Physics Letters B 675 (2009) 352–355

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Physics Letters B

www.elsevier.com/locate/physletb

Associated production of the Higgs boson and a single top quark in the littlestHiggs model at Large Hadron Collider

Shuo Yang

Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 12 December 2008Received in revised form 25 March 2009Accepted 10 April 2009Available online 16 April 2009Editor: T. Yanagida

In the context of the littlest Higgs model, we study the associated production of the Higgs boson anda top quark (th production) at the CERN Large Hadron Collider (LHC). The cross sections for s-channel,t-channel processes and the relative correction for the total cross section are presented. In a part ofparameter space, the cross sections can be distinctly deviated from the predictions of Standard Model.We also investigate the signal and backgrounds for the th production at the LHC. However, due to thelarge QCD backgrounds, it is not very hopeful to directly observe the th signal in most of the parameterspace of LH model. It is found that with 30 fb−1 of integrated luminosity, in a narrow range of theparameter space c = 0.8 and f � 1.62 TeV, a statistical significance of 3σ can be achieved. More than30 fb−1 luminosity will enhance the significance and the possibility of detecting the signal.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

For the Standard Model (SM) Higgs boson, the main discoverymodes at hadron colliders are the associated production of W h orZh [1], the vector boson fusion processes [2], the gluon–gluon fu-sion mode [3], and the Higgs associated production with heavy topquark pairs [4] or bottom quark pairs [5]. Compared with thesemodes, the cross section for the production of the Higgs bosonassociated with a single top quark is small [6–8] (th productionFeynman diagrams are shown in Figs. 1–3). However, measure-ments of the total rates for W h and tth processes only test theHiggs coupling to W and the Yukawa coupling to top. The thproduction contains the important relative phase information ofthe couplings of the Higgs to W and to top, and th productionis sensitive to some new physics [7,8]. As a class candidate ofphysics beyond SM, little Higgs models [9–15] predict new bosons,fermions and scalars. These new particles will contribute consid-erably to Higgs production. The Higgs phenomena in little Higgsmodels have been extensively studied in the literature [16,17]. Inthis Letter, we study the th production at the LHC in the frame ofthe littlest Higgs model.

The rest of this Letter is organized as follows. In Section 2 webriefly describe the general features of little Higgs models and thenfocus on the littlest Higgs model. The Feynman rules and formulasrelevant to our computation are also listed in this section. In Sec-tion 3, we study th production in the littlest Higgs model at theLHC. Finally, we give our conclusions in Section 4.

E-mail address: shuoyang@itp.ac.cn.

0370-2693/$ – see front matter © 2009 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2009.04.035

2. Littlest Higgs model

In this section we firstly introduce the general features of littleHiggs models and then describe the littlest Higgs model focusingon particle content and the couplings relevant to our computation.

The major motivation of little Higgs theory [9] is to curethe hierarchy problem of SM. Little Higgs models suppose thatHiggs boson is a Nambu–Goldstone boson (NGB) of some approxi-mate global symmetry and avoid one-loop quadratically divergentthrough collective breaking mechanism [9]. The collective symme-try breaking means that when one interaction breaks some of theglobal symmetries, it still exits unbroken global symmetry ensur-ing the Higgs’s identity as an exact NGB. The symmetries protect-ing Higgs is explicitly broken only when two or more couplings inthe Lagrangian are present. In this way, the collective symmetrybreaking protects the Higgs mass from receiving quadratically di-vergent radiative corrections at one-loop. The Coleman–Weinbergpotential generates the Higgs potential and triggers electroweaksymmetry breaking (EWSB). The implementation of collective sym-metry breaking results in the prediction of new gauge bosons, newfermions and new scalars at TeV scale. These new particles will beproduced at the LHC and contribute derivations to SM processes.

