Theory of Higgs to tau tau signatures at the LHC

Hiroshi Yokoya

Department of Physics, University of Toyama, Toyama 930-8555, Japan

Abstract

In this report, selected topics of tau leptons are collected in view of the high-energy collider experiments andthe Higgs-boson search. Those topics include decay modes, tau-jet tagging, collinear approximation and the taupolarization. Using these unique properties of tau leptons, it is possible to observe various properties of the Higgsboson or the associated scalars in the extended Higgs models at the LHC.

Keywords: Higgs boson, tau lepton, collider experiments

1. Introduction

In 2012, an evidence of the Higgs-boson-like parti-cle was observed at the CERN Large Hadron Colliderexperiments (LHC) [1, 2]. To identify the particle as aHiggs-boson, its spin and parity properties, as well ascouplings to the stantard-model particles must be con-firmed. Among the charged leptons, e, μ and τ, becauseof that the Yukawa coupling is proportional to the massof the fermion, τ has the largest coupling to the Higgs-boson in the standard-model (SM). This is in clear con-trast to the gauge coulings which are universal for threegenerations.

Furthermore, the Yukawa couplings of scalar-bosonsto charged leptons in the extended Higgs-sector can bemore enhanced, decays into τ pair may be the dominantdecay mode. Thus, τ lepton can be the critial probe ofthe Higgs-boson and also the additional scalars.

In this report, some basic properties of tau leptons arebriefly introduced in view of the collider experiments,and their usage is presented for the signals of Higgs-boson and extended scalars into tau leptons at colliders.

2. Tau at colliders

In this section, some basic properties of τ lepton iscollected in view of the collider experiments. Subjects

to discuss include the major decay modes, τ-jet tagging,collinear approximation and the polarization.

2.1. Tau decaysτ decay always includes ντ, thus, missing momentum.

Leptonic decay includes τ− → μ−ν̄μντ and τ− → e−ν̄eντwith the branching ratio of 17.4% and 17.8%, respec-tively [3]. The fragmentation functions of these decaysin the collinear limit are [5]

F�L(z) =43

(1 − z3), (1a)

F�R(z) = 2(1 − z)2 (1 + 2z) , (1b)

where z is the energy fraction of � to τ.Hadronic decay of τ− is characterized by the number

of charged hadrons, which are mostly π−. 1-prong de-cays amount to 50% and 3-prong decays to 15%. Theseare accompanied by a few neutral hadrons, mostly π0.The branching ratio of the τ− → π−ν mode is about11%. The branching ratio of the τ− → π−π0ν mode isabout 25%, and that of the τ− → π−π0π0νmode is about10%.

The fragmentation functions of the τ → πν mode aregiven as

FπL(z) = 2(1 − z), (2a)FπR(z) = 2z, (2b)

Available online at www.sciencedirect.com

Nuclear Physics B (Proc. Suppl.) 253–255 (2014) 167–170

0920-5632/© 2014 Elsevier B.V. All rights reserved.

www.elsevier.com/locate/npbps

http://dx.doi.org/10.1016/j.nuclphysbps.2014.09.041

Figure 1: Branching ratio of tau’s decay modes.

in the collinear limit [5]. The fragmentation functionsfor the other hadronic decay modes are also known [5,4].

2.2. Tau-jet tagging

At collider experiments, τ is highly boosted, γτ =Eτ/mτ � 1. Thus, decay products of the τ are alsoboosted, and would be found in a same direction of theparent τ’s momentum. It is called a τ-jet or a jet withτ-tagging. Among the all hadronic jets, τ-jet candidatescan be identified, for example, by the following criteria;a jet with pT ≥ 10 GeV and |η| ≤ 2.5 which contains 1 or3 charged hadrons in a small cone (R = 0.15) centered atthe jet momentum direction with the transverse energydeposit to this small cone more than 95% of the jet. Theoriginal jet cone (e.g. R = 0.5) acts as an isolation coneto reduce the mis-tagging probability for non-tau jets.Furthermore, it is possible to extract the pionic τ-jet byrequiring e.g. that the jet has only one charged track (1-prong) and its transverse energy dominates more than0.95 of the jet. Typically, at the LHC, about 50-70%tagging efficiency with a few percent mis-tagging prob-ability for light-flavor jets would be expected [6, 7].

