SUSY現象論 - 北海道大学理学部Example m 3=2: ð14Þ As noted in Section 2.5, the gravitino may naturally be the LSP. It may play an important cosmological role, as we will

Motoi Endo (Tokyo)

北大Winter School, 2013.2.14-15

SUSY現象論

Higgs Discovery

2012.7.4@CERN

素粒子標準理論の完成

~126GeV

標準理論を越える物理•証拠✓ニュートリノ振動→右巻きニュートリノが存在？

✓宇宙論- dark matter, dark energy, inflation, ...→正体は何か？

標準理論を越える物理は何か？その性質は？エネルギースケールはどこか？

新しい物理のヒント

•理論からのヒント：“naturalness”✓Higgs potentialの量子補正の大きさ

(100GeV)2に対して0.01×(cutoff)2の補正

•実験からのヒント残念ながらLHC実験による新しい粒子の直接検出の報告は無い

→精密測定によるヒントは無いか?

mode significance

muon anomalous magnetic moment (muon g-2) >3σBr(B→D*τν)/Br(B→D*lν) [cf. ≲2σ for Br(B→Dτν)] 2.8σinclusive and exclusive sin(2φ1) and Br(B→τν) >2σDirect CP violation of B→K+π- and B+→K+π0 [5σ from 0]inclusive and exclusive determinations of Vub 2-3σDirect CP violation of D→K+K- and D→π+π- [4σ from 0]like-sign dimuon charge asymmetry [D0] 3.9σtop forward-backward asymmetry [CDF, D0] >3σelectroweak precision [bottom FB asymmetry, NuTeV, SLD] >2σproton charge radius >5σneutrino anomalies [LSND, MiniBooNe, reactor, Gallium] >2σBr(W→τν)/Br(W→lν) [LEP] 2.8σ

たくさんのヒント（詳細略）

ICHEP2012

tight bound on Bs

mode significance

muon anomalous magnetic moment (muon g-2) >3σBr(B→D*τν)/Br(B→D*lν) [cf. ≲2σ for Br(B→Dτν)] 2.8σinclusive and exclusive sin(2φ1) and Br(B→τν) >2σDirect CP violation of B→K+π- and B+→K+π0 [5σ from 0]inclusive and exclusive determinations of Vub 2-3σDirect CP violation of D→K+K- and D→π+π- [4σ from 0]like-sign dimuon charge asymmetry [D0] 3.9σtop forward-backward asymmetry [CDF, D0] >3σelectroweak precision [bottom FB asymmetry, NuTeV, SLD] >2σproton charge radius >5σneutrino anomalies [LSND, MiniBooNe, reactor, Gallium] >2σBr(W→τν)/Br(W→lν) [LEP] 2.8σ

たくさんのヒント（詳細略）

ICHEP2012

tight bound on Bs

これら（のどれか）が本当にシグナルだとすると、新しい物理はTeVにあるはず

Energy Scale

gravity, GUT

neutrino, cosmology, SUSY breaking

~TeV MSSM

SM~100GeV “indirect search” CP, FCNC, g-2...

“direct search” LHC

Planck, GUT

this lecture

Contents• Review of MSSM (= minimal SUSY SM)- particle, Lagrangian, mass matrix, RGE- Higgs mass• Indirect Searches- CP violation: types of violations, EDM- cLFV and quark FCNC- features of SUSY contributions• Direct Searches: LHC- basic of collider phenomenology- brief review of Monte Carlo simulation

Not Included• motivation (→ e.g. Martin, PH/9709356)- hierarchy problem, gauge coupling unification, ...• superspace, superfield (→ Wess, Bagger)• SUSY breaking/mediation mechanism- O’Raifeataigh, Fayet-Iliopoulos, DSB- gravity mediation (mSUGRA), GMSB, AMSB, ...• non-perturbative SUSY dynamics (SUSY QCD),...

[Phenomenology]• cosmology (→ 郡さん)

• electroweak precision (→ 曹さん)

Review of MSSMRef.• S.P. Martin, PH/9709356• Hikasa, “Supersymmetric Standard Model for

Collider Physicists” (contact to Hikasa-san)

Supersymmetry

Standard Model

gauge boson (1):

Higgs (0):

quark (1/2):

lepton (1/2):

SUSY

gaugino (1/2):

higgsino (1/2):

squark (0):

slepton (0):

minimal SUSY extension of SM = MSSM

Supersymmetry (SUSY) = fermion ↔ boson

(...) : spin of particle

LagrangianSM:

SUSY extension soft SUSY breaking

Note: Higgs potential is not arbitrary

LagrangianSM:

MSSM:

‣ gaugino - matter ‣ scalar potential- sfermion mass- trilinear interaction- Higgs potential

Mass Eigenstate

SM

fermion: left ↔ right

Higgs:

SUSY

Higgs:

Mass Eigenstatesfermion: “left-right” mixing (Yukawa, A-term)

(type II) 2HDM

lepton, quark

SM

SUSY

Slepton, Squark

generation mixing:

(CP) phase:

“chirality” mixby Yukawa andA-term (=AY)

Slepton, SquarkExample: 2 generation

Red: flavor violation, CP violationBlue: CP violation

1st generation 2nd generation

Neutralino

(CP) phases inM1,2 and μ

Chargino

(CP) phases inM2 and μ

cf. gluino: Majorana with mass, M3, and (CP) phase

Higgs masstree level:

Higgs quartic coupling is only by gauge interactions

(D-term)

This prevents Higgs mass from becoming 126 GeV

Higgs massReview: Standard Model

Note: Higgs VEV

Higgs quartic coupling determines Higgs boson mass

Higgs mass“Decoupling limit”: mH, mA ≫ mZ

[(little) fine-tuning]

@ tree-level

Higgs massradiative corrections

Higgs boson mass can be much enhancedcf. Coleman-Weinberg potential

Higgs massradiative corrections

Higgs boson mass of 126 GeV can be explained• stop mass is much larger than top mass• top trilinear coupling is large appropriately

Higgs mass

[Draper,Meade,Reece,Shih]

1 loop level

FeynHiggs

error: mtop, scale

SU(3) 0.118 -7 -3

SU(2) 0.034 -19/6 +1

U(1) 0.017 +41/10 +33/5

RGE: gauge coupling

6 15. Grand Unified Theories

Figure 15.1: Gauge coupling unification in non-SUSY GUTs on the left vs. SUSYGUTs on the right using the LEP data as of 1991. Note, the di!erence in therunning for SUSY is the inclusion of supersymmetric partners of standard modelparticles at scales of order a TeV (Fig. taken from Ref. 24). Given the presentaccurate measurements of the three low energy couplings, in particular !s(MZ),GUT scale threshold corrections are now needed to precisely fit the low energy data.The dark blob in the plot on the right represents these model dependent corrections.

when is the SUSY breaking scale too high. A conservative bound would suggest that thethird generation quarks and leptons must be lighter than about 1 TeV, in order that theone loop corrections to the Higgs mass from Yukawa interactions remains of order theHiggs mass bound itself.