As a realistic implementation of little Higgs idea, the littlestHiggs (LH) model [11] base on a SU(5)/SO(5) coset. The SU(5)

global symmetry is spontaneously broken down to SO(5) globalsymmetry via a vacuum expectation value (VEV) of order f , simul-taneously, and the gauge group [SU(2) × U (1)]1 × [SU(2) × U (1)]2of SU(5) is broken down to its diagonal subgroup. The breaks re-sult in new heavy bosons W ±

H , Z H , B H and new scalar triplet Φ ,which acquire masses of order f . In order to implement the col-

S. Yang / Physics Letters B 675 (2009) 352–355 353

Fig. 1. Feynman diagrams for th production in t-channel process.

Fig. 2. Feynman diagrams for th production in s-channel process.

Fig. 3. Feynman diagrams for th production in W -associated process.

lective symmetry breaking mechanism in top sector, LH model alsointroduces a pair vector-like quarks. After EWSB, the physical statesin top sector are the top quark t and the heavy quark T . We listthe Feynman rules and formulas [18,19] relevant to our computa-tion as below where the terms of order ( v

f )2 has been neglected:

V W +μH ud = −i

g√2γμV ud

c

sP L, V W +μ

H tb = −ig√2γμVtb

c

sP L, (1)

V W +μH T b = −i

g√2γμVtb

c

s

v

f

x2λ

x2λ + 1

P L,

V W T b = ig√2

v

f

x2λ

x2λ + 1

γμVtb P L, (2)

V W +μH W −μ

H h = − i

2g2 vgμν,

V W +μH W −μh = − i

2g2 (c2 − s2)

2scvgμν, (3)

V HtT = −ixλ

mt

vP L, (4)

MW H = g f

2sc, ΓW H = αe

96 sin θ2W

[96c2

s2+ cos θ2

W (c2 − s2)2

s2 − c2

], (5)

MT = (xλ + x−1

λ

)mt

vf , ΓT = 1

8π

λ21

λ22

(mt

ν

)2

MT . (6)

In these formulas, c (s = √1 − c2 ) is the mixing parameter

between the SU(2)1 and SU(2)2 gauge bosons, f is the new sym-metry breaking scale, and xλ = λ1/λ2, where λ1 and λ2 are Yukawacoupling parameters in top sector. The couplings of Φ to fermionsare suppressed by 1/ f and the contribution of Φ to th productioncan be safely ignored, so we do not list the coupling of Φ here.

3. th Production in the littlest Higgs model at the LHC

As shown as in Figs. 1–3, the Higgs in association with a topquark can be produced at the LHC in t-channel, s-channel andW -associated process. In these Feynman diagrams, ti represents

t for SM and represents t and T for LH model, W i represents Wfor SM and represents W and W H for LH model. In SM, the t-channel process has the largest cross section and the s-channelhas the smallest cross section. However, in LH model both thecross sections in s-channel and t-channel can dominate over theW -associated process in a part of the parameter space as shownbelow.

In our computation (we compute th production including bothtop quark and antitop production), we have used Madgraph [20]package and CTEQ6L [21] parton distribution functions with thefactorization scale Q = mh . The SM input parameters relevantto our computation are taken as mt = 174.2 GeV [22], mh =120 GeV, mZ = 91.1876 GeV, sin2 θW = 0.2315, αe(M Z ) = 1/128.8and αs(M Z ) = 0.1176 [23].

In LH model, the new interactions will contribute the th pro-duction and cause deviation from the cross section of SM. Con-sidering the constraints of the electroweak precision data on LHmodel [24], we assumed xλ = 1, 1.5 TeV � f � 2.5 TeV and 0.4 �c � 0.8. A low f will result in a light B H which is disfavored byZ ′ limit from Tevatron and precision electroweak constrains. Thiscan be resolved by considering alternative embeddings of the twoU (1) generators or only gauging a U (1) group, i.e. the gauge groupis SU(2)1 × SU(2)2 × U (1)Y [24]. Figs. 4 and 5 show the cross sec-tions as a function of the scale parameter f for different value ofmixing parameter c for t-channel and s-channel th production, re-spectively. The computation results are very sensitive to the valueof c, which because the coupling of W H to fermions are in pro-portion to c

