In the Littlest Higgs model with T-parity, we study production processes of
new gauge bosons at the international linear collider (ILC). Through Monte
Carlo simulations of the production processes, we show that the heavy gauge
boson masses can be determined very accurately at the ILC for a representative
parameter point of the model. From the simulation result, we also discuss the
determination of other model parameters at the ILC.Comment: 4 pages, 2 figures. Talk given at LCWS08, Chicago, November 200

Asakawa, Eri

Asano, Masaki

Fujii, Keisuke

Kusano, Tomonori

Matsumoto, Shigeki

Sasaki, Rei

Takubo, Yosuke

Yamamoto, Hitoshi

English

arXiv

arXiv.org e-Print Archive

Measurements of the model parameter in the littlest Higgs model with
  T-parity

The Littlest Higgs model with T-parity is one of the attractive candidates for physics beyond the standard model. In the model, we study production processes of new gauge bosons at the international linear collider (ILC). Through Monte Carlo simulations of the production processes, we show that the heavy gauge boson masses can be determined very accurately at the ILC for a representative

parameter point of the model. From the simulation result, we also discuss the determination of other model parameters at the ILC

Asano, M.

Asakawa, E.

Fujii, K.

Kusano, T.

Matsumoto, S.

Sasaki, R.

Takubo, Y.

Yamamoto, H.