At present gauge coupling unification within SUSY GUTs works extremely well. Exactunification at MG, with two loop renormalization group running from MG to MZ , andone loop threshold corrections at the weak scale, fits to within 3 " of the present preciselow energy data. A small threshold correction at MG (#3 ! - 3% to - 4%) is su"cientto fit the low energy data precisely [25,26,27]. 2 This may be compared to non-SUSYGUTs where the fit misses by ! 12 " and a precise fit requires new weak scale states in

2 This result implicitly assumes universal GUT boundary conditions for soft SUSYbreaking parameters at MG. In the simplest case we have a universal gaugino mass M1/2,a universal mass for squarks and sleptons m16 and a universal Higgs mass m10, as motivatedby SO(10). In some cases, threshold corrections to gauge coupling unification can beexchanged for threshold corrections to soft SUSY parameters. See for example, Ref. 28and references therein.

June 18, 2012 16:19

strong motivation for GUT

RGE: gauge coupling

RGE: gaugino mass

c.f.

gaugino mass unification @ GUT

RGE: scalar mass

runnings are controlled by coupling constants

colored scalar mass: larger by M3up-type Higgs mass: strongly pulled down by top Yukawa

Example

m3=2: !14"

As noted in Section 2.5, the gravitino may naturally be the LSP. It may play animportant cosmological role, as we will see in Section 4. For now, however, we fol-low most of the literature and assume the gravitino is heavy and so irrelevant formost discussions.

The renormalization group evolution of supersymmetry parameters is shown inFig. 5 for a particular point in minimal supergravity parameter space. This figureillustrates several key features that hold more generally. First, as superpartnermasses evolve from MGUT to Mweak, gauge couplings increase these parameters,while Yukawa couplings decrease them. At the weak scale, colored particles aretherefore expected to be heavy, and unlikely to be the LSP. The Bino is typicallythe lightest gaugino, and the right-handed sleptons (more specifically, the right-handed stau ~sR) are typically the lightest scalars.

Second, the mass parameter m2Hu

is typically driven negative by the large top Yuk-awa coupling. This is a requirement for electroweak symmetry breaking: at tree-level,minimization of the electroweak potential at the weak scale requires

jlj2 #m2

Hd$ m2

Hutan2b

tan2b$ 1$ 1

2m2

Z % $m2Hu

$ 1

2m2

Z ; !15"

where the last line follows for all but the lowest values of tanb, which are phenom-enologically disfavored anyway. Clearly, this equation can only be satisfied ifm2

Hu< 0. This property of evolving to negative values is unique to m2

Hu; all other mass

Fig. 5. Renormalization group evolution of supersymmetric mass parameters. From [11].

10 J.L. Feng / Annals of Physics 315 (2005) 2–51

negative: EWSB

[from astro-ph/0301505]


Indirect SearchesExperiments at low energy scale

‣ probe of new physics by radiative corrections- CP violation: types of violations, EDM- cLFV and quark FCNCs- features of SUSY contributions

References- S.P. Martin, PH/9709356- Donoghue et. al., “Dynamics of the Standard Model”

Sequence1. Process- EDM, cLFV, quark FCNC, etc

2. effective Lagrangian- operators after decoupling heavy degrees of freedom

3. Status (experimental limit) & prospect4. SUSY contribution- Mass insertion approximation

CP Violation

Ref. Bigi, Sanda, “CP violation”, PDG review

CP violation = violation of processes/Lagrangian under CP transformation

CP ViolationExamples• CKM matrix (three generations)- decays and oscillations of K, D, B mesons• strong CP problem- : tight constraint from neutron EDM• baryogenesis- Sakharov condition (B, CP, non-equilibrium)

Types of CPV1. Decay, “direct CP violation”: e.g., mesons, leptogenesis

2 2CP

CP

cut

Types of CPV2. Oscillation, “indirect CP violation”: e.g., mesons

2 2CP

e.g.oscillation: extra phase

→ different from case 1

Types of CPV3. Interference of CP violations of decay and oscillation

M final state (CP eigenstate)

CP of M

decay

decayoscillation

clean signal of weak phase: determination of CKM matrix

(see e.g., Bigi, Sanda for details)

Types of CPV4. Electric Dipole Moment (T violation)

not asymmetry of decay, but energy shift under electric field

(not in Dirac equation)

c.f. magnetic dipole moment (CP invariant)

(included in Dirac equation)

MeasurementsB

spin

E B

spin

E

particle under electric field → use atoms and molecules

EDM in Scales2.1. Electric Dipole Moment 7

CP Violation

CP ViolationParticleEDM

HadronEDM

NuclearEDM

Atomic/ Molecular

EDM EDMObservable

Q

dlepton

chromo

dquark

quarkd MQM

dion

Schiff

eeqq eeNN

NNNN

dnnd

ddia

parad

µd

iond

parad

dn

diad

qqqq

GGG~

GG~

MaskawaKobayashiCabbibo

char

ged

syst

ems

neut

ral s

yste

ms

Higgs

Technicolor

Super−Symmetry

Left−RightSymmetry

Strong

Model for

Figure 2.2: A variety of theoretical speculative models exist in which an EDM could beinduced in fundamental particles and composite systems. Through different mechanismsor a combination of them, an EDM would be experimentally accessible[from [28]].

(ensemble average) and look for spin precession. In practice, most of the EDMexperiments employ the scheme developed by Purcell et al. [29]. The particlewith spin I under study is placed in external electric and magnetic fields E and B.The moment d interacts with electric field E. This contribution can be separatedfrom the magnetic interaction term -µ·B by reversing the electric field relativeto the magnetic field. The Hamiltonian for the interactions of the magnetic andelectric dipole moments for such a particle may be written as

H = (!dE+µB) ·I| I |

, (2.1)

where d and µ are the electric and magnetic dipole moments and I is the spin.The magnetic dipole moment µ is defined as

!µ = ge h

2mcI, (2.2)

where e is the charge of the electron, g is the gyromagnetic ratio, h = h/2π , his Planck constant, I=( h/2)·σ , σ is Pauli matrix, m is the mass of a particle, cis the velocity of light, and !I is the spin of a particle. In Dirac’s theory, thegyromagnetic ratio g is 2 for point-like spin 1/2 particles. Radiative corrections

Lagrangian

These induce CP-violating nucleon interactions→ many-body and/or hadronic calculations are required to relate atomic/molecule EDMs to particle EDMs

Appendix A are given in Appendix B. In Appendix C we present the e!ective vertices inthe mass eigenstate basis necessary for the numerical calculation. Appendix D containsthe formulae for the (C)EDMs in the mass eigenstate basis, using the e!ective vertices.In Appendix E and F the loop functions used in this paper are defined.

2 Jarlskog Invariants and Flavored EDMs at the LO

The e!ective CP-odd Lagrangian, which contributes to the (C)EDMs, is given as

Le! =g2

s

32!2"Ga

µ!Gµ!,a !

!

i=u,d,s,e,µ

idf

2#i(F · $)%5#i !

!

i=u,d,s

idc

f

2gs#i(G · $)%5#i

+1

3w fabcGa

µ!G!",bGµ,c

" +!

i,j

Cij (#i#i)(#ji%5#j) + · · · , (1)

where Fµ! and Gaµ! are the electromagnetic and the SU(3)C gauge field strengths, respec-

tively. The first term of Eq. (1) is the well-known QCD theta term. The second and thirdterms of Eq. (1) are the fermion EDMs and CEDMs, respectively, while the second lineof Eq. (1) contains dimension-six CP-odd operators, such as the Weinberg operator andthe CP-odd four-Fermi interactions.

The QCD theta parameter is tightly constrained by the neutron EDM at the level of"<" 10!(9!10); this naturalness problem is commonly referred to as the strong CP problem.

