1. The Studying very light gravitino using ILD detector simulation Ryo Katayama (Tokyo) Collaborators: T.Suehara(ICEPP), T.Tanabe(ICEPP), Y.Satoru(ICEPP), M. Sigeki(IPMU), M. Takeo(IPMU), F.Keisuke(KEK) 1

2. Introduction In the case of Gauge mediated SUSY breaking (GMSB), the gravitino appears as the lightest supersymmetric particle(LSP) The O(1 eV) very light gravitino is very attractive from view of Cosmology 2

3. 3 NLSP stau By measuring the NLSP mass and lifetime, gravitino mass be determined For example, the following value give a stau life time of m LSP =6.5eV, m NLSP = 120 GeV  c  = 100  m For comparison, the tau lifetime is  c  = 87.11  m ~ e+e+ τ−τ− τ+τ+ τ−τ− ~ Z ＊, γ* e-e- ~ ~ τ+τ+ [arXiv:1104.3624]

4. The measurement of stau lifetime The impact parameter is defined as the shortest length between track and IP. By using the impact parameter distribution,we can measure the stau lifetime. The stau decay to cascade products.  The impact parameter enhance. We do not use the impact parameter in the z direction because of the large uncertainty of the primary vertex in that direction.  We use the d0 component (projection onto the x-y plane). 1st layer Gravitino stau  Hadronic decay (π ±, K ±, etc.) Impact parameter  16mm IP Leptonic decay (e ±, μ ±, ν.) 4 Decay products ~ e+e+ τ−τ− τ+τ+ τ−τ− ~ Z ＊, γ* e-e- ~ ~ τ+τ+

5. Signal and Background Signal & Background processes 5

6. Condition stau mass :120GeV decay life time :cτ = 100μm Center of mass energy : 500GeV, Integrated luminosity : 500fb -1, Beam polarization : (P e-,P e+ )=(+0.8,-0.3) τ decay mode :1-prong ~ 85 ％ Selection: 1-prong+1-prong event [PDG] 6

7. Cut 7 stau-stau  ->  WW, ZZ -> l l No cut 680776308051.861e+9158091 Track=2 456363064548.516e+875261 p T > 5 GeV for each track 388232616677.393e+669519 |cos  miss | < 0.9 358611495271.856e+640099 E vis > 20 GeV 3563214940861541440067 |cos  |< 0.8 for each track 2914711630337876315090 Acoplanarity > -0.93 192261174508398   / E vis > 3.0/400 (stau lifetime) 1859480405652 |d 0 |/  d 0 ) > 2.0 for each track (stau mass) 167284550565

8. stau mass accuracy (preliminary) From fitting track energy upper limit, the stau mass can be determined from kinematic relation. By running Poisson statics fluctuation to high statistics track energy distribution samples, we make a experiment (Toy MC). By running Toy MC 10,000 times, the mass fit distribution can be acquired. From the error estimation from the mass fit distribution, we acquired following result. 8

9. stau lifetime accuracy1(preliminary) The d o distribution reflect the lifetime stau->tau. High statistics sample was prepared for c  = 90  m, 100  m, 110  m (Template samples). By using for c  = 100  m, the d o distribution was created from Toy MC. 9 注 ) 右上二段目の Background 分布は c  ~ 100  m のデータを使用

10. stau lifetime accuracy2(preliminary) At first, we compute the reduced chi2   between Toy MC sample and template sample. The chi2 minimum indicates the most probable value of the lifetime given by the fit. By Evaluating the error from Toy MC 10,000 times, we obtained following result. 10

11. Gravitino mass accuracy (preliminary) The NLSP lifetime and mass substitute to the following gravitino mass accuracy formula 11 The relative accuracy of gravitino mass can was determined about 3%.

12. open issues The Cross Section of Bhabha scattering and  ->ll have order ~ nb,event number~O(10 9 ). Since MC statistics is insufficient, preselected samples should be prepared. If Bhabha is found to be problematic, we may choose to drop theelectron channel. Estimate the accuracy of the stau mass by using the threshold scan Changing stau mass and lifetime, evaluate the accuracy of gravitino mass. 12

13. Summary 13 In the case that stau mass is 120GeV and lifetime is c  = 100  m, using ILD detector simulation, we acquired the following result: From track energy fit, the accuracy of stau mass is 1.1% From template fit, the accuracy of stau lifetime is 1.4% Combiding above results, the accuracy of gravitino mass is estimeted to be about 3%.

14. Back Up 14

15. Constraint from cosmology 15

16. Acoplanarity (with all other cuts applied)

17. Visible Energy (with all other cuts applied)

18. Transverse momentum (with all other cuts applied)

19. |cos  mis | (with all other cuts applied)

20. |cos  | (with all other cuts applied)

21.  12 /E vis (with all other cuts applied)

22. Transverse momentun(after only 2-prong) 注 ) ただしシグナルは無偏極である

23. Visible energy ( after only 2-prong ) 注 ) ただしシグナルは無偏極である

24. |cos  | (after only 2-prong) 注 ) ただしシグナルは無偏極である

25. Acoplanarity (After only 2-prong) 注 ) ただしシグナルは無偏極である

26. track energy(GeV) d0/d0error Yellow:Signal Red:Tau pair Blue:AA->tautau Green:WW+ZZ