity, relying on the object selection described above. We start requiringthe events with two same flavour leptons, plus M(`, `) > 300GeV . We thenrequire alternatively at least two jets or at least one large-radius jet, addinga request on jets tagged as d quark jets, that could be useful to reduce the ttbackground. Finally we compared the significances of these two selections.The significance is defined as S = s√
s+b, where s is the expected number
of signal events and b the expected number of background events, from MCsamples normalised to 2.3 fb−1. We find that the selection with at least onelarge-radius jets has the highest significance and that the request on b-tag isnot relevant. This results are shown in fig. 6.3 for the eeqq and in fig. 6.4for the µµqq channel.
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Figure 6.4: Significance plot for the various jet requests for the µµqq channel.Λ is set to 5 TeV and the neutrino mass is set to 500, 1500 and 2500 GeV .
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DY tt tW tW WJets WW WZ ZZElectron channel 0.001±0.000 0.002±0.000 0.003±0.001 0.004±0.001 0.000±0.000 0.001±0.000 0.001±0.000 0.003±0.001
Muon channel 0.001±0.000 0.004±0.000 0.007±0.001 0.007±0.001 0.000±0.000 0.001±0.000 0.001±0.000 0.002±0.000
Table 6.5: The cumulative efficiencies in the signal regions for the back-grounds.
6.3.4 Summary of signal region selection
The final selections of the signal region for the electron and muon channelsare summarised below:
electron channel
• HLT Ele105 CaloIdVT GsfTrkIdT
• 2 electrons, with pT (e1) > 110GeV , pT (e2) > 35GeV and |η| < 2.4
• M(e1, e2) > 300GeV
• at least 1 large-radius jet, with pT > 190GeV and |η| < 2.4
e1 and e2 indicate respectively the leading and sub-leading electron.
muon channel
• HLT Mu50
• 2 muons, with pT (µ1) > 53GeV , pT (µ2) > 30GeV and |η| < 2.4
• M(µ1, µ2) > 300GeV
• at least 1 large-radius jet, with pT > 190GeV and |η| < 2.4
µ1 and µ2 indicate respectively the leading and sub-leading muon.
In fig. 6.5 we show the expected trigger efficiency for both channels.In fig. 6.6 we show the cumulative efficiencies in the signal region as a
function of the composite Majorana neutrino mass for the signal at Λ = 3,5, 9, 13 TeV in both the considered channels. In table 6.5 we show thecumulative efficiencies in the signal regions for the backgrounds.
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Figure 6.5: The trigger efficiency for the electron channel (left) and themuon channel (right).
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Figure 6.6: The cumulative efficiency in the signal region as function of theneutrino mass for the signal at Λ =3, 5, 9, 13 TeV in the electron (left) andmuon (right) channels.
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Figure 6.7: Distribution of the variable M(`, `, J) after the signal selectionfor the backgrounds (stackplots) and the signal (lines), having considered thesignal parameters Λ = 5TeV and M(N) = 2500, 3500GeV , for the electronchannel on the left and the muon channel on the right.
6.4 Choice of the variable for the signal ex-
traction
The variable used for extracting the signal is the invariant mass of the twoleptons and the leading large-radius jet, M(`, `, J). This variable can clearlyseparate the signal from the background, as shown in Fig. 6.7. In Fig.6.7 we report also the number of events in the signal region for signal, asexpected from simulations, and for backgrounds, as estimated in section 6.5.The backgrounds considered are DY , tt, tW , WJets, WW , WZ, ZZ, QCDmultijets. From Fig. 6.7 we can see that DY , tt and tW are the morerelevant, while the other backgrounds are expected to contribute less andthey will be referred all together as “Other”.
6.5 Background estimation
In this section we describe the estimation of the standard model backgroundsthat enter the signal region. We use semi data driven techniques for the DYand tt, tW processes, while we evaluate the QCD multijet contribution witha complete data driven method. The other standard model backgrounds areexpected to play a minor role and are estimated relying completely on thesimulations.
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Figure 6.8: Measurement of the DY scale factor in the controlo region. Theelectron channel is on the left and the muon channel on the right.
6.5.1 Estimation of DY background
The Drell-Yan process represents a source of background when two leptonsare produced together with initial state radiation that results in a large-radiusjet.
The DY contribution to the signal region (NSRDY ) is estimated normalizing
the MC simulation (NSRMCDY ) to the data. This is accomplished measuring a
scale factor in a control region defined with the same cuts of the signal region,but using a dilepton invariant mass around the Z-peak, 80 < M`` < 100GeV .The scale factor (SFDY ) is defined as
SFDY =NCRdata−MCnonDY
NCRMCDY
(6.2)
where NCRdata−MCnonDY indicates the data in the control region from which
the MC nonDY contributions are subtracted and NCRMCDY indicates the MC
expectation for the DY events in the control region. The scale factor is foundto be 1.04±0.02 for the electron channel and 1.12±0.02 for the muon channel.Fig. 6.8 shows the dilepton invariant mass distribution in the control regionfor the MC events and the data on the top part and the measurement of thescale factor in the bottom part, for both the channels of interest. The scalefactor measured in the control region is assumed to be valid for the signalregion, so that we finally measure
NSRDY = NSR
MCDY × SFDY (6.3)
In order to cross-check the validity of the measured scale factors in a massrange beyond the Z peak, we extend the scale factor measurement in the
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Figure 6.9: Result of the scale factor cross-check at higher dilepton invariantmass.