One natural way to achieve the required suppression for " is to impose the Peccei-Quinnsymmetry, since the axion field makes " dynamically vanishing. Under the above assump-tions, the quark (C)EDMs are very suppressed in the SM as they are generated only atthe three-loop level by the phase of the CKM matrix. Long-range e!ects to the neutronEDM, arising at the two-loop level, are still far below the current bound. In this paperwe assume the Peccei-Quinn symmetry, for simplicity.

Among the various atomic and hadronic EDMs, a particularly important role is playedby the thallium EDM (dTl) and by the neutron EDM (dn) that can be estimated as [14–16]

dTl = !585 de ! e 43 GeV C(0)S , (2)

where C(0)s has been evaluated as [17]

C(0)S = Cde

29 MeV

md+ Cse

&# 220 MeV

ms+ Cbe

66 MeV(1 ! 0.25&)

mb, (3)

with & $ 0.5 [18]. Moreover, dn can be estimated as [19, 20]

dn = (1 ± 0.5)"

1.4 (dd ! 0.25 du) + 1.1 e (dcd + 0.5 dc

u)#

. (4)

In our analysis, we will use the above formulae for the evaluation of the (C)EDMs 1.

1 It has been argued in Ref. [21] that the evaluation of the neutron EDM still su!ers from sizableuncertainties even when evaluated within the QCD sum rules approach.

4

electric EDM chromo EDM

Weinberg four-Fermi

θ term

Neutron EDM

･･･

e.g.

[recent calculation by Hisano et. al. 1211.5228]

c.f. mercury EDM: sensitive to chromo EDM and EDM between nucleons (quarks)

Electron EDM

Measured by (special) atoms and molecules• paramagnetic atoms: Tl- one unpaired electron (Cs, Rb)- dTl/de ~ 103 - 104, due to

“many body” effect- (eiγ5e)(NN) operator also

contributes to dTl

• paramagnetic molecule: YbF

5

are expected to strengthen the present limit by anotherorder of magnitude or more for YbF, and many more sys-tems are explored as well, see e.g. [48] for a recent list,making for an expected improvement of at least the onefrom atoms.

In the future, trapped molecular ions might also beused as sensitive probes for EDMs, however, at the mo-ment there are still severe experimental and theoreticalchallenges to overcome. Furthermore, also solid statesystems are being explored as sensitive probes for theelectron EDM [49, 50]. While again some experimentalas well as theoretical progress is necessary before com-petitive results can be achieved, recent results show theprogress in this field [51]. Finally, new techniques are be-ing explored for measuring the EDMs of charged particlesdirectly by using a storage ring [52–55]. While the mainfocus here is on other systems, there are also proposalsto use the technique for molecular ions, see e.g. [56].

The plethora of ongoing and planned experiments, allaiming at the strengthening of present limits by severalorders of magnitude, will take this field to a new level.Especially if one or several of these experiments shouldresult in a significant non-zero signal, the question ofa more refined analysis of the various uncertainties willbe posed, making a global analysis obligatory. We willexplore steps in this direction below.

V. A ROBUST LIMIT ON THE ELECTRONEDM

With the results of the last sections at hand, weproceed to derive limits on the electron EDM and theelectron-nucleon coupling. We do this in two steps: first,we derive the limit just from the measurements withTl and YbF, to avoid even input from the conservativebound on CS from Hg. Then we add this as a third con-straint, obtaining a much stronger limit on both, de andCS . We use the data as given in Table II, i.e. not (yet)transforming the given values into symmetric bounds.

The results are shown in Figs. 1 and 2 for the two inputsets, where the constraint from each system is shown inthe de� CS–plane. We illustrate by the light grey area inFig. 1 the bound on the electron EDM obtained by thecombination of the Tl and YbF constraints only (comparealso to [17]). For input set II, these two constraints arebasically parallel; therefore no bound can be obtained inthis case without further assumptions. The dark area inthe middle is the global fit to all three constraints. Theprojections on the parameters of interest read

dIe = (0.026± 0.065)⇥ 10�26e cm and (15)

CIS = (�0.08± 0.36)⇥ 10�7 (16)

for input set I and

dIIe = (0.024± 0.066)⇥ 10�26e cm and (17)

CIIS = (�0.12± 0.36)⇥ 10�7 (18)

FIG. 1: Bounds from Hg, Tl and YbF in the de–CS-plane,using input set I. The very light grey vertical bound indi-cates the 1D-limit on de when using only the Tl and YbFconstraints without the aid of Hg.

FIG. 2: Bounds from Hg, Tl and YbF in the de–CS-plane,using input set II.

for input set II. These values are to be compared withde = (�0.31± 0.35)⇥ 10�26e cm and CS = (3.2± 3.3)⇥10�7, obtained using only the two constraints from Tl(input set I) and YbF. The corresponding upper limitsat 95% C.L. are

|dI,IIe | 0.14⇥ 10�26e cm and (19)

|CI,IIS | 0.72(0.74)⇥ 10�7 (20)

for the global fit, whereas |de| 0.89 ⇥ 10�26e cm and|CS | 8.6 ⇥ 10�7 when excluding the input from Hg.Independent of the input set, the global fit therefore re-sults in a limit on the electron EDM very similar to theone obtained naively from YbF alone, but is obtained in

[figure from 1301.1681]

Current Limits

particle bound [e cm]electron 1.6 x 10-27 (90%)

muon 1.9 x 10-19 (95%)

tau 4.6 x 10-17 (95%)

proton 0.54 x 10-23

neutron 2.9 x 10-26 (90%)

mercury 3.1 x 10-29 (95%)

strong CP θ < 10-10

Standard Model1. θ term: - c.f. related to phases of quark mass matrix by chiral

rotation

2. CKM phase- quark EDM at three loop

- lepton EDM at four loop

[use 1211.5228]

SUSY• sources of CP phases: combinations

• typical diagram

too simple...

Mass Insertion Approx.• electron EDM

• quark EDM

Numerical Results

dYbFdYbF dndndHgdHg

-0.1 0 0.1

-0.4

-0.2

0

0.2

0.4

qmp

qAp

FIGURE 1. The plot shows the power of combining the results of different best EDM experiments(see Table 1). The showcased Susy example is a 1-loop calculation with O(1)-phases and assumes ageneric mass scale of 1 TeV for all contributing superpartners sfermions (the stop mostly affects 2-loopcontributions and can still be relatively light) and tan b=3. In that case, similar limits apply as in thecMSSM and the scenario is under pressure now from direct Susy mass limits [14]. The plot has beenkindly provided by A. Ritz and updates an earlier version in [2].

has been collected [18]. The field of EDM searches is still in a phase pushing towardsthe discovery of the first finite permanent EDM. Therfore it is most important to pursuemany different efforts regarding the source of CP violation but also regarding differenttechnologies in order to further develop and establish the most sensitive and powerfultechniques. Obviously, improving EDM limits severely constrains parameter spaces ofmany models of CP violation. If finite EDM will eventually be discovered, certain setsof EDM measurements may allow to disentangle the underlying physics. We may forinstance expect the neutron EDM in combination with proton and deuteron EDM todecide the question whether or not the QCD Q-term is at work. Various combinationsof nuclear, atomic and molecular EDM might establish how an EDM of the electron

soft mass = 1TeV, tanβ = 3

similar for mercury

Probe of ≲O(10)TeV soft mass scalec.f. Higgs mass implies O(10)TeV

Prospect

Cs, RbYbF

Fr

Possibly probe up to O(102-103)TeV soft mass scale!!

w/ flavor

w/o flavor

* flavor:

current limit

* msoft includes μ

How difficult to control?