2.3. Collinear approximation

τ’s decays always include missing energies, whichmake event reconstructions rather complicated. How-ever, for an energetic τ, the missing momentum fromits decay tends to be oriented to the same direction ofthe observed charged track. Therefore, it is a good ap-proximation to assume the τ’s momentum direction tothat of the charged track. The energy fraction of theτ to the charge track is only the remaining uncertainty.Depending on the process, it could be resolved by us-ing the energy-momentum conservation or the on-shellcondition for the resonance particles.

At hadron colliders, since only the transverse mo-mentum conservation condition are available to resolveτ’s momenta from missing momentum, events kinemat-ics with up to two τ’s can be reconstructed, if there is noother source of large missing transverse momentum [8].On the other hand, at e+e− colliders, all the four compo-nents of the energy-momentum conservation are avail-able, therefore event kinematics with up to four τ’s canbe reconstructed [9]. The 4τ event reconstruction at theILC and the LHC is discussed in Sec. 3.2.

2.4. Polarization

The polarization of τ’s is known to be probed by theenergy distributions of its decay products. The analyz-ing power is large for hadronic decay mode, especiallyfor single-pionic decay. On the other hand, it is smallfor the leptonic decay mode. With this property, τ is theunique indicator to probe the spin structure of the parentparticle [5, 10].

In Fig. 2, polarization dependence of the pionic andgeneral τ-jets, which are defined in Sec. 2.2 is shownby the numerical simulation using TAUOLA. The pionicτ-jet indicates large polarization dependence which re-flect the maximum spin analyzing power of the τ → πνdecay. The generic τ-jet has still measurable polariza-tion dependence [11].

τπ

z0 0.2 0.4 0.6 0.8 1

0

200

400

600

800

1000

1200

τ

jz0 0.2 0.4 0.6 0.8 1

0

1000

2000

3000

4000

5000

Figure 2: Polarization dependence of the energy distributions for thepionic tau-jet (left) and the general tau-jet (right) . Red dashed curvesare for left-handed and blue solid curves are for right-handed.

3. Tau and Higgs physics

Both ATLAS and CMS collaborations have alreadyreported the search for the SM Higgs-boson in the h →ττ decay mode using the 2011 and 2012 data [12, 13].Although the error is still large, it is consistent with theSM predictions. The advantage of this decay mode isthat it could be observed with various production mech-anism, such as the gluon-fusion, vector-boson-fusion

H. Yokoya / Nuclear Physics B (Proc. Suppl.) 253–255 (2014) 167–170168

and associated Vh production processes. Thus, by mea-suring these processes, universality of the h → ττ decayand the ratio of the cross-sections for the above produc-tion mechanism could be probed.

3.1. Multi-Tau signatures at the LHCThe two Higgs doublet model (THDM) is one of the

simple extension of the SM Higgs sector. Since it re-spects the custodial symmetry, therefore free from theconstraint by electroweak precision test, namely the ρ-parameter. The constraint from the flavor changing neu-tral current can be avoided by imposing the Z2 symme-try to the two doublets. Under the symmetry, there arefour types of Yukawa interactions depending on the Z2charge assignments.

An interesting possibility would be the Type-XTHDM, where one Higgs doublet couples with quarksand the other with leptons [14]. In the limit that oneof the CP-even scalar behave as the SM Higgs-boson,the Yukawa couplings of the other scalar-bosons, CP-even H, CP-odd A and charged H±, tend to be lepton-specific. Since Yukawa coupling constants are propor-tional to the fermion mass, these scalars predominantlydecay into τ’s for the wide range of the parameter space.

At hadron colliders, these scalars are produced in pairfollowed by their decays involving τ’s:

qq̄ → Z∗ → HA → ττττ, (3)qq̄′ → W∗ → H(A)H± → τττν. (4)

Thus, it would be observed as the multi-τ events (4τ’sor 3τ’s). Depending on the decay patterns of τ’s, thereare various signatures at the LHC [15]. In the Type-XTHDM, the masses of these scalars are less constrained.Thus, the search for the rather light scalars would beinteresting at the LHC.

In Ref. [15], detailed simulation studies are per-formed and it is shown that these signatures could beobserved with large signal-to-background ratio by re-quiring high-pT τ-jets, especially for 4 τ-jets, 3 τ-jets +1 lepton and 2 τ-jets + 2 leptons events. The expectedbackground processes are di-boson productions, tt̄ pro-duction and V + jets where V = W or Z. The massreconstruction of the scalars is also possible in princi-pal, however thousands fb−1 of the integrated luminos-ity may be required to have enough number of events.

