1. 1 Simulation study of e + e -  W H + W H - Introduction Observable to be measured Analysis framework Event selection Results Rei Sasaki (Tohoku University) with LCWS08 at Chicago 2008/11/18 S.Matsumoto (Toyama Univ.) M.Asano (ICRR) K.Fuji (KEK) Y.Takubo (Tohoku Univ.) T.Kusano (Tohoku Univ.)

2. 2 Introduction Littlest Higgs model with T-parity T LH A, W ±, Z, h A H, W H ±, Z H,  f F f - F - LH TT Gauge-Higgs sectorMatter sector A H W H ± 1TeV A H and W H ± can be searched by ILC (1TeV). f : Breaking scale m h : Higgs mass

3. 3 Introduction e + e -  W H + W H - e + e -  W H + W H - is the best one to investigate the property of the dark matter predicted in the model. mass spin W H 368.2(GeV) 1 A H 81.85(GeV) 1 SM LHT e + e -  W H + W H - (W H ±  A H W ± with 100% ratio ) - Large cross section - Dark matter (A H ) appears

4. 4 Observable to be measured 1) Energy edges of W ±  lead to masses of W H ± and A H bosons 2) Production angle of W H ±  lead to spin of W H ± boson 3) Angular distribution of reconstructed jets from associated W ± boson decays  lead to helicity of W ± boson e-e- e+e+ WH+WH+ WH-WH-  W±W± j j  e-e- e+e+ WH+WH+ W+W+ AHAH WH-WH- AHAH W-W-

5. 5 Analysis framework MadGraph : for LHT process Physsim : for Standard Model process - helicity amplitude calculation - gauge boson polarization effect - phase space integration and generation of parton 4-momenta PYTHIA - parton showering and hadronization JSFQuickSimulator - create vertex-detector hits - smear charged-track parameters in central tracker - simulate calorimeter signals as from individual segments QuickSim PYTHIA Physsim MadGraph

6. 6 Analysis framework Center-of-mass energy: 1TeV Integrated luminosity: 500 fb -1 Beam polarization: no Crossing angle of beams: no Beamstrahlung: ignored Initial-state radiation: ignored Ref) GLD Detector Outline Document Ver.1.2.1

7. 7 Event selection e + e -  W H + W H - - W H ± decays to A H W ± - followed by W ±  qq-bar Large missing energy 4 jets in final state A/Z

8. 8 Event selection (Large cross section) e + e -  W + W - e + e -  e + e - W + W - (Small cross section) e + e -   W + W - e + e -  W + W - Z - followed by W ±  qq-bar Z  -bar e + e -  Z H Z H - Z H decays to A H h - followed by h  qq-bar

9. 9 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 :  2 for W ± reconstruction from jets P T miss : Missing transverse momentum

10. 10 Result 1)Energy edge of W ± - Fit method - Result of fit 2) Production angle of W H ± - Reconstruction of W H ± from W ± - cos  distribution 3) Angular distribution of reconstructed jets from associated W ± boson decays - Boost jets to W ± rest frame - |cos  | distribution

11. 11 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 )

12. 12 1) Energy edges of W ± (True) m AH =81.85 m WH =368.2 m AH = 82.49±1.10: 0.58 m WH = 367.7±1.0: 0.50 accuracy= m True -m Fit  Fit with high accuracy Masses of A H and W H ± are determined with high accuracy!! Signal (with all error) Fit line Subtract B.G.

13. 13 2) Production angle of W H ± 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- sol1 sol2 true 

14. 14 2) Production angle of W H ± e-e- e+e+ WH+WH+ WH-WH-  spin-1 This shape shows W H ± spin as spin-1.

15. 15 3) Angular distribution of jets longitudinal This shape shows W ± helicity as longitudinal mode. W+W+ j1j1 j2j2  e-e- e+e+ WH+WH+ W+W+ AHAH j1j1 j2j2 Boost

16. 16 Conclusion e + e -  W H + W H - is the best mode to investigate the LHT model. Background candidates are W + W -, e + e - W + W -, Z H Z H, W + W - and W + W - Z. Selection cuts,  W 2 50(GeV), reduce effectively backgrounds. 1) Masses of A H and W H ± are determined with high accuracy: 0.58 and 0.40. 2) Spin of W H ± can be determined as spin-1. 3) Helicity of W ± can be determined as longitudinal mode.