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

1. Measurements of the model parameterin the Littlest Higgs model with T-parity arXiv:0901.1081 Masaki Asano (ICRR, Univ. of Tokyo) Collaborator: E. Asakawa (Meiji-gakuin Univ.), K. Fujii (KEK), T. Kusano (Tohoku Univ.), S. Matsumoto(Univ. of Toyama), R. Sasaki (Tohoku Univ.), Y. Takubo (Tohoku Univ.), H. Yamamoto (Tohoku Univ.)

2. Littlest Higgs model with T-parity (LHT) is one of attractive models for TeV new physics. LHT could solve the little hierarchy problem, & contains a dark matter candidate. • Particles & these partners are same spin. • New particles get mass by VEV f ~ 1 TeV. • New gauge boson masses depend only on VEVf. Higgs Gauge boson Fermion In LHT, g W Z A H SM q l Same Spin qHlH ΦH NEW WH ZH AH In this study, we estimate… • measurement accuracy of new heavy gauge boson masses • determination of VEV f& other model parameters • the dark matter relic abundance @ ILC.

3. Introduction • What is the LHT? • How to measure the LHT at ILC? • Simulation results • Summary Plan

4. What is the LHT?

5. The SM is the successful model describing physics below ~ 100 GeV. But ... Hierarchy problem (related to quadratic divergence to the Higgs mass term) If we assume that SM is valid all the way up to the GUTs scale,Λ~1015 GeV, mh2 = m02+ Λ2 1002 ⇔10000000000000002 EW scale higgs mass requires Fine-tuning!

6. The SM is the successful model describing physics below ~ 100 GeV. But ... Hierarchy problem (related to quadratic divergence to the Higgs mass term) If we require that there are no fine-tuning for Higgs massterm, mh2 = m02+ Λ2 1002 ⇔10002 No fine-tuning Cut off scale Λ ~ 1 TeV No fine-tuning

7. The SM is the successful model describing physics below ~ 100 GeV. But ... Hierarchy problem (related to quadratic divergence to the Higgs mass term) However… LEP experiments require that the cut off scale is larger than 5 TeV! mh2 = m02+ Λ2 1002 ⇔50002 Still fine-tuning appear! Cut off scale Λ ~ 1 TeV No fine-tuning Little Hierarchy problem! LEP experiments R.Barbieri and A.Strumia (’00)

8. LHT solves little hierarchy problem! Even if Λ ~ 10TeV, there are still no fine-tuning! Because of … • Collective symmetry breaking (VEV f ) N. Arkani-Hamed, A. G. Cohen, H. Georgi (’01) • Higgs boson: A Pseudo NG bosonof a global symmetry at some higher scale. • Explicit breaking of the global symmetry is specially arranged to cancel quadratic divergent corrections to mhat 1-loop level. W WH Λ can be ~10 TeV without fine-tuning! (Little Higgs mechanism) h h + h h – g2 g2 • T-parity H. C. Cheng, I. Low (’03) In order to avoid constraints from EWPM, Z2 symmetry (T-parity) are introduced. SM ⇔ SM, New ⇔ - New Lightest T-odd particle becomes dark matter candidate! (Heavy photon AH)

9. In order to Implement the Little Higgs mechanism… • The non-linear sigma model breakingSU(5)/SO(5). • The subgroup [SU(2)×U(1)]2in SU(5) isgauged, which is broken down to the SM gauge group by vev f. [Arkani-Hamed, Cohen, Katz and Nelson (2002)] [SU(5)] [SO(5)] Global sym. VEV f ~ O(1) TeV [SU(2)×U(1)]SM Gauge sym. [SU(2)×U(1)]2 Particle contents Fermion sector Gauge-Higgs sector cancel A, W±, Z, h t T b… cancel AH, WH±, ZH, Φ Top sector Due to the cancelation of quadratic divergences, partners are introduced. In the fermion sector, only top partner is required to cancel the quadratic divergences because other fermion Yukawa couplings are small.

10. In order to Implement the Little Higgs Mechanism… • The non-linear sigma model breakingSU(5)/SO(5). • The subgroup [SU(2)×U(1)]2in SU(5) isgauged, which is broken down to the SM gauge group by vev f. [Arkani-Hamed, Cohen, Katz and Nelson (2002)] [SU(5)] [SO(5)] Global sym. VEV f ~ O(1) TeV [SU(2)×U(1)]SM Gauge sym. [SU(2)×U(1)]2 Particle contents Fermion sector Gauge-Higgs sector cancel A, W±, Z, h t T b… T-even T-parity cancel T-parity T-parity AH, WH±, ZH, Φ tHTH bH… T-odd Top sector In order to implement the T-parity… T-odd partners are introduced for each fermions.

