1. Measurements of the model parameter in the Littlest Higgs model with T-parity 1 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. ) arXiv:0901.1081

2. 2 In LHT, SM NEW H ΦHΦH W H Z H A H q H l H q l g W Z A Particles & these partners are same spin. New particles get mass by VEV f ~ 1 TeV. New gauge boson masses depend only on VEV f. 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. Gauge bosonFermion Higgs 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. Same Spin

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

4. What is the LHT? 4

5. m h 2 = m 0 2 + Λ 2 Fine-tuning! The SM is the successful model describing physics below ~ 100 GeV. If we assume that Hierarchy problem (related to quadratic divergence to the Higgs mass term) 100 2 ⇔ 1000000000000000 2 But... SM is valid all the way up to the GUTs scale, Λ~10 15 GeV, EW scale higgs mass requires

6. m h 2 = m 0 2 + Λ 2 No fine-tuning The SM is the successful model describing physics below ~ 100 GeV. If we require that Hierarchy problem (related to quadratic divergence to the Higgs mass term) 100 2 ⇔ 1000 2 But... there are no fine-tuning for Higgs mass term, No fine-tuning Λ ~ 1 TeV Cut off scale

7. m h 2 = m 0 2 + Λ 2 No fine-tuning The SM is the successful model describing physics below ~ 100 GeV. However… Hierarchy problem (related to quadratic divergence to the Higgs mass term) 100 2 ⇔ 5000 2 But... LEP experiments require that the cut off scale is larger than 5 TeV! Λ ~ 1 TeV R.Barbieri and A.Strumia (’00) LEP experiments Cut off scale Little Hierarchy problem! Still fine-tuning appear!

8. LHT solves little hierarchy problem! Even if Λ ~ 10TeV, there are still no fine-tuning! Because of … Collective symmetry breaking (VEV f ) T-parity SM ⇔ SM, New ⇔ - New (Heavy photon A H ) W h h g2g2 + WHWH h h – g 2 N. Arkani-Hamed, A. G. Cohen, H. Georgi ( ’ 01) H. C. Cheng, I. Low ( ’ 03) In order to avoid constraints from EWPM, Z 2 symmetry (T-parity) are introduced. Higgs boson: A Pseudo NG boson of a global symmetry at some higher scale. Explicit breaking of the global symmetry is specially arranged to cancel quadratic divergent corrections to m h at 1-loop level. Λ can be ~10 TeV without fine-tuning! (Little Higgs mechanism) Lightest T-odd particle becomes dark matter candidate!

9. A, W ±, Z, h A H, W H ±, Z H, Φ t T cancel Particle contents Gauge-Higgs sector 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. In order to Implement the Little Higgs mechanism… The non-linear sigma model breaking SU(5)/SO(5). The subgroup [SU(2)×U(1)] 2 in SU(5) is gauged, which is broken down to the SM gauge group by vev f. Fermion sector b… cancel [Arkani-Hamed, Cohen, Katz and Nelson (2002)] [SU(2)×U(1)] 2 [SU(2)×U(1)] SM [SU(5)][SO(5)] VEV f ~ O(1) TeV Global sym. Gauge sym.

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

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

12. How to measure the LHT at ILC? 12

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

14. can produce @ 500 GeV: m AH + m ZH < 500 GeV cross section is small It is difficult to produce @ 500 GeV cross section is large In the gauge sector, 14 O (f) O (v) 500 GeV Dark Matter 1. Using e + e -  A H Z H @ 500 GeV ILC, Using e + e -  W H W H @ 1 TeV ILC, we determine gauge boson masses. 2. gauge boson mass  vev f 3. Cross section  heavy lepton mass (e H, ν H ) 4. Production angle of W H  W H spin e + e -  A H Z H e + e -  W H W H

15. Representative point of our simulation 15

16. 16 Relic abundance Mode &Representative point WMAP allowed region Dark matter (A H ) M. A, S. Matsumoto, N. Okada,Y. Okada PhysRevD.75.063506 Main DM annihilation mode: A H A H  h  WW(or ZZ) The relic density depends only on f & m h ! 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!

17. 17 Relic abundance Mode &Representative point WMAP allowed region Which particle can produced at the ILC ? → It depends on VEV f. Because heavy gauge boson massed depend only on vev f. M. A, S. Matsumoto, N. Okada,Y. Okada PhysRevD.75.063506 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! e + e -  A H Z H e + e -  W H W H Dark matter (A H ) Fine-tuning Λ ~ 4π f > 10TeV If f is larger than ~800GeV, the hierarchy problem appears again.