region 80 < M`` < 300GeV . We find that the scale factors remain costant inthe all M`` range considered. In order to estimate quantitatively the stabilityof the scale factors we perform a fit with a line and we find values comparableto the scale factors measured in the region 80 < M`` < 100GeV . We finda ≈ 2% difference in both channels, which is used to assign a systematicuncertainty on the assumption of the validity of the scale factors in the massregion beyond M`` = 300GeV . The results of the cross-check at higherdilepton invariant mass are shown in fig. 6.9
6.5.2 Estimation of QCD multijet background
QCD multijet events with at least three jets may enter the signal region iftwo of these jets are misidentified as same-flavour leptons and the third oneis reconstructed as large-radius jet.
We evaluate the QCD multijet background from poorly identified, non-isolated lepton candidates selected from data and weighted by a correctionfactor that allows to extrapolate the final contribution to the signal region.We rely on the method developed in CMS in searches of high-mass Z ′-likeresonance in the dilepton final state [85]. The used formula is
QCDSR = QCDCR ×W iSR/CR ×W
jSR/CR (6.4)
where QCDSR is the multijet contribution estimated in the signal region;QCDCR is taken from data from a control region defined as the signal region,except that the leptons are selected according to a looser selection, named“Fake-rate preselection”, that is defined in table 6.6 for the electrons and in
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table 6.7 for the muons; the variables in the tables are described in section 6.2.The WSR/CR is the weight applied to QCDCR in order to estimate QCDSR.
variable barrel endcapFull 5× 5σiηiη < 0.13 < 0.34
H/E < 0.15 < 0.10Number of Lost Hits ≤ 1 ≤ 1
|dxy| < 0.02 < 0.05
Table 6.6: Fake rate preselection for the electrons.
variable cut value|dz| < 1.0
Number of tracker layers with means > 5Number of pixel hits > 0
Table 6.7: Fake rate preselection for the muons.
WSR/CR is defined as MR/(1 − MR), where MR is the pT ,η dependentmisidentification rate, i.e. the probability of reconstructing a jet as a lepton,measured in the search for Z ′ → `` resonances [85]. The MR are reportedin table 6.8 for electrons and in table 6.9 for muons.
region ET range (GeV) functional form35 ≤ ET ≤ 76.1 0.0524− 0.000589× ET
barrel 76.1 ≤ ET ≤ 145.6 0.0124− 6.38× 10−5 × ETET ≥ 145.6 0.00315
35 ≤ ET ≤ 75.8 0.0953− 0.000815× ETendcap |η| ≤ 2.0 75.8 ≤ ET ≤ 186.9 0.0377− 0.000558× ET
ET ≥ 186.9 0.027335 ≤ ET ≤ 88.6 0.0824− 0.000492× ET
endcap |η| ≥ 2.0 88.6 ≤ ET ≤ 145.7 0.0321 + 7.52× 10−5 × ETET ≥ 245.7 0.0506
Table 6.8: Functional form of misidentification rate used for electrons in theQCD multijet estimation.
In the electron channel we find out that QCDSR is ∼ 0.3. As it is lowerthan the other backgrounds, we decided to neglect it.
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Eta region pT range (GeV) functional formBarrel pT > 50 2.22× 10−2 + exp(−3.16 + 2.80× 10−3 × pT )
Endcap pT < 110 8.83× 10−3 + exp(5.93− 1.33× 101 × pT )Endcap pT > 110 −2.91 + exp(1.08 + 1.32× 10−4 × pT )
Table 6.9: Functional form of the misidentification rate used for muons inthe QCD multijet estimation.
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Figure 6.10: M(µ, µ, J) shape of the estimated QCD contribution in themuon channel.
In the muon channel we find out that QCDSR is 1.5 ± 1.2. As it is low,but not negligible, we decided to include it among the minor backgroundslabelled as “Other”. The QCD contribution is higher in the muon channelthan in the electron channel, due to the lower lepton pT thresholds requestedin this channel. The M(µ, µ, J) shape of the QCD contribution in the muonchannel is shown in fig. 6.10
6.5.3 Estimation of the tt and tW backgrounds
tt and tW processes represent irreducible backgrounds that enter the signalregion when two same-flavour leptons and a large-radius jet are selected.
For their estimation we evaluate the shape of the M(`, `, J) distributionfrom data in a control region (CR) defined exactly as the signal region, butsubstituting the sub-leading lepton with a lepton of different flavour. Thiswill be a High-pt muon selected with loose tracker isolation and the samekinematic requirements of the sub-leading electron in the signal region ofelectron channel; and a HEEP electron with the same kinematic require-ments of the sub-leading muon in the signal region of the muon channel.
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Figure 6.11: Comparison of the dilepton plus large-radius jet invariant massfor the MC expectation and the data in CR for electron channel on the leftand muon channel on the right. In the legend also the number of events foreach samples is shown.