• A parameter phase/size- may favor GMSB or AMSB• μ (Bμ) parameter phase- related to solution of μ problem• gravitational correction (AMSB)

(personal view)

excluded

[Endo,Yamaguchi,Yoshioka]

→ Im[Mi Mj*] (also Im[Mi At*])

Suppression Mechanism

• accidental cancellation- unnatural, but still allowed if phases of Mi, A, B are

not aligned to each other- need more atoms and molecules to refute

• A = B = 0 @ cutoff (mediation scale of SUSY breaking)- induced by radiative corrections, e.g., of gravitational

effects- for instance, Im[Mi Mj*] contributes to B phase

• decoupling of 1st and 2nd generations- emerges at 2 loop- emerges by FCNC

• hypothesis of CP invariance in high energy scale- CKM phase induced by spontaneous

CP violation → other CP phases? • ...

mass matrices of quark and squark are not always diagonalized simultaneously flavor flavor


Summary of CP• Several types of CPV observables• EDM: electron, neutron, mercury, ... (atoms, molecules)• SUSY CP phases- challenging to suppress/control all phases- currently probe of soft mass scale up to O(10) TeV- dependence: δ(CP)/msoft2

- future: muon, deuteron, electron [Cs, Rb, Fr, YbF], ...→ potential sensitivity up to O(102-103)TeV




Lepton Flavor Violation and quark FCNC

Currently most sensitive probe of high energy physics• lepton flavor violation:• quark FCNC:

References• S.P. Martin, PH/9709356• Donoghue et. al., “Dynamics of the Standard Model”

Lepton Flavor ViolationForbidden (highly suppressed) in Standard Model

Ref. e.g., Hocker, 1201.5093 for status

• measurement:• backgrounds

• monochromatic energy of e-

• Ee ~ mμ - E1S-binding

• less accidental backgrounds 1S state

Experimental status: CLFV

Decay Current Limit

! ! µ" 4.4 · 10!8

! ! e" 3.3 · 10!8

µ ! e" 1.2 · 10!11

! ! 3µ 2.1 · 10!8

!! ! e!µ+µ! 2.7 · 10!8

!! ! e+µ!µ! 1.7 · 10!8

!! ! µ!e+e! 1.8 · 10!8

!! ! µ+e!e! 1.5 · 10!8

! ! 3e 2.7 · 10!8

µ ! 3e 1 · 10!12

All values from:

Particle Data Group

http://pdg.lbl.gov/

MEG 2011,

PRL107, 171801:

Br(µ ! e!)" 2.4 # 10!12

Limit on µ ! 3e from:

SINDRUM 1988

New experiment could reach:

Br(µ ! 3e) $ 10!16 (?)

A. Schoning et al.,

Physics Procedia 17 (2011) 181

IMFP 2012, 25/05/2012 – p.14/45

Status & ProspectsExperimental status: CLFV

Capture Current Limit

µ! 32S ! e! 32S 7 · 10!11

µ! 32S ! e+ 32Si 9 · 10!10

µ!T i ! e!T i 4.3 · 10!12

µ!T i ! e+Ca 3.6 · 10!11

µ!Pb ! e!Pb 4.6 · 10!11

µ!Au ! e!Au 7 · 10!13

All values from:

Particle Data Group

http://pdg.lbl.gov/

Future experiments:

Sensitivities of O(10!16) (?)

COMET:

Letter of interest @:

http://j-parc.jp/

Mu2E:

Proposal @:

http://mu2e.fnal.gov/

Timeline: 2016 (?)

IMFP 2012, 25/05/2012 – p.15/45

• sources of LFV

c.f. relations with high scale physics: RH neutrino, GUT

SUSY

μ → eγ

(AR as well)

Probe of O(10)TeV

Other Modes

• common LFV operator in most cases (c.f. Higgs mediation)

[Cirigliano,Kitano,Okada,Tuzon,0904.0957]

Nuclei Dependence

20 40 60 800.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Z

B!!"e;Z"#B!!"e#"

Figure 2: Ratio R(Z) of µ ! e conversion over B(µ ! e!) versus Z in the case of Dipoledominance model.

3.3 Target dependence of µ ! e conversion

In principle, any single-operator model can be tested with two conversion rates, even ifµ ! e! is not observed. To illustrate this point, we update the analysis of Ref. [6] andplot in Fig. 3 the conversion rate (normalized to the rate in Aluminum) as a function ofthe Z of the target nucleus, for the four classes of single-operator models defined above.Compared to Ref. [6], the novelty here is the inclusion of a second vector model (V (Z)).

The results of Fig. 3 show some noteworthy features. First, we note the quite di!erenttarget dependence of the conversion rate in the two vector models considered. This can beunderstood as follows: in the case of the V (!) model, the behavior in Fig. 3 simply tracesthe Z-dependence of V (p) (the photon only couples to the protons in the nucleus). Onthe other hand, in the case of the V (Z) model, the Z boson couples predominantly to theneutrons in the nucleus and the target dependence of the ratio V (n)/V (p) " (A # Z)/Zgenerates the behavior observed in Fig. 3.

Next, let us focus on the actual discriminating power of the Z-dependence. Clearly,the plot shows that the model-discriminating power tends to increase with Z. This isa simple reflection of the fact that the whole e!ect is of relativistic origin and increasesin heavy nuclei. So in an ideal world, in order to maximize the chance to discriminateamong underlying models, one would like to measure the conversion rate in a light nucleus,say Aluminum or Titanium, as well as in a large-Z nucleus, like Lead or Gold. Thissimplified view, however, has to be confronted both with theoretical uncertainties and theactual experimental feasibility. Concerning the uncertainties, a simple analysis shows thatthe dominant uncertainty coming from the scalar matrix elements almost entirely cancelswhen taking ratios of conversion rates (even using the conservative range y $ [0, 0.4] forthe strange scalar density matrix element). Moreover, in the large-Z tail of the plot, someresidual uncertainty arises from the input on the neutron density profile. When polarized

10

Ti

Al Au[SINDRUM-II][COMET, Mu2E]

Experimental status: CLFV

Decay Current Limit

! ! µ" 4.4 · 10!8

! ! e" 3.3 · 10!8

µ ! e" 1.2 · 10!11

! ! 3µ 2.1 · 10!8

!! ! e!µ+µ! 2.7 · 10!8

!! ! e+µ!µ! 1.7 · 10!8

!! ! µ!e+e! 1.8 · 10!8

!! ! µ+e!e! 1.5 · 10!8

! ! 3e 2.7 · 10!8

µ ! 3e 1 · 10!12

All values from:

Particle Data Group

http://pdg.lbl.gov/

MEG 2011,

PRL107, 171801:

Br(µ ! e!)" 2.4 # 10!12

Limit on µ ! 3e from:

SINDRUM 1988

New experiment could reach:

Br(µ ! 3e) $ 10!16 (?)

A. Schoning et al.,

Physics Procedia 17 (2011) 181

IMFP 2012, 25/05/2012 – p.14/45

Status & ProspectsExperimental status: CLFV

Capture Current Limit

µ! 32S ! e! 32S 7 · 10!11

µ! 32S ! e+ 32Si 9 · 10!10

µ!T i ! e!T i 4.3 · 10!12

µ!T i ! e+Ca 3.6 · 10!11

µ!Pb ! e!Pb 4.6 · 10!11

µ!Au ! e!Au 7 · 10!13

All values from:

Particle Data Group

http://pdg.lbl.gov/

Future experiments:

Sensitivities of O(10!16) (?)