18. 18 Relic abundance Mode &Representative point WMAP allowed region e + e -  A H Z H e+e-  WHWHe+e-  WHWH Which particle can produced at the ILC ? → It depends on VEV f. Because heavy gauge boson massed depend only on vev f. New gauge bosons are too heavy m WH +m WH > 1TeV m AH + m ZH > 500GeV M. A, S. Matsumoto, N. Okada,Y. Okada PhysRevD.75.063506 Fine-tuning Λ ~ 4π f > 10TeV 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! Dark matter (A H )

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

20. Simulation results 20

21. 1.Event generation MadGraph : for LHT process Physsim : for SM process - helicity amplitude calculation, gauge boson polarization effect - phase space integration and generation of parton 4- momenta 2.Hadronization 3.Detector simulation PYTHIA - parton showering and hadronization 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 -  A H Z H  A H A H h e + e -  W H W H  A H A H WW Integrated luminosity 500 fb -1 Cross section 1.9 fb Integrated luminosity 500 fb -1 Cross section 121 fb

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

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

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

25. Cosmological impact 25

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

27. Summary 27

28. 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 - → A H Z H. @ 1 TeV ILC, using e + e - → W H W H. 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) 28 Summary

29. Back up 29

30. 30 e-e- e+e+ AHAH AHAH eHeH 1.No signal 2.Vertex is suppressed e+e+ e-e- γ, Z WHWH WHWH 1.Depend only on f 2.Large Cross section II. LHT at the ILC

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32. 32 Phase space integration and the generation of parton 4-momenta helicity amplitudes (effect of gauge boson polarizations properly) BASES/SPRING HELAS library 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. 33 Event selection W + W - e + e - W + W - W + W - and e + e - W + W - are effectively reduced by P T miss cut. Z H Z H Z H Z H is negligible after  W 2 cut. W + W - and W + W - Z remain after 2 cuts. #event (efficiency) All events are forced to 4 jets in final state  W 2 < 10 :  2 for W ± reconstruction from jets P T miss >50 GeV/c : Missing transverse momentum

34. 34 1) Energy edges of W ± 1)Cheat E min,E max F fit1 = F error (par[1,2])  Get resolution(par[1,2]) 2)Cheat E min,E max & Fix par[1,2] F fit2 = F error x F poly (par[3~9])  Get shape(par[3~9]) 3)Fix par[1~9] F fit3 = F error (E min,max ) x F poly (E min,max )  Get edge(E min,E max )  Calculate mass(m AH,m WH )

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

36. 36 Mass determination m AH = 82.5 ± 7.7 GeV, m ZH = 370. ± 12. GeV true(81.85) true(368.2) f determination f = 581 ± 17. GeV true(580) An energy distribution of Higgs from Z H A H 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. @ 500 GeV ILC

37. 37 Signal Background Large missing energy 4 jet in final state All events are forced to 4 jets in final state  W 2 < 10 :  2 for W ± reconstruction from jets P T miss >50 GeV/c : Missing transverse momentum Selection Cut W + W - e + e - W + W - W + W - and e + e - W + W - are effectively reduced by P T miss cut. Z H Z H Z H Z H is negligible after  W 2 cut. W + W - and W + W - Z remain after 2 cuts. Event @ 1 TeV ILC e + e -  W H W H  A H A H WW

38. 38 Mass determination m AH = 81.85 ± 0.65 GeV, m WH = 368.1 ± 0.62 GeV true(81.85) true(368.2) f determination f = 580 ± 0.68 GeV true(580) An energy distribution of W’s from W H W H 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. High accuracy ! @ 1 TeV ILC

39. 39 e-e- e+e+ WH+WH+ W+W+ AHAH WH-WH- AHAH W-W- W H ± candidates are reconstructed as corn around W ±. If W H + and W H - are assumed as back-to-back, there are 2 solutions for W H ± candidates. In this mode, however, 2 solutions should be close to true W H ±. W+W+ W-W- WH+WH+ WH-WH- W H + of generator information  Production angle of W H ± spin-1 This shape shows W H ± spin as spin-1. Angular distribution of jets W+W+ j1j1 j2j2  j1j1 j2j2 longitudinal W ± helicity as longitudinal mode.

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