11. Fermion sector Gauge-Higgs sector cancel A, W±, Z, h t T b… T-parity cancel T-parity T-parity AH, WH±, ZH, Φ tHTH bH… Top sector • New particle masses are ~ f O (f) O (v) Dark Matter • f: VEV of SU(5) -> SO(5) • λ, κ: Yukawa coupling of new fermions • + SM parameters (mh, … ) Model parameters

12. How to measure the LHT at ILC?

13. In order to verify the LHT, we should measure the Little Higgs mechanism! O (f) Fermion sector Gauge-Higgs sector O (v) 500 GeV cancel A, W±, Z, h t T b… cancel Dark Matter AH, WH±, ZH, Φ tHTH bH… Top sector Top sector S. Matsumoto, T. Moroi, K. Tobe (08) and ……. • can be measured at LHC. • too heavy to produced at ILC. Gauge sector Q. H. Cao, C. R. Chen (07) • can be produced at ILC! • cannot measure masses at LHC • masses depend only on vev f! We should measure the gauge sector in the LHT at ILC.

14. O (f) In the gauge sector, • can produce @ 500 GeV: • mAH + mZH < 500 GeV • cross section is small e+e- AHZH O (v) 500 GeV • It is difficult to produce @ 500 GeV • cross section is large Dark Matter e+e- WHWH 14 1. Usinge+e- AHZH @ 500 GeV ILC, Using e+e- WHWH @ 1 TeV ILC, we determine gauge boson masses. 2. gauge boson mass  vev f 3. Cross section  heavy lepton mass (eH, νH) 4. Production angle of WH WHspin

15. Representative point of our simulation

16. Mode &Representative point • Main DM annihilation mode: • AHAH h  WW(or ZZ) • The relic density depends only on f & mh! • M. A, S. Matsumoto, N. Okada,Y. Okada PhysRevD.75.063506 Relic abundance Dark matter (AH) Shaded area is WMAP allowed region . DM abundance is determined by the Higgs mass & vev f. At this WMAP allowed region, the model also satisfys other experimental constraints! WMAP allowed region

17. Mode &Representative point Which particle can produced at the ILC ? → It depends on VEV f . Because heavy gauge boson massed depend only on vev f. e+e- AHZH If f is larger than ~800GeV, the hierarchy problem appears again. e+e- WHWH • M. A, S. Matsumoto, N. Okada,Y. Okada PhysRevD.75.063506 Relic abundance Dark matter (AH) Shaded area is WMAP allowed region . DM abundance is determined by the Higgs mass & vev f. At this WMAP allowed region, the model also satisfys other experimental constraints! Fine-tuning Λ ~ 4π f > 10TeV WMAP allowed region

18. Mode &Representative point Which particle can produced at the ILC ? → It depends on VEV f . Because heavy gauge boson massed depend only on vev f. e+e- AHZH e+e- WHWH • M. A, S. Matsumoto, N. Okada,Y. Okada PhysRevD.75.063506 Relic abundance Dark matter (AH) Shaded area is WMAP allowed region . DM abundance is determined by the Higgs mass & vev f. At this WMAP allowed region, the model also satisfys other experimental constraints! Fine-tuning Λ ~ 4π f > 10TeV New gauge bosons are too heavy mWH+mWH > 1TeV mAH + mZH > 500GeV WMAP allowed region

19. Mode &Representative point Which particle can produced at the ILC ? → It depends on VEV f . Because heavy gauge boson massed depend only on vev f. e+e- AHZH e+e- WHWH • M. A, S. Matsumoto, N. Okada,Y. Okada PhysRevD.75.063506 Relic abundance Mass spectrum f 580 eH 410 ZH 369 WH 368 AH 82 Higgs 134 Fine-tuning Λ ~ 4π f > 10TeV New gauge bosons are too heavy mWH+mWH > 1TeV Point I (GeV) mAH + mZH > 500GeV WMAP allowed region Sample points satisfy all experimental & cosmological constraints.

20. Simulation results

21. 1.Event generation MadGraph : for LHT process Physsim : for SM process - helicity amplitude calculation, gauge boson polarization effect - phase space integration and generationof parton 4-momenta • Integrated luminosity 500 fb-1 • Cross section 1.9 fb 2.Hadronization PYTHIA - parton showering and hadronization 3.Detector simulation JSFQuickSimulator - create vertex-detector hits - smear charged-track parameters in central tracker - simulate calorimeter signals as from individual segments @ 500 GeV ILC @ 1 TeV ILC e+e- AHZH  AHAH h e+e- WHWH  AHAHWW • Integrated luminosity 500 fb-1 • Cross section 121 fb

22. @ 500 GeV ILC Energy distribution of reconstructed Higgs bosons after subtracting BG e+e-AHZHAHAH h Event • Large missing energy • 2 jet in final state Masses of AH and ZH can be determined from edges of Higgs energy distribution. • mAH= 83.2 ±13.3 GeV, mZH = 366. ±16. GeV • f = 576. ±25. GeV Results

23. @ 1 TeV ILC Energy distribution of reconstructed W bosons after subtracting BG e+e- WHWH AHAHWW Event • Large missing energy • 4 jet in final state Masses of AH and WH can be determined from edges of W energy distribution. • mAH= 81.58 ±0.67 GeV, mWH = 368.3 ±0.63 GeV • f = 580 ±0.69 GeV Results High accuracy !