3.2. Kinematical reconstruction in the 4-Tau eventsFinally, we consider the event kinematics of the 4τ

events at the LHC and the ILC. Such events can be a sig-nature of the doubly charged scalar bosons in the Higgstriplet model (HTM) or the Type-X THDM. It is able

to replace some τ-jets by leptons which are supposed tocome from the decay of τ’s. However, the event selec-tion to reduce background events becomes more com-plicated.

At the ILC, the event kinematics can be resolved withno ambiguity by solving the 4-momentum conservationconditions,

0 = pτ1 + pτ2 + pτ3 + pτ4 , (5)√s = Eτ1 + Eτ2 + Eτ3 + Eτ4 , (6)

with pμτi = pμjτi/zi, where pμjτi is the four-momentum ofthe ith τ-jet.

In Ref. [9] the 4τ event reconstruction is demon-strated for the e+e− → HA → 4τ process whereH and A are the CP-even and odd scalars in theType-X THDM. In Fig. 3, histograms of the τ-jetpair invariant-masses (left) and the reconstructed di-τinvariant-masses (right) are plotted. In order to con-struct the di-τ invariant-mass from 4τ’s, we choose thecombination of the opposite-signed τ pair which givesthe highest pT pair.

Figure 3: Two-dimensional histograms of the jτ jτ invariant-masses(left) and the reconstructed ττ invariant-masses (right) for the e+e− →HA → 4τ process with mH = 130 GeV and mA = 170 GeV.

At the LHC, it is not the case that the full eventkinematics is resolved, because only the transverse-momentum conservation conditions are available. How-ever, when the di-τ’s come from the decay of particleswith the same mass, it is possible to determine the res-onance mass and fully solve the kinematics [16]. Themethod is described as follows: (1) By putting the massof the two resonances to the trial mass Min, solve thesystem of equations:

z−11 pT, jτ1 + z−1

2 pT, jτ2 + z−13 pT, jτ3 + z−1

4 pT, jτ4 =QT , (7)

(z−11 p jτ1 + z−1

2 p jτ2 )2 = (z−13 p jτ3 + z−1

4 p jτ4 )2 = M2in. (8)

Here, QT = −∑ j pT, j is the recoil transverse momen-tum from initial-state-radiation (ISR) jets. The equa-tions reduce to a quartic equation, therefore up to four

H. Yokoya / Nuclear Physics B (Proc. Suppl.) 253–255 (2014) 167–170 169

solutions are obtained after removing unphysical ones.(2) Count the number of solutions over all the available4τ events for a given Min. Then, see the number-of-solution distribution as a function of the trial mass Min.It is observed that the distribution has the largest gradi-ent at the true mass. Thus, if one takes a derivative of thedistribution, it shows a peak at the true mass. Therefore,by finding the peak, the true mass of the di-τ resonancescan be determined.

In Fig. 4, derivatives of the number-of-solution distri-butions as a function of the trial mass are plotted for theinput mass of mH = 200 GeV, 400 GeV and 600 GeV.

0 200 400 600 800 1000Trial Mass [GeV]

0

100

200

300

400

500

Deri

vati

ve

Figure 4: Derivatives of the number-of-solution distributions as afunction of the trial mass for the event reconstruction in the 4τ eventsat the LHC. Numerical simulation is performed using Pythia andTAUOLA for mH = 200 GeV, 400 GeV and 600 GeV.

4. Summary

In this report, we have presented some selected top-ics of tau leptons, such as decay modes, tau-jet tag-ging, collinear approximation and the tau polarization,in view of the high-energy collider experiments and theHiggs-boson search. Because of that Yukawa couplingsare proprotional to the mass of the fermion, h → ττ de-cay mode has significant branching ratio, thus τ couldbe a critical probe of the SM Higgs-boson or scalars inthe model with the extended Higgs-sector.

We present the multi-τ signatures in the Type-XTHDM, and the kinematical reconstruction technique inthe 4τ event at the LHC and ILC. Furthermore, using thepolarization information of the τ from its decay energydistribution and its correlation, spin and CP propertiesof the parent particle can be studied.

Acknowledgments. The author thanks K. Hagiwara,S. Kanemura, H. Sugiyama and K. Tsumura for collab-orations. The author would like to thank K. Hayasakafor invitation and kindly hospitality.

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