We subtract the MC expectation of the non(tt+ tW ) backgrounds from thedata in the control region. We further verify, using the method describedin section 6.5.2, that the QCD multijet contamination is negligible in thiscontrol region with an electron and a muon. Then we use the summed tt andtW MC samples to estimate the ratio of events of the signal region over thecontrol region (RSR/CR). Finally we estimate the tt and tW contribution tothe signal region as
NSR(tt)+tW = (NCR
Data −NCRNon−(tt+tW )Bkg,MC)×RSR/CR (6.5)
Since we perform a shape analysis, the previous formula has to be consideredbin by bin over all the M(`, `, J) distribution.
For this method to be valid, the control region should have a high purityin tt and tW backgrounds and the MC simulation should be well modeled forthese processes. The distribution in Fig. 6.11, where the dilepton plus large-radius jet invariant mass for the MC expectation and the data in the controlregion are compared, assures that these conditions are verified. Anotheraspect to be checked is the consistency of the dilepton plus large-radius jetdistributions in the control region and signal region. In order to check thisconsistency we compare the shape of the mass distributions normalized to 1and, as we can see from Fig. 6.12, also this condition is verified.
After having verified the previous conditions, we can measure the correc-tion factors from the CR to the SR, by plotting the dilepton plus large-radius
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bin (GeV) 400-600 600-800 800-1000 1000-1400 1400-2000 2000-3500
e-channel 0.56±0.09 0.64±0.05 0.55±0.05 0.59±0.06 0.63±0.10 0.62±0.24µ-channel 0.67±0.07 0.69±0.04 0.72±0.04 0.74±0.05 0.83±0.10 0.92±0.28
Table 6.10: Values of RSR/CR for the tt+ tW .
jet invariant mass distributions for the MC tt plus tW normalized to the in-tegrated luminosity of the data (2.32 fb−1) and evaluating in each bin theratio between the two orthogonal regions. This distributions are illustratedin Fig. 6.13 and the values of their ratios, which represents the final transferfactors, are explicitly reported in Table 6.10 The final estimation of the ttand tW backgrounds is shown in Fig. 6.14, where also the nominal MC ex-pectation for the same backgrounds is shown for comparison. The agreementbetween the data-driven estimation and the MC expectation is found to begood, thus validating the method itself and avoiding introducing a systematicuncertainty on it.
6.6 Systematic uncertainties
Systematic effects on the background estimations must be considered beforedealing with the statistical interpretation of the results.
We consider ten systematic uncertainties: one for each selection step.They are related to the luminosity, the pileup, the electron and muon scalefactors, the electron energy scale/resolution, the muon pT scale/resolution,
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Figure 6.13: Measurement of the ratio RSR/CR comparing the dilepton pluslarge-radius jet invariant mass distribution for tt+ tW MC normalised to theluminosity in SR and CR.
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Figure 6.14: Comparison between the data driven estimation of the tt andtW backgrounds and their MC expectation for the electron channel on theleft and the muon channel on the right.
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the jet energy correction, the jet energy resolution, the methods used for thebackground estimation and the theoretical cross sections.
The uncertainty related to the normalization of the simulation to theintegrated luminosity of the data has a value of 2.7%, as measured in [86].
For the uncertainties related to the corrections which we apply to the MCsamples we take the central value of our measurement given by the distribu-tion M(`, `, J), then for every systematic effect we repeat the whole analysistwice, considering the deviation up and down, whose values are given bydedicated CMS groups named POG (“Physics object group”), and produc-ing two distributions: M(`, `, J)Up and M(`, `, J)Down, we then perform thesubtractions |M(`, `, J)Up−M(`, `, J)| and |M(`, `, J)Down−M(`, `, J)| andtake the maximum difference in every bin as the estimation of the systematicuncertainty. This procedure is used for the following systematic effects:
• Pileup: The simulated events are reweighted according to the instanta-neous luminosity measured in data. The error on the average numberof pileup interactions measured in data and the simulation of modellingand physics aspects of the pileup simulation provide an uncertainty ofat most 5% on the distribution used in the reweighting procedure.
• Lepton ID and trigger efficiency: Scale factors for the efficiency of themuon ID, trigger and isolation selections are used to reweight simu-lated events, as a function of the muon pT and η; similarly, data/MCscale factor for the electron ID efficiency are applied as a function ofthe electron pT and η. The corresponding systematic uncertainty isobtained by varying each scale factor by its ±1σ error.
• Muon momentum and electron energy scale and resolution: The mo-mentum scale of leptons has relatively large uncertainties due to differ-ent detector effects. They depend on pT and η of the lepton.
• Jet energy scale: The systematic uncertainty due to jet energy scalecorrections is evaluated by varying the JEC applied on each jet by its±1σ error, which depends on pT and η of the jet.
• Jet energy resolution: The energy resolution of the jet in simulatedevents is corrected to match the energy resolution measured in data;The JER scale factors depend on the jet η. The corresponding sys-tematic uncertainty is measured by varying these scale factors by their±1σ error.