s and the cross section for relevant diagrams will besensitive to ( c

s )4. In LH model, the cross section both in s-channel

process and t-channel process can reach the level of 70 fb in apart of parameter space. The cross section for W -associated chan-nel is not sensitive to the variation of parameters and in most ofthe parameter space the deviation from the SM prediction is small,so we do not show the cross section for W -associated th produc-tion. Different from the case in SM where the t-channel processhas the largest cross section and s-channel has the smallest one, inLH model both the cross sections in s-channel and t-channel can

354 S. Yang / Physics Letters B 675 (2009) 352–355

Fig. 4. Cross section for t-channel th production as a function of the parameter ffor c = 0.4 (dot line), c = 0.7 (dash line), c = 0.8 (solid line).

Fig. 5. Cross section for s-channel th production as a function of the parameter ffor c = 0.4 (dot line), c = 0.5 (dash dot line), c = 0.7 (dash line), c = 0.8 (solid line).

dominate over the W -associated process in a part of the parameterspace. This is mainly because the couplings of W H W h and T th aresuppressed by mixing parameters as shown in Feynman rules, sothe contributes from new particles are very weak in W -associatedchannel. In t-channel and s-channel, the new contributes mainlycome from W H qq′ and W H W H h which are not suppressed. How-ever, the effects from new particles become weak and the crosssections of th production converge to the values of SM as f in-crease and c decrease. In order to describe the deviation of totalth cross section from the SM prediction, we define a relative cor-rection function

R = σLH − σSM

σSM(7)

and show the R as a function of f for c = 0.4, c = 0.7 and c =0.8 in Fig. 6. As shown in Fig. 6, it is found that in most of theparameter space, the th cross section in LH model is larger thanthe prediction of SM which will enhance the detecting possibilityin this mode.

Now we further consider the signature of th production atthe LHC. In order to provide a efficient lepton trigger the semi-leptonical decay of top is considered, and the decay of h → bb is

Fig. 6. Relative correction R of total th production as a function of the scale param-eter f for c = 0.4 (dot line), c = 0.7 (dash line), c = 0.8 (solid line).

required for the large branching ratio.1 In this case for t-channelmode the signal is 3b + l± + /pT + 1 forward jet and for s-channelthe signal is 4b + l± + /pT . However, Ref. [8] has pointed thatit is difficult to extract the signal 3b + l± + /pT + 1 forward jetfrom the large backgrounds and the hopeful signal for t-channelis 4b + l± + /pT + 1 forward jet where the additional b comesfrom the splitting of virtual gluons into bb pairs. From a phe-nomenological point the difference between s-channel 4b signaland t-channel 4b signal is that all the jets are high pT central jetsin s-channel while t-channel signal has a forward jet and a lowpT b-jet. We may separate them by rejecting or tagging a forwardjet. But the s-channel signal will always be accompanied by a jetcoming from QCD radiation. If we consider the s-channel signaland t-channel signal separately, each of them will be the impor-tant backgrounds for the other. So, in this Letter, we consider thesignal is 4b + l± + /pT + 1 jet which include t-channel events ands-channel events with a radiated jet. We study the signal and back-grounds in a idealized case that the top is reconstructed with 100%efficiency, so the b coming from top decay can be separated fromother b quarks.

For the 4b + l± + /pT + 1 jet signal, t Zb j with Z decay to bbpair, tbbb j are two of the main backgrounds. The process ttbb →W +W −bbbb → j jlvbbbb contributes to backgrounds when one ofthe jets from W decay is missed or in the case that one of the jetsfrom W decay is mistagged as a b-jet and another jet (including b)is missed. Due to the large rate of tt j, when both c and s quarksfrom the hadronically decaying W are mistagged, this process alsocontributes to the backgrounds.