24. Other parameters Cross section Heavy lepton mass! Production angle of WH± WHis spin 1 particle! Angular distribution of jets from W± The dominance of the longitudinal mode! The coupling arises from EWSB! For details, next Sasaki san’s talk Beam polarization WH has SU(2)L charge, but no U(1)Y charge!

25. Cosmological impact

26. Cosmological Impact DM relic abundance can be determined at ILC Probability density Simulation results : f +mh DM annihilation cross section σv (f, mh) Probability density of DM relics • DM abundance will be determined withO(10%) accuracy @ 500 GeV. • DM abundance will be determined withO(1%) accuracy @ 1 TeV. • It is possible to consistency check of the model using PLANCK.

27. Summary

28. Summary • Littest Higgs model with T-parity (LHT) is one of attractive models for physics beyond the SM. • Important model parameter are determined by measurements of heavy gauge boson sector with good accuracy • @ 500 GeV ILC, using e+e- → AHZH. • @ 1 TeV ILC, using e+e- → WHWH. • Heavy gauge boson masses can be determined by model-independent way. • The property of dark matter also can be investigated at ILC. • Results obtained from the collider experiments will be compared to those from astrophysical experiments(PLANCK)

29. Back up

30. II. LHT at the ILC AH e- • No signal • Vertex is suppressed eH e+ AH e- WH γ, Z • Depend only on f • Large Cross section e+ WH

32. HELAS library helicity amplitudes (effect of gauge boson polarizations properly) Phase space integration and the generation of parton 4-momenta BASES/SPRING TAUOLA final-state tau leptons (their polarizations correctly) Detector Parameters hits by charged particles at the vertex detector and track parameters at the central tracker are smeared according to their position resolutions realistic simulation of cluster overlapping (calorimeter signals are simulated in individual segments) Track-cluster matching is performed for the hit clusters at the calorimeter (in order to achieve the best energy flow measurements)

33. Event selection <Selection cut> All events are forced to 4 jets in final state cW2 < 10 : c2 for W± reconstruction from jets PTmiss > 50 GeV/c : Missing transverse momentum <Cut statistics and breakdown of efficiency> #event (efficiency) W+W- and e+e-W+W- are effectively reduced by PTmiss cut. ZHZH is negligible after cW2 cut. nnW+W- andW+W-Z remain after 2 cuts.

34. 1) Energy edges of W± <Fit function> <Fit step> 1) Cheat Emin,Emax Ffit1 = Ferror(par[1,2])  Get resolution(par[1,2]) 2) CheatEmin,Emax & Fixpar[1,2] Ffit2 = Ferror x Fpoly(par[3~9])  Get shape(par[3~9]) 3) Fixpar[1~9] Ffit3 = Ferror(Emin,max) x Fpoly(Emin,max)  Get edge(Emin,Emax)  Calculate mass(mAH,mWH)

35. Event @ 500 GeV ILC Signal Background e+e-AHZH AHAH hAHAH jj • Large missing energy • 2 jet in final state Selection Cut All events are forced to 2 jets in final state |cosθ|< 0.6 : c2 for angular dist. of Higgs 100 < mh <140 GeV : reconstracted Higgs mass we can calculate mass of AH and ZH by using the edge of the Higgs energy distribution.

36. @ 500 GeV ILC An energy distribution of Higgs from ZHAH after subtraction of the backgrounds, whose number of events was estimated by independent background samples. The distribution is fitted by a polynomial function convoluted with an error function. • Mass determination mAH = 82.5 ±7.7 GeV, mZH = 370. ±12. GeV true(81.85) true(368.2) • f determination f = 581 ±17. GeV • true(580)

37. Event @ 1 TeV ILC e+e- WHWH  AHAHWW Signal Background • Large missing energy • 4 jet in final state Selection Cut All events are forced to 4 jets in final state cW2 < 10 : c2 for W± reconstruction from jets PTmiss > 50 GeV/c : Missing transverse momentum W+W- and e+e-W+W- are effectively reduced by PTmiss cut. ZHZH is negligible after cW2 cut. nnW+W- andW+W-Z remain after 2 cuts.

38. @ 1 TeV ILC An energy distribution of W’s from WHWH after subtraction of the backgrounds, whose number of events was estimated by independent background samples. The distribution is fitted by a polynomial function convoluted with an error function. • Mass determination mAH = 81.85 ±0.65 GeV, mWH = 368.1 ±0.62 GeV true(81.85) true(368.2) • f determination f = 580 ±0.68 GeV • true(580) High accuracy !

39. j1 W+ q W+ WH- j2 WH+ W+ W- WH+ e+ AH AH e- WH- W- Production angle of WH± WH+ of generator information WH± candidates are reconstructed as cornaround W±. If WH+ and WH- are assumed as back-to-back, there are 2 solutions for WH± candidates. In this mode, however , 2 solutions should be close to true WH±. j1 j2 This shape shows WH± spin as spin-1. q Angular distribution of jets Angular distribution of jets <Rest frame of W+> W±helicity as longitudinal mode.