We further consider a systematic uncertainty associated to the methodsused for estimating the backgrounds. In this analysis all the backgrounds are
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estimated with a formula that can be generalised as BkgSR = BkgCR × w,where BkgSR represents the background contribution extrapolated to thesignal region, BkgCR the background in a given control region and w a weightused to normalise BkgCR to the signal region. The systematic uncertaintyon the estimation of the background in the signal region is therefore:√
(δBkgCR × w)2 + (BkgCR × δw)2 (6.6)
Moreover we have the theoretical uncertainties that may affect theM(`, `, J)distribution of the Drell-Yan and signal processes. They are due to the choiceof the PDF and of the renormalization and factorization scale. The system-atic uncertainty associated to the PDF choice is evaluated by reweighting theoriginal MC sample independently for each eigenvector of its PDF set, rely-ing on the PDF4LHC prescription [87]. The systematic uncertainty relatedto the choice of the renormalization and factorization Q2-scales is estimatedby using scales equal to Q2/4 as lower value and 4Q2 as higher value.
ele-channel muon-channelSystematic Bkg Sig Bkg SigLuminosity 2.7 2.7 2.7 2.7
Pileup 4 2 4 1Electron SFs 1 2 1 (TT+tW only) -
Electron en scale 5 3 - -Muon SFs 2 (TT+tW only) - 6 10
Muon pT scale - - 6 4JER 2 0.4 2 0.4JES 3 1 4 1
Background 15 - 15 -Drel-Yan theory 10% - 10% -
Table 6.11: Average systematic uncertainties considered in the analysis. Re-sults are in percentage.
Table 6.11 reports the average uncertainties for each systematics effect,while in appendix B there are plots showing the values of the systematicuncertaities for each bin.
6.7 Unblinded results
In this section we illustrate unblinded results, comparing our expectationswith the data.
83
In table 6.12 we present the estimated background yields, the total num-ber of observed events for each channel and the number of events for thesignal considering Λ = 9TeV and two hypotheses for the masses of N, 1.5and 2.5 TeV . The uncertainties on the estimated background events are thesum of the statistical and systematic uncertainties. The Top part of the ta-ble shows the number of events for all the values of the reconstructed mass,while the bottom part of the table shows the number of events for values ofthe mass higher than 1.4 TeV .
In fig. 6.15 we show the distribution of the variable M(`, `, J) for theestimated SM backgrounds (stackplots), the signal (lines) having consideredΛ = 5TeV and mass of 2.5 and 3.5 TeV , Λ = 9TeV and mass of 0.5, 1.5,2.5 TeV , and the data (black points) for the electron channel (top) and themuon channel (bottom). The error bars stand for statistical plus systematicuncertainties.
The observations are in agreement with the standard model background.Since there is no evidence of new physics for a final state with two leptons anda large radius jet, we set upper limits on the existence of a heavy compositeMajorana neutrino.
6.8 Statistical interpretation of the results
In this section we give a statistical interpretation of the results, setting upperlimits on the existence of a composite Majorana neutrino.
6.8.1 Upper limit extraction
The CLs technique [88] is used to extract the upper limits on the product ofthe cross section and branching fraction of the signal process. This providesa quantitative assessment about the incompatibility of the signal − plus −background model and the only−background hypotheses, provided no excessof data relative to background-only expectation is observed.
The probability P to observe k events under a model that predicts λevents is computed by means of the Poisson statistic as
P (k|λ) =λke−λ
k!(6.7)
In this analysis λ is the sum of expected background yields. Since notonly event yields are considered but also the shape of the invariant massdistribution (or any quantity), P must be promoted to the Poisson likelihood,
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M(eeJ) (GeV)
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nts
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20
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DY
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data
5, M 2.5 [TeV]Λ 5, M 3.5 [TeV]Λ 9, M 0.5 [TeV]Λ 9, M 1.5 [TeV]Λ 9, M 2.5 [TeV]Λ
(13 TeV)-12.3 fbCMSPreliminary
J) (GeV)µµM(
310 410
Eve
nts
0
5
10
15
20
25
30
35
40+tWtt
DYOtherBkg stat. and syst.data
5, M 2.5 [TeV]Λ 5, M 3.5 [TeV]Λ 9, M 0.5 [TeV]Λ 9, M 1.5 [TeV]Λ 9, M 2.5 [TeV]Λ
(13 TeV)-12.3 fbCMSPreliminary
Figure 6.15: Distribution of the variableM(`, `, J) for the data (black points),the estimated SM backgrounds (stackplots), and the signal (lines) havingconsidered the parameters Λ = 5 TeV and mass of 2.5 and 3.5 TeV , Λ =9TeV and mass of 0.5, 1.5, 2.5 TeV , for the electron channel (top) andthe muon channel (bottom). The error bars stand for the statistical plussystematic uncertainty. The last bin includes the overflow entries.