COMET:

Letter of interest @:

http://j-parc.jp/

Mu2E:

Proposal @:

http://mu2e.fnal.gov/

Timeline: 2016 (?)

IMFP 2012, 25/05/2012 – p.15/45Comparable in future!!

Prospects

current limitMEG expectedMEG proposal

Possibly probe up to 100TeV soft mass scale

Assumption:photo dipole dominance

Summary of cLFV• best sensitivity from muon lepton flavor violation

• SUSY LFV- generation mixings in soft masses

(induced by right-hand neutrino in see-saw)- currently probe of soft mass scale up to O(10) TeV- dependence: Br ∝ [δμe/msoft2]2

- future: all three processes have similar sensitivity- best sensitivity from μN-eN transition- useful for model discrimination

Quark FCNC

• Quark flavor is violated by CKM matrix in SM- W± exchange

• neutral currents, i.e., charge-conserved transitions, are induced by W± loop

• FCNCs are often associated by CP violation- for instance, CKM phase

vertices can haveCP violating phase

Ref. Bigi, Sanda, “CP Violation” PDG review

Energy Scale

New Physics

Standard Model

hadron

~TeV

~100 GeV

~GeV

heavy particlesdecouple

effectiveLagrangian

(QCD) running

observables(non-perturbative)

Lagrangian• low-energy scale, i.e., after decoupling heavy degrees

of freedom (W boson, SUSY particles)• depends on processes in interest- neutral meson oscillation, (semi-) leptonic decay,

hadronic decay, etc• For instance, K0-K0 oscillation

2

computed in Ref. [11] and rescaled to our value of !! andto the more recent average of the B parameter BK givenin Ref. [12] (see Section 3).The current experimental values |"K |exp and !mexp

Kare given by[13]

!mexpK = (3.483± 0.006) · 10!15GeV , (5)

|"K |exp = (2.229± 0.010) · 10!3 , (6)

which together with Eq. (3) imply the following boundon the NP contribution:

ImMNP12 = (1.7± 1.6) · 10!18 GeV . (7)

The most general e"ective Hamiltonian for K-K mix-ing beyond the SM is given by

He! =5!

i=1

Ci(µ)Qi(µ) +3!

i=1

"Ci(µ) "Qi(µ) , (8)

where the SUSY basis of operators is

Q1 = d"#µPLs" d##µPLs#

Q2 = d"PLs" d#PLs#Q3 = d"PLs# d#PLs" (9)

Q4 = d"PLs" d#PRs#Q5 = d"PLs# d#PRs"

together with the chirally-flipped operators "Q1,2,3 ob-tained from Q1,2,3 with the substitution L ! R. Thechiral projectors are defined as PL,R = (1 " #5)/2.The New Physics amplitude is then given by

MNP12 =

!

i

CNPi (µ)#K0|Qi(µ)|K0$ . (10)

The matrix element for the SM operator Q1 is relatedto the bag parameter BK (in the non-relativistic conven-tion)

#K0|Q1(µ)|K0$ = 1

3mKf2

KBK(µ) , (11)

and the matrix elements of the operatorsQ2,3,4,5 are usu-ally normalized to #Q1$, defining the ratios Ri as

Ri(µ) %#K0|Qi(µ)|K0$#K0|Q1(µ)|K0$

. (12)

The NP Wilson coe#cients must be given in the samerenormalization scheme as the matrix elements, and atthe same renormalization scale µ. Since the matchingconditions are computed at the matching scale $ relatedto the masses of the heavy particles, the Wilson coe#-cients must be evolved down by means of the Renormal-ization Group. The evolution matrix at NLO in QCD for

! = 1 TeV - RI scheme

!11(!) = 0.762 !22(!) = 2.544 !23(!) = !0.002

!32(!) = !0.591 !33(!) = 0.390 !44(!) = 4.823

!45(!) = 0.186 !54(!) = 1.351 !55(!) = 0.875

TABLE I: Values from ref. [14] for the NLO"F = 2 evolutioncoe#cients from ! = 1 TeV to µ = 2 GeV in the Landau RIscheme and in the SUSY basis.

µ = 2 GeV in the RI scheme is given in Ref. [14]. Takingthis into account, we can write

MNP12 =

1

3mKf2

KBK

#$11($)(C

NP1 ($) + "CNP

1 ($))

+ [$22($)R2 + $23($)R3](CNP2 ($) + "CNP

2 ($))

+ [$32($)R2 + $33($)R3](CNP3 ($) + "CNP

3 ($))

+ [$44($)R4 + $45($)R5]CNP4 ($)

+ [$54($)R4 + $55($)R5]CNP5 ($)

$, (13)

where the NLO evolution coe#cients $ij($) for $ = 1TeV in the Landau-RI scheme are collected in Table I.Including NLO matching conditions for the Wilson coef-ficients Ci, the combination $ij($)Cj($) is independentof the matching scale at NLO. Eqs. (7) and (13) will beused in the following sections to study the constraintsfrom "K on NP.

3. REVIEW OF LATTICE QCD RESULTS FOR"S = 2 MATRIX ELEMENTS

The bag parameter BK has been calculated in fullQCD by lattice groups since 2004 [15]. The average re-sult up to 2010 for the corresponding renormalization-independent parameter BK is given by [16]: BK =0.738(20). Recently, new refined lattice studies have be-come available [17–20]. Here, we use the updated worldaverage of Ref. [12]:

BK = 0.7643(97) . (14)

This leads to the following value for the B-parameter inthe Landau-RI renormalization scheme:

B(RI)

K (2GeV) = 0.546(7) . (15)

This year, the ratios Ri in Eq. (12) have been calcu-lated in full QCD for the first time, by the ETMC andRBC-UKQCD collaborations [3, 4], with Nf = 2 and2+1 active flavors respectively. These results supersedeprevious ones in the quenched approximation [21, 22].The RBC-UKQCD and ETMC matrix elements are

given in the SUSY basis, at a renormalization scale of3 GeV and in the MS scheme of Ref. [24]. We perform

2

computed in Ref. [11] and rescaled to our value of !! andto the more recent average of the B parameter BK givenin Ref. [12] (see Section 3).The current experimental values |"K |exp and !mexp

Kare given by[13]

!mexpK = (3.483± 0.006) · 10!15GeV , (5)

|"K |exp = (2.229± 0.010) · 10!3 , (6)

which together with Eq. (3) imply the following boundon the NP contribution:

ImMNP12 = (1.7± 1.6) · 10!18 GeV . (7)

The most general e"ective Hamiltonian for K-K mix-ing beyond the SM is given by

He! =5!

i=1

Ci(µ)Qi(µ) +3!

i=1

"Ci(µ) "Qi(µ) , (8)

where the SUSY basis of operators is

Q1 = d"#µPLs" d##µPLs#

Q2 = d"PLs" d#PLs#Q3 = d"PLs# d#PLs" (9)

Q4 = d"PLs" d#PRs#Q5 = d"PLs# d#PRs"

together with the chirally-flipped operators "Q1,2,3 ob-tained from Q1,2,3 with the substitution L ! R. Thechiral projectors are defined as PL,R = (1 " #5)/2.The New Physics amplitude is then given by

MNP12 =

!

i

CNPi (µ)#K0|Qi(µ)|K0$ . (10)