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2010-10599-7Colloquia: LC09IL NUOVO CIMENTO Vol. 33 C, N. 2 Marzo-Aprile 2010Measurements of model parameters in the Littlest Higgs modelwith T -parity in ILCM. Asano(1), E. Asakawa(2), K. Fujii(3), T. Kusano(1), S. Matsumoto(4),R. Sasaki(1), Y. Takubo(1) and H. Yamamoto(1)(1) Department of Physics, Tohoku University - Sendai, Japan(2) Institute of Physics, Meiji Gakuin University - Yokohama, Japan(3) High Energy Accelerator Research Organization (KEK) - Tsukuba, Japan(4) Department of Physics, University of Toyama - Toyama, Japan(ricevuto il 15 Febbraio 2010; approvato il 23 Marzo 2010; pubblicato online il 15 Giugno 2010)Summary. — The Littlest Higgs model with T -parity is one of the attractive can-didates for physics beyond the standard model. In the model, we study productionprocesses of new gauge bosons at the international linear collider (ILC). ThroughMonte Carlo simulations of the production processes, we show that the heavy gaugeboson masses can be determined very accurately at the ILC for a representativeparameter point of the model. From the simulation result, we also discuss the de-termination of other model parameters at the ILC.PACS 12.60.-i – Models beyond the standard model.PACS 13.66.Jn – Precision measurements in e−e+ interactions.1. – IntroductionThe Little Higgs model [1,2] has been proposed for solving the little hierarchy problem.In this scenario, the Higgs boson is regarded as a pseudo Nambu-Goldstone (NG) boson.The global symmetry breaking is specially arranged to cancel quadratically divergentcorrections to the Higgs mass term at 1-loop level. As a result, the scale of new physicscan be as high as 10TeV without a fine-tuning on the Higgs mass term. In order toavoid electroweak precision constraints, the implementation of the Z2 symmetry calledT -parity to the model has been proposed [3]. In this study, we focus on the Littlest Higgsmodel with T -parity as a simple and a typical example of the model.In order to test the model, determinations of properties of Little Higgs partners aremandatory, because these particles are directly related to the cancellation of quadrat-ically divergent terms. In particular, measurements of heavy gauge boson masses arequite important because these masses arise from the vacuum expectation value (VEV)of the global symmetry breaking which is the most important parameter of the model.c© Societa` Italiana di Fisica 137138 M. ASANO, E. ASAKAWA, K. FUJII, ETC.Table I. – Representative point used in our simulation study.f mh λ2 κl mAH mWH mZH mΦ580 (GeV) 134 (GeV) 1.5 0.5 81.9 (GeV) 368 (GeV) 369 (GeV) 440 (GeV)Furthermore, because the heavy photon is a candidate for dark matter [4, 5], the de-termination of its property gives a great impact not only on particle physics but alsoon astrophysics and cosmology. The International Linear Collider (ILC) will provide anideal environment to measure the properties of heavy gauge bosons [6]. We study thesensitivity of the measurements to the Little Higgs parameters at the ILC based on arealistic Monte Carlo simulation [7]. We have used MadGraph [8] and Physsim [9] togenerate signal and Standard Model (SM) events, respectively. In this study, we havealso used PYTHIA6.4 [10], TAUOLA [11] and JSFQuickSimulator [12].2. – Littlest Higgs model with T -parityThe Littlest Higgs model with T -parity is based on a non-linear sigma model describ-ing an SU(5)/SO(5) symmetry breaking with a VEV, f ∼ O(1)TeV. An [SU(2)×U(1)]2subgroup in the SU(5) is gauged, which is broken down to the SM gauge groupSU(2)L ×U(1)Y . Due to the presence of the gauge and Yukawa interactions, the SU(5)global symmetry is not exact and the SM doublet and triplet Higgs bosons (H and Φ)arise as pseudo NG bosons. The triplet Higgs boson mass is given by mΦ =√2mhf/v,where mh is the SM Higgs mass and 〈H〉 = (0, v/√2)T . The triplet Higgs boson is T -odd,while the SM Higgs is T -even.This model contains gauge fields of the gauged [SU(2)×U(1)]2 symmetry; the linearcombinations W a = (W a1 +Wa2 )/√2 and B = (B1+B2)/√2 correspond to the SM SU(2)Land U(1)Y gauge bosons. The other linear combinations W aH = (Wa1 − W a2 )/√2 andBH = (B1−B2)/√2 are additional gauge bosons called heavy gauge bosons, which acquiremasses of O(f) through the SU(5)/SO(5) symmetry breaking. After the electroweaksymmetry breaking, the neutral components of W aH and BH are mixed with each otherand form mass eigenstates AH and ZH. The masses of heavy gause bosons are givenby mWH  mZH  gf and mAH √0.2g′f , where g (g′) is the SU(2)L (U(1)Y ) gaugecoupling constant. Heavy gauge bosons behave as T -odd particles, while SM gaugebosons are T -even.To implement T -parity, two SU(2) doublets l(1) and l(2) are introduced for eachSM lepton. The quantum numbers of l(1) and l(2) under the [SU(2) × U(1)]2 are(2,−3/10;1,−1/5) and (1,−1/5;2,−3/10), respectively. The lSM = (l(1) − l(2))/√2gives the left-handed SM lepton and another linear combination lH = (l(1) + l(2))/√2 isvector-like T -odd partner. The masses depend on κl : meH  mνH √2κlf . In addition,new particles are also introduced in quark sector. (For details, see ref. [13].)3. – Simulation studyThe representative point (f,mh, λ2, κl) used in our simulation study is shown in table Iwhere λ2 is an additional Yukawa coupling in the top sector. The model parameter satis-fies not only the current electroweak precision data but also the WMAP observation [14].MEASUREMENTS OF MODEL PARAMETERS ETC. 139Table II. – Cross sections for the production of heavy gauge bosons.