85
Process (All M(``J)) eeqq (stat.+sys.) µµqq (stat.+sys.)tt+ tW 26±4±3 44±6±5
Drell-Yan 22±1±5 30±1±7Other 3.4±0.8±0.1 4.8±0.9±0.4Total 51±4±6 80±6± 8
Observed 64 88N (Λ = 9TeV ,M = 1.5TeV ) 9.96±0.05±4.01 13.15±0.05±6.03N (Λ = 9TeV ,M = 2.5TeV ) 2.50±0.01±0.89 3.32±0.01±1.30
Process (M(``J) > 1.4 TeV) eeqq (stat.+sys.) µµqq (stat.+sys.)tt+ tW 2.8±1.5±0.9 2.9±1.8±1.3
Drell-Yan 3.2±0.3±2.0 4.3±0.4±2.7Other 0.37±0.11±0.04 0.25±0.10±0.11Total 6.4±1.5±2.2 7.5±1.8±3.0
Observed 8 10N (Λ = 9TeV ,M = 1.5TeV ) 9.66±0.05±4.01 12.69±0.05±6.03N (Λ = 9TeV ,M = 2.5TeV ) 2.49±0.01±0.89 3.30±0.01±1.30
Table 6.12: Number of events observed in data compared to expected yieldsform backgrounds and hypothetical heavy composite Majorana neutrino sig-nal with Λ = 9TeV and mass 1.5 and 2.5 TeV . The first uncertainty quotedon backgrounds and MC signal yields is the statistical one, while the secondis the systematic one. The top table gives inclusive yields, the bottom tablegives the yields in the region M(`, `, J) > 1.4TeV .
L, which reads
L(k|λ) =
Nbins∏i=1
P (ki|λi) =
Nbins∏i=1
λkii e−λi
ki!(6.8)
where Nbins is the total number of bins, while i is the bin iterator. Thesystematic uncertainties are taken into account in the measurement of λ, byintroducing n nuisance parameters, θ = θ1, θ2, ..., θn. Furthermore a float-ing signal strength parameter, µ, effectively allows for the determination ofthe most compatible product of the signal cross section and branching ratioprovided the measurement data. Finally λ is given by
λ = µS(θ) +B(θ) (6.9)
86
where S and B are the signal and background estimates respectively.The Poisson likelihood thus reads
L(k|µ, θ) =
Nbins∏i=1
[µS(θ)i +B(θ)i]kie[µS(θ)i+B(θ)i]
ki!(6.10)
A test statistic, tµ, is defined as the ratio of likelihoods so that θ and µmaximise the numerator and the denominator respectively,
tµ = −2 ln
[L(s|µ, θµ)
L(s|µ, θ)
](6.11)
where the numerator represents the best agreement to the observed datafor a fixed-size signal, while the denominator is the configuration of signal-plus-background models that best fits the observed data. An array of tµ isproduced by generating a large number of pseudo-experiments, in which tµare determined by considering the pseudo-data as k. Pseudo-experimentsare randomly drawn from a pool based on the average expectations derivedfrom the analysis, which are then shifted up and down as a function of theuncertainties. The resulting distribution is compared to the observed value,tobs, which is calculated from the observed data. The CLs is the ratio ofp-values for the signal-plus-background (ps+b) and the background-only (pb)hypothesis,
CLs =ps+bpb
(6.12)
where
ps+b = P[tµ > tobsµ |µS(θobsµ ) +B(θobsµ )
](6.13a)
pb = P[tµ > tobs0 |B(θobs0 )
](6.14)
The confidence level (CL) is given by (1−CLs). Consequently this procedureis reiterated for varying µ until CLs = 0.05 in order to obtain a limit at the95% CL.
6.8.2 Limits
In our analysis the CLs technique has been used to set upper limit at 95% onthe cross section of the heavy composite Majorana neutrino produced in as-sociation with a lepton times its branching fraction to a same-flavour leptonand two quarks, σ(pp → `N) × B(N → `qq). The M(`, `, J) distributions
87
(TeV)eNM
0 1 2 3 4 5 6 7
eqq
) (p
b)→ e
BR
(N×
) e e
N→
(pp
σ -410
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-210
-110
1
10
210
310
410
510Observed
1 s.d.±Expected 2 s.d.±Expected
)eN = MΛHCMN (
Theory error) 6 TeVΛHCMN () 7 TeVΛHCMN () 8 TeVΛHCMN () 9 TeVΛHCMN () 10 TeVΛHCMN () 11 TeVΛHCMN () 12 TeVΛHCMN (
(13 TeV)-12.3 fb
CMS
(TeV)µNM
0 1 2 3 4 5 6 7
qq)
(pb)
µ → µ
BR
(N×
) µNµ
→(p
p σ
-410
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-210
-110
1
10
210
310
410
510Observed
1 s.d.±Expected 2 s.d.±Expected
)µN = MΛHCMN (
Theory error) 6 TeVΛHCMN () 7 TeVΛHCMN () 8 TeVΛHCMN () 9 TeVΛHCMN () 10 TeVΛHCMN () 11 TeVΛHCMN () 12 TeVΛHCMN (
(13 TeV)-12.3 fb
CMS
Figure 6.16: The observed 95% CL upper limits (solid black lines) on σ(pp→`N) × B(N → `qq), obtained in the analysis of electron channel (left) andmuon channel (right), as a function of the composite Majorana neutrinomass. The corresponding expected limits are shown by the dotted lines.The coloured bands represents the one (green) and two (yellow) standarddeviation on the limit. The blue curves indicates the theoretical predictionof σ(pp → `N) × B(N → `qq) for MN = Λ, while the light red curves thesame theoretical prediction for seven Λ values ranging from 6 to 12 TeV instep of 1 TeV and different values of the mass of N.