The matrix element for the SM operator Q1 is relatedto the bag parameter BK (in the non-relativistic conven-tion)

#K0|Q1(µ)|K0$ = 1

3mKf2

KBK(µ) , (11)

and the matrix elements of the operatorsQ2,3,4,5 are usu-ally normalized to #Q1$, defining the ratios Ri as

Ri(µ) %#K0|Qi(µ)|K0$#K0|Q1(µ)|K0$

. (12)

The NP Wilson coe#cients must be given in the samerenormalization scheme as the matrix elements, and atthe same renormalization scale µ. Since the matchingconditions are computed at the matching scale $ relatedto the masses of the heavy particles, the Wilson coe#-cients must be evolved down by means of the Renormal-ization Group. The evolution matrix at NLO in QCD for

! = 1 TeV - RI scheme

!11(!) = 0.762 !22(!) = 2.544 !23(!) = !0.002

!32(!) = !0.591 !33(!) = 0.390 !44(!) = 4.823

!45(!) = 0.186 !54(!) = 1.351 !55(!) = 0.875

TABLE I: Values from ref. [14] for the NLO"F = 2 evolutioncoe#cients from ! = 1 TeV to µ = 2 GeV in the Landau RIscheme and in the SUSY basis.

µ = 2 GeV in the RI scheme is given in Ref. [14]. Takingthis into account, we can write

MNP12 =

1

3mKf2

KBK

#$11($)(C

NP1 ($) + "CNP

1 ($))

+ [$22($)R2 + $23($)R3](CNP2 ($) + "CNP

2 ($))

+ [$32($)R2 + $33($)R3](CNP3 ($) + "CNP

3 ($))

+ [$44($)R4 + $45($)R5]CNP4 ($)

+ [$54($)R4 + $55($)R5]CNP5 ($)

$, (13)

where the NLO evolution coe#cients $ij($) for $ = 1TeV in the Landau-RI scheme are collected in Table I.Including NLO matching conditions for the Wilson coef-ficients Ci, the combination $ij($)Cj($) is independentof the matching scale at NLO. Eqs. (7) and (13) will beused in the following sections to study the constraintsfrom "K on NP.

3. REVIEW OF LATTICE QCD RESULTS FOR"S = 2 MATRIX ELEMENTS

The bag parameter BK has been calculated in fullQCD by lattice groups since 2004 [15]. The average re-sult up to 2010 for the corresponding renormalization-independent parameter BK is given by [16]: BK =0.738(20). Recently, new refined lattice studies have be-come available [17–20]. Here, we use the updated worldaverage of Ref. [12]:

BK = 0.7643(97) . (14)

This leads to the following value for the B-parameter inthe Landau-RI renormalization scheme:

B(RI)

K (2GeV) = 0.546(7) . (15)

This year, the ratios Ri in Eq. (12) have been calcu-lated in full QCD for the first time, by the ETMC andRBC-UKQCD collaborations [3, 4], with Nf = 2 and2+1 active flavors respectively. These results supersedeprevious ones in the quenched approximation [21, 22].The RBC-UKQCD and ETMC matrix elements are

given in the SUSY basis, at a renormalization scale of3 GeV and in the MS scheme of Ref. [24]. We perform

-

FCNC w/ CP in K meson• Currently most sensitive probe of new physics• Decay modes:- “selection rule” by CP property• K meson oscillation

: not mass eigenstate, not CP eigenstate

• K meson oscillation (contd.)

: CP eigenstate, but not mass eigenstate

: mass eigenstate if CP is conserved

diagonal degenerateby CPT invariance

FCNC w/ CP in K meson

non-Hermitian

• K meson oscillation (contd.)

mass eigenstate in presence of CP violation

KL decay into 2π induced by CP violation

FCNC w/ CP in K meson

• 2π channel also by CP violation at decay

Direct CP Violation

CPV at oscillation

CPV at decay

both CP violations are determined by π+π- and π0π0 modes

SM Prediction

• error dominated by charm loop and Vcb

• long-distance contribution known by lattice

SUSY• sources of CP-violating K-K oscillation

• gluino contribution

Note: chirality structure of quarks

Lower bound on soft mass (CP phase maximized)

Allowed @ 2σ

Currently probe of O(103-104)TeV soft mass scale

SUSY

• decoupling of 1st and 2nd generations- induced by mixings with 3rd generation

• mediation mechanism- GMSB: constraint on gravity mediation- AMSB: note on negative slepton problem

• flavor symmetry- CKM mixing of O(λ) is not sufficient → models

Other quark FCNCs (B, D mesons): not discussed- some important modes:


Summary of quark FCNC• Processes include both decay and oscillation• SM FCNCs are suppressed by loop and CKM• SUSY contributions• quark flavor violations from soft masses (w/. CPV)• currently best sensitivity to probe soft mass scale- εK probes up to 103-104 TeV for mixing of 0.1-1- dependence: δΔF/msoft2 (ΔF = 2 for K oscillation)• future- challenge to reduce hadronic uncertainties- error of εK dominated by charm loop and Vcb

- more experimental data and lattice required




Features of SUSY contributions

• effective operators- four-Fermi or magnetic operators• SUSY contributions• Mass Insertion Approximation (MIA)• GIM mechanism

Effective Lagrangian

Q: operators after decoupling heavy degrees of freedom (heavy = W boson, SUSY particles)

four-fermi magnetic dipolenote: chirality of fermion

SUSY ContributionsFour-fermi operators:

Magnetic dipole operators:

Calculation• simple and full calculation- use mass eigenstates for loop diagrams

- hard to know size of SUSY contributionchiral suppression, GIM mechanismtanβ enhancementCP phase...

Mass Insertion Approx.• Expand mass matrices by mSM/msoft and small off-diagonal

chargino, neutralino, sfermion off-diagonal

=

+

00

expand by small masseschirality structure explicit

e.g.

Muon g-2

leading contributions

electron EDM

CP phase

tanβ

quark EDM

CP phase

tanβ

μ → eγ

tanβ

flavor violation

K0-K0 mixing

flavor violation

-

Calculation• simple and full calculation- use mass eigenstates for loop diagrams- good for numerical calculations- hard to know size of SUSY contribution

chiral suppression, GIM mechanismtanβ enhancementCP phase...

Mass Insertion Approx.

provides clear picture, but calculations are complicated

GIM MechanismSM

Note:

GIM MechanismSUSYnot MIA

“super GIMmechanism”

Note:

GIM Mechanism in MIA

GIM mechanism?

for massc.f.

Technicssee Moroi, PH/9512396

• expand integrand by (small) external momentum

• loop integrals are reduced to benote:

and so on

→ use Mathematica!!

(Feynman parameters not appear)

Summary of SUSY cont.• low-energy phenomena are represented by effective

Lagrangian→ four-Fermi and magnetic dipole operators• SUSY contributions- scaled by 1/msoft2 with tanβ enhancement for

magnetic dipole operators of down-type fermions- mass insertion approximation is useful

size of SUSY contributionchiral suppression, GIM mechanismtanβ enhancementCP phase...


LHC

• basic of collider phenomenology• brief review of Monte Carlo simulation

Ref.Ellis, Stirling, Webber, “QCD and Collider Physics”

20 1 Monte-Carlo event generation

Figure 1.1: Pictorial representation of a tth event as produced by an event genera-tor. The hard interaction (big red blob) is followed by the decay of bothtop quarks and the Higgs boson (small red blobs). Additional hard QCDradiation is produced (red) and a secondary interaction takes place (pur-ple blob) before the final-state partons hadronise (light green blobs) andhadrons decay (dark green blobs). Photon radiation occurs at any stage(yellow).

possible to apply a universal hadronisation model independent of the hard scattering

process in which the partons were produced.