Because for many events in our signal the final particles fromnew heavy particles’ contributions are more energetic and withhigh-pT than the events in SM, So we raise the minimum pb

T to20 GeV and loose the forward jet constrain compared with the cutsin Ref. [8]. The cuts are shown as below:

pbT > 20 GeV, |ηb| < 2.5,

pTl,v > 20 GeV, |ηl| < 2.5,

1 In our calculation, we ignored the corrections to branching ratio of h → bb

(BR(h → bb)) in LH model. Because in LH model couplings of fermions and gaugebosons of SM to the Higgs are only shifted by an order of (v/ f )2, and only decaywidths of h → γ γ , h → gg and h → γ Z are modified due to new particles in loops.For a light Higgs, there is no new decay channel and the dominant decay channel isstill h → bb. So the change of BR(h → bb) is not distinct in most of the parameterspace and the change converges to zero as f increases. Detailed analysis of Higgsdecay in LH model have been studied in Ref. [17].

S. Yang / Physics Letters B 675 (2009) 352–355 355

Table 1Cross section and events with 30 fb−1 of integrated luminosity for the signal andbackgrounds for the th production. For the signal, the parameter values c = 0.8,f = 1.6 TeV, xλ = 1 are chosen.

Signal t Zb j tbbb ttbb tt j

Cross section σ (fb) 0.482 0.054 0.039 0.61 0Events with 30 fb−1 14.5 1.6 1.2 18.3 0

pTj > 30 GeV, |η j | < 5, �Rij > 0.4.

At least one bb pair |mbb − mh| < 22 GeV.

All bb pairs min mbb > 90 GeV.

At least one bb pair |mbb −mh| < 22 GeV means that we requireat least one bb pair (not including the b that reconstructs the top)accord with |mbb − mh| < 22 GeV. All bb pairs min mbb > 90 GeVmeans that the invariant mass of all b pairs (not including the bthat reconstructs the top) is required in this range.

At luminosity 30 fb−1, only in a very narrow part of the pa-rameter space c = 0.8 and f < 1.62 TeV of LH model, we canachieve the statistical significance of 3σ . We list the cross sec-tion and events with 30 fb−1 which pass the cuts for the signaland the important backgrounds in Table 1, in which for the signalthe parameter values c = 0.8, f = 1.6 TeV, xλ = 1 are taken. Theb-tagging efficiency εb = 60%, lepton-tagging efficiency εl = 90%and the mistag probability εc = 10%, εs = 1% have been includedin computation.

4. Conclusion

In the frame of the littlest Higgs model we calculate the pro-duction of the Higgs bosons associated a top quark at the LHC.Due to the new interactions of new gauge boson W H and newfermion T with Higgs boson, these new particles can contributeto th production cross section. We find that in a large part ofthe parameter space the cross section of th in s-channel and t-channel production can deviate largely from the SM prediction.Different from the case in SM, in LH model both the cross sectionsin s-channel and t-channel are larger than that in W -associatedprocess in a part of the parameter space. We also consider the sig-nal 4b + l± + /pT + 1 jet and backgrounds for the th production.However, due to the large QCD backgrounds, it is not very hope-ful to observe the th signal in most of the parameter space of LHmodel. It is found that with 30 fb−1 of integrated luminosity, in anarrow range of the parameter space c = 0.8 and f � 1.62 TeV, astatistical significance of 3σ can be achieved. More than 30 fb−1

luminosity will enhance the significance and the possibility of de-tecting the signal.

Acknowledgements

The author would like to thank Chun Liu, Jin Min Yang, Chong-Xing Yue and Lei Wang for useful discussions. This work wassupported in part by the National Science Foundation of Chinaunder Grant No. 90503002 and the Project of Knowledge Inno-vation Program (PKIP) of Chinese Academy of Sciences, Grant No.KJCX2.YW.W10.

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