from MC signal, SM backgrounds and observed data, together with the sys-tematic uncertainties, are used as input in the limit evaluation. The observedand expected upper limit on σ(pp→ `N)×B(N → `qq) as a function of themass of the heavy composite Majorana neutrino are shown in Fig. 6.16. Thecoloured bands represent expected variation of the limit to one (green) andtwo (yellow) standard deviations. The blue curve indicates the theoreticalprediction of σ(pp → `N) × B(N → `qq) for MN = Λ, while the light redcurves the same theoretical prediction for seven Λ values ranging from 6 to 12TeV in step of 1 TeV . The corresponding exclusion limits in the parameterspace (MN ,Λ) are displayed in Fig. 6.17. At low neutrino masses, the com-positness scale Λ can be excluded up to 12 TeV in the electron channel andup to 10 TeV in the muon channel. The sensitivity to Λ decreases at higherneutrino masses. For the case MN = Λ the resulting exclusion limits are upto 4.60 TeV in the electron channel and 4.70 TeV in the muon channel.
88
(TeV)eNM
0 1 2 3 4 5
(T
eV)
Λ
0
2
4
6
8
10
12
14
16
18
20
σ 1±Expected
σ 2±Expected
Observed
eN < MΛ
(13 TeV)-12.3 fb
CMS
(TeV)µNM
0 1 2 3 4 5
(T
eV)
Λ
0
2
4
6
8
10
12
14
16
18
20
σ 1±Expected
σ 2±Expected
Observed
µN < MΛ
(13 TeV)-12.3 fb
CMS
Figure 6.17: The observed 95% CL upper limits (solid black lines) on thecomposite Majorana neutrino in the parameter space (MN ,Λ), obtained inthe analysis of the electron channel (left) and the muon channel (right). Thecorresponding expected limits are represented by the dotted lines. The greyzone represents the phase space of Λ < MN , which is not allowed by themodel.
89
Chapter 7
Conclusions
We started from the composite models scenario, in which ordinary quarksand leptons may have an internal substructure. In particular we consideredmodels that analyse the spectroscopy of the weak isospin symmetry. Anessential feature of the composite scenario is the existence of massive exci-tations of the SM fermions, the so called excited quarks and leptons. Thegauge interaction between excited and ordinary fermions is of the magnetictype. The contact interaction is an effective approach to take into account theresidual effects of the unknown internal dynamics. In the higher weak isospinmultiplets (IW = 1 and IW = 3/2) there are exoticly charged fermions.
We studied the phenomenology of excited quarks with charge 5/3e and4/3e and the phenomenology of an excited Mjorana neutrino. In both caseswe implemented the model in CalcHEP that allows simulations at generatorlevel and we performed fast detector simulations with DELPHES, providing,in the end, the statistical significance in different phase space points. Theresults are quite encouraging and certainly endorse the interest and feasibilityof a full fledged analysis of experimental data of the LHC Run II for a searchof these exotic states.
In the case of the composite Majorana neutrino, this analysis has beendone using the 2015 data corresponding to an integrated luminosity of 2.3fb−1 collected by the CMS detector in pp collisions at
√s = 13TeV . The
data is in good agreement with the standard model expectations and we setan upper limit at 95% CL on σ(pp→ `N)×B(N → `qq), being ` an electronor a muon. We provided the limits in the parameter space (MN ,Λ). Forthe representative case MN = Λ the exclusion limits are up to 4.60 (4.55)TeV in the electronic channel and 4.70 (4.75) TeV in the muonic channel,considering the observation (SM expectation). This measurement is the firstsearch that considers as benchmark scenario a Majorana neutrino stemmingfrom a composite model.
90
Appendix A
The parton model
When two protons (or hadrons in general) collide, two of their partons(quarks and gluons) can take part in a hard interaction with high transferredpT . To describe this situation we use the parton model.