At this stage it should become clear that the simulation of a particle scattering event in

a Monte-Carlo event generator is factorised into several event phases. In the description

of each of these phases di↵erent approximations are employed. To pictorially represent

these phases, Figure 1.1 sketches a hadron-collider event, where a tth final state is

produced and evolves by including e↵ects of QCD Bremsstrahlung and hadronisation.

In general the central piece of the event simulation is provided by the hard process

(the dark red blob in the figure), which can be calculated in fixed order perturbation

theory in the coupling constants owing to the correspondingly high scales. This part

of the simulation is handled by computations based on matrix elements, which are ei-

ther hard-coded or provided by special programs called parton-level or matrix-element

(ME) generators. The QCD evolution (red in the figure) described by parton showers

then connects the hard scale of coloured parton creation with the hadronisation scale

where the transition to the colourless hadrons occurs. The parton showers model mul-

LHC event

skeleton

CollisionLHC: pp collision at high energy

The SUSY theory describes just the hard scattering, which is all we’ll talk about.

The rest is left to the lectures of Spannowsky and of Alwall.

X. Tata, Pre-SUSY 2012, Peking University, Beijing, Aug. 2012 53




New Physics

Collision

Cross Section

• initial state: A, B (= proton), momentum fraction x1,2

- parton information by PDF (+DGLAP)• hard scattering: e.g.- energy scale: Q2 → scale of SUSY particle mass- perturbation works• cascade decay: e.g.• hadronization: non-perturbative

initial state(long-distance)

scattering(short-distance)

decay, hadronize(short→long)

Fact

oriz

atio

n

Soft ↔ Hard• relation between long- and short-distances- radiation of gluon and quark jets

- DGLAP, parton showering: soft and collinear- harder radiations should be treated by matrix element

(c.f. ME-PS matching)

soft hard･･･

initial state radiation (ISR), final state radiation (FSR)

SUSYHard scattering: production of SUSY particles

q

q−

gq

q−

g

k1

k2

p1

p2

(a)

(b)

(c)

(d)

(e)

(f)

Figure 1: Feynman diagrams for the production of squarks and gluinos in lowest order.The diagrams without and with crossed final-state lines [e.g. in (b)] represent t- and u-channel diagrams, respectively. The diagrams in (c) and the last diagram in (d) are aresult of the Majorana nature of gluinos. Note that some of the above diagrams contributeonly for specific flavours and chiralities of the squarks.

6

q

q−

gq

q−

g

k1

k2

p1

p2

(a)

(b)

(c)

(d)

(e)

(f)


6

SUSY

q

q−

gq

q−

g

k1

k2

p1

p2

(a)

(b)

(c)

(d)

(e)

(f)


6

q

q−

gq

q−

g

k1

k2

p1

p2

(a)

(b)

(c)

(d)

(e)

(f)


6

Hard scattering: production of SUSY particles

Cross Section

(c.f. ATLAS: 5.8 fb-1)

Cascade Decay• heavier SM and SUSY particles decay into lighter one- R-parity conservation → missing energy (or track for stau)

off-shell

LSP

Cascade Decay

jet

jet

leptonjets (W,Z,τ)

missing

R-parityat production

signal: multi jets + missing transverse momentum (+leptons)

+ jets from ISR

Signal vs Background

(incl.) [GeV]effm0 500 1000 1500 2000 2500 3000 3500 4000

even

ts /

100

GeV

1

10

210

310 -1L dt = 5.8 fb∫ = 8 TeV)sData 2012 (

SM TotalSM+SU(1600,400,0,10)Multijet

& single topttW+jetsZ+jetsDiboson

PreliminaryATLASSRC - 4 jets

(incl.) [GeV]effm0 500 1000 1500 2000 2500 3000 3500 4000

DAT

A / M

C

00.5

11.5

22.5

(incl.) [GeV]effm0 500 1000 1500 2000 2500 3000 3500 4000

even

ts /

100

GeV

1

10

210

310-1L dt = 5.8 fb∫ = 8 TeV)sData 2012 (



PreliminaryATLASSRC - 4 jets

(incl.) [GeV]effm0 500 1000 1500 2000 2500 3000 3500 4000

DAT

A / M

C

00.5

11.5

22.5

Figure 3: Observed me↵(incl.) distributions for channel C for “loose” or “medium” (left) and “tight”(right) cuts. The histograms denote the MC background expectations, normalised to cross section timesintegrated luminosity. In the lower panels the yellow error bands denote the experimental and MC statis-tical uncertainties, while the green bands show the total uncertainty. The red arrows indicate the valuesat which the cuts on me↵(incl.) are applied. The expected distributions for a MSUGRA/CMSSM bench-mark model point with m0=1600 GeV, m1/2=400 GeV, A0=0, tan �=10 and µ > 0 are also shown forcomparison.

(incl.) [GeV]effm0 500 1000 1500 2000 2500 3000 3500 4000

even

ts /

100

GeV

1

10

210

-1L dt = 5.8 fb∫ = 8 TeV)sData 2012 (



PreliminaryATLASSRD - 5 jets

(incl.) [GeV]effm0 500 1000 1500 2000 2500 3000 3500 4000

DAT

A / M

C

00.5

11.5

22.5

Figure 4: Observed me↵(incl.) distribution for channel D. The histograms denote the MC backgroundexpectations, normalised to cross section times integrated luminosity. In the lower panels the yellowerror bands denote the experimental and MC statistical uncertainties, while the green bands show thetotal uncertainty. The red arrow indicate the value at which the cut on me↵(incl.) is applied. The expecteddistributions for a MSUGRA/CMSSM benchmark model point with m0=1600 GeV, m1/2=400 GeV,A0=0, tan �=10 and µ > 0 are also shown for comparison.

8

[ATLAS-CONF-2012-109]

optimize cuts to suppress/reject backgrounds

Monte Carlo Simulation




new physics (perturbation)

detectorsimulation

experimental data and simulation (and model)for non-perturbative/long-distance effects

Detector• Particle detections and measurements in detectors

Information:• (smeared) energy and direction• MET determined by sum of transverse momentum

jet reconstruction(bottom, tau)

Trigger and Cut• detector: photon, electron, muon, jet (bottom, tau), MET

• trigger: keep only “hard” events for signals- signal cuts often satisfy trigger conditions

otherwise, number of signals is reduced• cut: suppression/rejection of (SM) backgrounds- both signal and background decreases- increase signal/background

Need Trigger

9/50QCD Màster, UB, Feb-March'12 David d'Enterria (CERN)

LHC: cross sectionsLHC: cross sections

■ QCD processes:

■ New Physics:

s ~ m-2 ~ 1/(1 TeV)2

SUSYSUSYHiggsHiggs

BSMBSM

QCDQCD

EWEW10-8 !

s ~ m-2 ~1/(100 MeV)2

“needle” (10-8 m3)

“in haystack”(100 m3)