√s e+e− → AHZH e+e− → ZHZH e+e− →W+H W−H500GeV 1.91 (fb) — —1TeV 7.42 (fb) 110 (fb) 277 (fb)Furthermore, no fine-tuning is needed at the sample point to keep the Higgs mass on theelectroweak scale [15,16]. Heavy leptons are heavier than heavy gauge bosons.In the model, there are four processes whose final states consist of two heavy gaugebosons: e+e− → AHAH, AHZH, ZHZH, and W+H W−H . The first process is undetectable.At the representative point, the largest cross section is expected for the fourth process(See table II.) On the other hand, because mAH +mZH is less than 500GeV, the secondprocess is important at the√s = 500GeV. We, hence, concentrate on e+e− → AHZHat√s = 500GeV and e+e− → W+H W−H at√s = 1TeV with an integrated luminosity of500 fb−1. Feynman diagrams for the signal processes are shown in fig. 1.3.1. The AHZH production. – We define AHZH → AHAHh → AHAHbb as our signalevent. The AH and ZH boson masses can be estimated from the edges of the distributionof the reconstructed Higgs boson energies.The energy distribution of the reconstructed Higgs bosons with remaining back-grounds is depicted in fig. 2(a). The signal distribution after backgrounds have beensubtracted is shown in fig. 2(b). The endpoints have been estimated by fitting the distri-bution with a lineshape determined by a high statistics signal sample. The fit resultedin mAH and mZH being 83.2± 13.3GeV and 366.0± 16.0GeV, respectively.3.2. The WHWH production. – We have used 4-jet final states, W+H W−H →AHAHW+W− → AHAHqqqq, as the signal. The masses of AH and WH bosons canbe determined from the edges of the reconstructed W energy distribution. The energydistribution is depicted in fig. 3(a). After subtracting the backgrounds from fig. 3(a), thedistribution has been fitted with a lineshape determined by a high statistics signal sampleas shown in fig. 3(b). The fitted masses of AH and WH bosons are 81.58± 0.67GeV and368.3± 0.63GeV, respectively. Using the process, it is also possible to confirm that thespin of W±H is consistent with one and the polarization of W± from the W±H decay isdominantly longitudinal. Furthermore, the gauge charges of the WH boson could be alsomeasured using a polarized electron beam. Figure 4 shows the probability contours formasses of AH and WH at 1TeV together with that of AH and ZH at 500GeV. The massresolution improves dramatically at√s = 1TeV, compared to that at√s = 500GeV.e+−ee HAZHHνHe+−e WH−WH+γ, Ze+−e WH−WH+Fig. 1. – Diagrams for signal processes; e+e− → AHZH and e+e− →W+H W−H .140 M. ASANO, E. ASAKAWA, K. FUJII, ETC.[GeV]hE100 120 140 160 180 200 220 240 260 280-60-40-2002040608010016 = 366ZHm13.3 = 83.2AHm???[GeV]hE100 120 140 160 180 200 220 240 260 280050100150200250300350SignalhννZhttγZ,ZννZZ,???Fig. 2. – (a) Energy distribution of the reconstructed Higgs bosons with remaining backgroundsafter the mass cut. (b) Energy distribution of the Higgs bosons after subtracting the back-grounds.W energy(GeV)0 50 100 150 200 250 300 350 400 450 500050010001500200025003000350040000.6685 mass : 81.58HA0.626 mass : 368.3HWSignalFit line???W energy(GeV)0 50 100 150 200 250 300 350 400 450 50005001000150020002500300035004000 Signal−W+WWZνe−W+WννZ−W+WOthers???Fig. 3. – (a) The energy distribution of the reconstructed W bosons with remaining backgroundsafter the selection cuts. (b) The energy distribution of the W bosons after the subtraction ofthe backgrounds. mass(GeV)HA0 20 40 60 80 100 120 140 mass(GeV)HZ300320340360380400420440ModelMeanσ1σ2??? mass(GeV )HA77 78 79 80 81 82 83 84 85 86 mass(GeV)HW364365366367368369370371372373ModelMeanσ1σ3σ5???Fig. 4. – Probability contours corresponding to (a) 1- and 2-σ deviations from the best-fit point,and (b) 1-, 3-, and 5-σ deviations. The shaded area in (a) shows the unphysical region ofmAH + mZH > 500GeV.MEASUREMENTS OF MODEL PARAMETERS ETC. 1414. – ConclusionsIn the Littlest Higgs model with T -parity, we have shown that the masses of theheavy gauge bosons can be determined very accurately at the ILC. Furthermore, sincethe masses of the heavy gauge bosons are determined by the VEV f , it is possible toaccurately determine f . From the results obtained in our simulation study, it turns outthat the VEV f can be determined to accuracies of 4.3% at√s = 500GeV and 0.1%at 1TeV. Another Little Higgs parameter κl could also be estimated from productioncross sections for the heavy gauge bosons, because the cross sections depend on themasses of heavy leptons. At the ILC with√s = 500GeV and 1TeV, κl could be obtainedwithin 9.5% and 0.8% accuracies, respectively.∗ ∗ ∗The authors would like to thank all the members of the ILC physics subgroup [17] foruseful discussions. They are grateful to the Minami-tateya group for the help extended inthe early stage of the event generator preparation. This work is supported in part by theCreative Scientific Research Grant (No. 18GS0202) of the Japan Society for Promotionof Science and the JSPS Core University Program.REFERENCES[1] Arkani-Hamed N., Cohen A. G. and Georgi H., Phys. Lett. B, 513 (2001) 232;Arkani-Hamed N., Cohen A. G., Katz E., Nelson A. E., Gregoire T. and WackerJ. G., JHEP, 0208 (2002) 021.[2] Arkani-Hamed N., Cohen A. G., Katz E. and Nelson A. E., JHEP, 0207 (2002) 034.[3] Cheng H. 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Measurements of model parameters in the Littlest Higgs model

with T-parity in ILC

Measurements of the model parameter in the littlest Higgs model with T-parity

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