The parton model considers a proton (or a hadron in general) of momen-tum P to be constituted of partons with longitudinal momentum xiP , wherethe momentum fractions fulfill the relations:
0 ≤ xi ≤ 1∑i
xi = 1 (A.1)
The energy in the protons center of mass frame is given by√s, while the par-
tons center of mass energy is given by√s =√τs; in this way the parameter
τ is defined:
τ =s
s(A.2)
This parameter and the momentum fractions of the colliding partons arerelated. Shall define the four-momentum of the partons as:
pµ1 =
(x
√s
2, 0, 0, x
√s
2
)(A.3a)
pµ2 =
(y
√s
2, 0, 0,−y
√s
2
)(A.3b)
Therefore we have:
s = (p1 + p2)µ(p1 + p2)µ ' 2p1 · p2 = 2(xys
4+ xy
s
4
)= sxy
substituting s = τs we obtain
sxy = τs⇒ xy = τ (A.4)
91
Therefore the energy available in the partons center of mass frame is equalto the product of the longitudinal momentum fraction of the partons. Thecross section of a process starting from the proton-proton collision is givenby:
σ(a, b→ c,X) =∑ij
∫dxdyfai (x,Q2)f bj (y,Q
2)σ(i, j → c,X ′) (A.5)
where σ is the partonic cross section calculated as the quarks were free.fai (x,Q2) is the parton distribution function that represents the probabilityof finding the constituent i with the momentum fraction x at a value ofthe transferred momentum Q in the hadron a; This function can not becalculated from the QCD, but it has been determined experimentally. Nowsubstituting the eq.A.4 in the eq.A.5 and considering that the parton i cancome from both the proton a and the proton b, one obtains:
σ =1
1 + δij
∑ij
∫ 1
M2
s
dτ
∫ 1
τ
dx
x
[fai (x,Q2)f bj
(τx,Q2
)+
+fai
(τx,Q2
)f bj (x,Q
2)]σ (A.6)
The M in the inferior extreme of the integral in dτ represents the sum of themasses os the products of the partons interaction. The eq.A.6 can be writtenas:
σ =∑ij
∫ 1
M2/s
dτdLijdτ
σ (A.7)
where σ is the partonic cross section evaluated at a center of mass energy√s =√τs and the differential luminosity is defined as:
dLijdτ
=1
1 + δij
∫ 1
τ
dx
x
[fai(x,Q2
)f bj
(τx,Q2
)+ fai
(τx,Q2
)f bj(x,Q2
)](A.8)
92
Appendix B
Plots of systematicuncertainties
B.1 eejj channel
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Figure B.1: Pileup systematic uncertainties.
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Figure B.2: Electron scale factor systematic uncertainties.
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Figure B.3: Muon scale factor systematic uncertainties. Some plots areempty because the corresponding processes are not affected by the uncer-tainty on the muon scale factor.
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2JER systematics for L5000_M4500JER systematics for L5000_M4500
Figure B.4: JER systematic uncertainties.
97
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
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(in %
)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5JES systematics for OtherJES systematics for Other
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
10
12JES systematics for DYJES systematics for DY
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
10
20
30
40
50
JES systematics for TTtWJES systematics for TTtW
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
5
10
15
20
25JES systematics for L5000_M500JES systematics for L5000_M500
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
5
10
15
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25JES systematics for L5000_M1500JES systematics for L5000_M1500
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
5
10
15
20
25JES systematics for L5000_M2500JES systematics for L5000_M2500
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
5
10
15
20
25JES systematics for L5000_M3500JES systematics for L5000_M3500
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
5
10
15
20
25JES systematics for L5000_M4500JES systematics for L5000_M4500
Figure B.5: JES systematic uncertainties.
98
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.5
1
1.5
2
2.5
3
3.5
4
eleScale systematics for OthereleScale systematics for Other
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
5
10
15
20
25
30
35
40eleScale systematics for DYeleScale systematics for DY
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
10
20
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50
eleScale systematics for TTtWeleScale systematics for TTtW
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
1
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3
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5
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9
eleScale systematics for L5000_M500eleScale systematics for L5000_M500
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
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e di
ffere
nce
(in %
)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
eleScale systematics for L5000_M1500eleScale systematics for L5000_M1500
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
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22eleScale systematics for L5000_M2500eleScale systematics for L5000_M2500
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.5
1
1.5
2
2.5
3eleScale systematics for L5000_M3500eleScale systematics for L5000_M3500
M(e,e,J) [GeV]0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.5
1
1.5
2
2.5
3
3.5eleScale systematics for L5000_M4500eleScale systematics for L5000_M4500
Figure B.6: Electron energy Scale/Resolution systematic uncertainties.
99
0
10
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30
40
50
60
70
80
0 2000 4000 6000 8000 10000
Syste
matic u
ncert
ain
ty (
%)
M(e,e,J) [GeV]
Systematic uncertaities for TT+tW estimation (e-chan.)
Figure B.7: tt+ tW estimation systematic uncertainties.
0
20
40
60
80
100
0 2000 4000 6000 8000 10000
Syste
matic u
ncert
ain
ty (
%)
M(e,e,J) [GeV]
Systematic uncertaities for DY estimation (e-chan.)
Figure B.8: DY estimation systematic uncertainties.
0
5
10
15
20
25
30
0 2000 4000 6000 8000 10000
Syste
matic u
ncert
ain
ty (
%)
M(e,e,J) [GeV]
Systematic uncertaities for QCD scale and PDF of DY MC (e-chan.)
Figure B.9: DY theoric (QCD scale and PDF) systematic uncertainties.
100
B.2 µµjj channel
101
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
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rel
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e di
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(in %
)
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22Pileup systematics for OtherPileup systematics for Other
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
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4
6
8
10
12
14
16
Pileup systematics for DYPileup systematics for DY
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
1
2
3
4
5
6Pileup systematics for TTtWPileup systematics for TTtW
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
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4
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12
Pileup systematics for L5000_M500Pileup systematics for L5000_M500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
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(in %
)
0
2
4
6
8
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12
14
Pileup systematics for L5000_M1500Pileup systematics for L5000_M1500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.5
1
1.5
2
2.5
3Pileup systematics for L5000_M2500Pileup systematics for L5000_M2500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
10
12
14
Pileup systematics for L5000_M3500Pileup systematics for L5000_M3500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
10
12
14
16
18
20
22
Pileup systematics for L5000_M4500Pileup systematics for L5000_M4500
Figure B.10: Pileup systematic uncertainties.