~100 mb

~50 nb

~30 pb

more events

physics target

Cut / Signal Region

RequirementChannel

A B C D E

2-jets 3-jets 4-jets 5-jets 6-jets

EmissT [GeV] > 160

pT( j1) [GeV] > 130

pT( j2) [GeV] > 60

pT( j3) [GeV] > – 60 60 60 60

pT( j4) [GeV] > – – 60 60 60

pT( j5) [GeV] > – – – 60 60

pT( j6) [GeV] > – – – – 60

��(jet,EmissT )min [rad] > 0.4 (i = {1, 2, (3)}) 0.4 (i = {1, 2, 3}), 0.2 (pT > 40 GeV jets)

EmissT /me↵(N j) > 0.3/0.4/0.4 (2j) 0.25/0.3/– (3j) 0.25/0.3/0.3 (4j) 0.15 (5j) 0.15/0.25/0.3 (6j)

me↵(incl.) [GeV] > 1900/1300/1000 1900/1300/– 1900/1300/1000 1700/–/– 1400/1300/1000

Table 1: Cuts used to define each of the channels in the analysis. The EmissT /me↵ cut in any N jet channel

uses a value of me↵ constructed from only the leading N jets (indicated in parentheses). However, the finalme↵(incl.) selection, which is used to define the signal regions, includes all jets with pT > 40 GeV. Thethree Emiss

T /me↵(N j) and me↵(incl.) selections listed in the final two rows denote the ‘tight’, ‘medium’and ‘loose’ selections respectively. Not all channels include all three SRs.

(SR’s) with ‘tight’, ‘medium’ or ‘loose’ selections distinguished by requirements placed on EmissT /me↵

and me↵(incl.). The SR’s requiring large values of EmissT /me↵ are optimised for sensitivity to models with

small sparticle mass splittings, where the presence of initial state radiation jets may allow signal events tobe selected even in cases where the sparticle decay products are soft. The lower jet multiplicity channelsfocus on models characterised by squark pair production with short decay chains, while those requiringhigh jet multiplicity are optimised for gluino pair production and/or long cascade decay chains.

In Table 1, ��(jet,EmissT )min is the smallest of the azimuthal separations between Emiss

T and the re-constructed jets. For channels A and B, the selection requires ��(jet,Emiss

T )min > 0.4 radians using upto three leading jets with pT > 40 GeV if present in the event. For the other channels an additionalrequirement ��(jet,Emiss

T )min > 0.2 radians is placed on all jets with pT > 40 GeV. Requirements on��(jet,Emiss

T )min and EmissT /me↵ are designed to reduce the background from multi-jet processes.

Standard Model background processes contribute to the event counts in the signal regions. Thedominant sources are: W+jets, Z+jets, top quark pairs, single top quarks, and multiple jets. Dibosonproduction is a minor component. The majority of the W+jets background is composed of W ! ⌧⌫events, or W ! e⌫, µ⌫ events in which no electron or muon candidate is reconstructed. The largestpart of the Z+jets background comes from the irreducible component in which Z ! ⌫⌫ decays generatelarge Emiss

T . Top quark pair production followed by semi-leptonic decays, in particular tt ! bb⌧⌫qqwith the ⌧-lepton decaying hadronically, as well as single top quark events, can also generate largeEmiss

T and pass the jet and lepton requirements at a non-negligible rate. The multi-jet background inthe signal regions is caused by misreconstruction of jet energies in the calorimeters leading to apparentmissing transverse momentum, as well as by neutrino production in semileptonic decays of heavy quarks.Extensive validation of the Monte Carlo (MC) simulation against data has been performed for each ofthese background sources and for a wide variety of control regions (CRs).

To estimate the backgrounds in a consistent and robust fashion, four control regions are defined foreach of the 12 signal regions, giving 48 CRs in total. The orthogonal CR event selections are designed to

3

[ATLAS-CONF-2012-109]

Example: multi jets + large METmeff = scalar sum of jet pT and ETmiss: choose heavy particle prod.

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Figure 6: 95% CL exclusion limits for MSUGRA/CMSSM models with tan � = 10, A0 = 0 and µ > 0presented (left) in the m0–m1/2 plane and (right) in the mg–mq plane. Exclusion limits are obtained byusing the signal region with the best expected sensitivity at each point. The blue dashed lines show theexpected limits at 95% CL, with the light (yellow) bands indicating the 1� excursions due to experimen-tal uncertainties. Observed limits are indicated by medium (maroon) curves, where the solid contourrepresents the nominal limit, and the dotted lines are obtained by varying the cross section by the the-oretical scale and PDF uncertainties. Previous results from ATLAS [17] are represented by the shaded(light blue) area. The theoretically excluded regions (green and blue) are described in Ref. [63].

Data from all the channels are used to set limits on SUSY models, taking the SR with the bestexpected sensitivity at each point in several parameter spaces. A profile log-likelihood ratio test in com-bination with the CLs prescription [59] is used to derive 95% CL exclusion regions. Exclusion limits areobtained by using the signal region with the best expected sensitivity at each point. The nominal signalcross section and the uncertainty are taken from an ensemble of cross section predictions using di↵erentPDF sets and factorisation and renormalisation scales, as described in Ref. [52]. Observed limits arecalculated for both the nominal cross section, and ±1� uncertainties. For each of these three individuallimits, the best signal region at each point is taken. Numbers quoted in the text are evaluated from theobserved exclusion limit based on the nominal cross section less one sigma on the theoretical uncertainty.In Fig. 6 the results are interpreted in the tan � = 10, A0 = 0, µ > 0 slice of MSUGRA/CMSSM models2. For the nominal cross sections, the best signal region is E-tight for high m0 values, C-tight for low m0values and D-tight between the two. Results are presented in both the m0–m1/2 and mg–mq planes. Thesparticle mass spectra and decay tables are calculated with SUSY-HIT [60] interfaced to SOFTSUSY [61]and SDECAY [62].

An interpretation of the results is presented in Figure 7 as a 95% CL exclusion region in the (mg,mq)-plane for a simplified set of SUSY models with m�0

1= 0. In these models the gluino mass and the masses

of the squarks of the first two generations are set to the values shown on the axes of the figure. All othersupersymmetric particles, including the squarks of the third generation, are decoupled.

In Fig. 8 limits are shown for three classes of simplified model in which only direct production of (a)gluino pairs, (b) ‘light’-flavor squarks (of the first two generations) and gluinos or (c) light-flavor squarkpairs is kinematically possible, with all other superpartners, except for the neutralino LSP, decoupled.This forces each light-flavor squark or gluino to decay directly to jets and an LSP. Cross sections areevaluated assuming decoupled light-flavor squarks or gluinos in cases (a) and (c), respectively. In allcases squarks of the third generation are decoupled. In case (b) the masses of the light-flavor squarks are

2Five parameters are needed to specify a particular MSUGRA/CMSSM model: the universal scalar mass, m0, the universalgaugino mass m1/2, the universal trilinear scalar coupling, A0, the ratio of the vacuum expectation values of the two Higgs fields,tan �, and the sign of the higgsino mass parameter, µ = ±.

11

Summary

• SUSY is a well-motivated candidate of TeV physics• It can be searched for- indirect searches: CPV (EDM), LFV and FCNC- direct searches: LHC• more experimental data will be published• they are expected to open new window for physics

beyond SM

Documents

SUSY現象論 - 北海道大学 理学部Example m 3=2: ð14Þ As noted in Section 2.5, the gravitino may naturally be the LSP. It may play an important cosmological role, as we will

SUSY現象論 - 北海道大学理学部Example m 3=2: ð14Þ As noted in Section 2.5, the gravitino may naturally be the LSP. It may play an important cosmological role, as we will