102
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2eleSF systematics for OthereleSF systematics for Other
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2eleSF systematics for DYeleSF systematics for DY
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2eleSF systematics for TTtWeleSF systematics for TTtW
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2eleSF systematics for L5000_M500eleSF systematics for L5000_M500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2eleSF systematics for L5000_M1500eleSF systematics for L5000_M1500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2eleSF systematics for L5000_M2500eleSF systematics for L5000_M2500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2eleSF systematics for L5000_M3500eleSF systematics for L5000_M3500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2eleSF systematics for L5000_M4500eleSF systematics for L5000_M4500
Figure B.11: Electron scale factor systematic uncertainties. Some plots areempty because the corresponding processes are not affected by the uncer-tainty on the electron scale factor.
103
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
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rel
ativ
e di
ffere
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(in %
)
0
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10
15
20
25
muSF systematics for OthermuSF systematics for Other
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
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rel
ativ
e di
ffere
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(in %
)
0
2
4
6
8
10
12
14muSF systematics for DYmuSF systematics for DY
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
10
12
14muSF systematics for TTtWmuSF systematics for TTtW
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
10
12
14muSF systematics for L5000_M500muSF systematics for L5000_M500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
10
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14muSF systematics for L5000_M1500muSF systematics for L5000_M1500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
10
12
14muSF systematics for L5000_M2500muSF systematics for L5000_M2500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
10
12
14muSF systematics for L5000_M3500muSF systematics for L5000_M3500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
10
12
14muSF systematics for L5000_M4500muSF systematics for L5000_M4500
Figure B.12: Muon scale factor systematic uncertainties.
104
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
5
10
15
20
25
30
JER systematics for OtherJER systematics for Other
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
10
12
14
16
18JER systematics for DYJER systematics for DY
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.5
1
1.5
2
2.5
3JER systematics for TTtWJER systematics for TTtW
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1JER systematics for L5000_M500JER systematics for L5000_M500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1JER systematics for L5000_M1500JER systematics for L5000_M1500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
10
12
14
16
18JER systematics for L5000_M2500JER systematics for L5000_M2500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1JER systematics for L5000_M3500JER systematics for L5000_M3500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1JER systematics for L5000_M4500JER systematics for L5000_M4500
Figure B.13: JER systematic uncertainties.
105
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
5
10
15
20
25
30
JES systematics for OtherJES systematics for Other
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
5
10
15
20
25
30
35
40
45
JES systematics for DYJES systematics for DY
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
1
2
3
4
5
6
7
8JES systematics for TTtWJES systematics for TTtW
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
10
12
14
16
18
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22JES systematics for L5000_M500JES systematics for L5000_M500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
10
20
30
40
50
60
70
80
90
100JES systematics for L5000_M1500JES systematics for L5000_M1500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
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8
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22JES systematics for L5000_M2500JES systematics for L5000_M2500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
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22JES systematics for L5000_M3500JES systematics for L5000_M3500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
1
2
3
4
5
6
7JES systematics for L5000_M4500JES systematics for L5000_M4500
Figure B.14: JES systematic uncertainties.
106
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
5
10
15
20
25muScale systematics for OthermuScale systematics for Other
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
10
20
30
40
50
muScale systematics for DYmuScale systematics for DY
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
10
muScale systematics for TTtWmuScale systematics for TTtW
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
2
4
6
8
10
muScale systematics for L5000_M500muScale systematics for L5000_M500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
10
20
30
40
50
muScale systematics for L5000_M1500muScale systematics for L5000_M1500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
5
10
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25muScale systematics for L5000_M2500muScale systematics for L5000_M2500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
5
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15
20
25
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35muScale systematics for L5000_M3500muScale systematics for L5000_M3500
,J) [GeV]µ,µM(0 1 2 3 4 5 6 7 8 9 10
310×Max
imum
rel
ativ
e di
ffere
nce
(in %
)
0
0.5
1
1.5
2
2.5
3
3.5
4muScale systematics for L5000_M4500muScale systematics for L5000_M4500
Figure B.15: Muon pT Scale/Resolution systematic uncertainties.
107
0 5
10 15 20 25 30 35 40 45 50
0 2000 4000 6000 8000 10000
Syste
matic u
ncert
ain
ty (
%)
M(µ,µ,J) [GeV]
Systematic uncertaities for TT+tW estimation (µ-chan.)
Figure B.16: tt+ tW estimation systematic uncertainties.
0
20
40
60
80
100
0 2000 4000 6000 8000 10000
Syste
matic u
ncert
ain
ty (
%)
M(µ,µ,J) [GeV]
Systematic uncertaities for DY estimation (µ-chan.)
Figure B.17: DY estimation systematic uncertainties.
0
2
4
6
8
10
12
14
16
18
0 2000 4000 6000 8000 10000
Syste
matic u
ncert
ain
ty (
%)
M(µ,µ,J) [GeV]
Systematic uncertaities for QCD scale and PDF of DY MC (µ-chan.)
Figure B.18: DY theoric (QCD scale and PDF) systematic uncertainties.
108
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