1. New Physics Search through  → t t → l X / b X Kazumasa OHKUMA (Fukui Tech.) 7/Oct./2005@Shonan Village hep-ph/0508183 7th International Symposium on Radiative Corrections PLB593 (2004) 189 & NPB689 (2004) 108 Based on Z. Hioki （ Tokushima Univ. ） B.Grzadkowski (Warsaw Univ.), J.Wudka （ UC Riverside ) In collaboration with

2. I. Introduction II. Framework III. Optimal-Observable Analysis IV. Summary Plan of talk

3. I. Introduction ★ Standard Model is composed by Electro-weak theory and Quantum chromodynamics Highly Successful Model There are some unsolved problems But!! Many parameters (Couplings, CKM, ‥‥ ) Origin of masses Hierarchy New Physics beyond Standard Model Page-1 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

4. How to search for the signal of new physics ? One of answers: Top quark physics. Why? Ans. (1) Heaviest particle observed to date ! ! There are some advantageous properties; (i) Sensitive to SSB (ii) Decay as a free quark ! Clear information about top quark τ<< 10 -23 [s] (2) On top quark sector, C P is negligible in SM ! ! Large CP indicates new physics contribution. Higgs Page-2 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

5. Interesting option of ILC. Initial CP parity is controllable !! Only CP-even state at ee collider We estimate In order to study non-standard effect, we focus on Couple to CP-odd scalar particles Statistical Significance of non-Standard Couplings Photon Collider at and probe Optimal Beam Polarizations for New Physics Search Page-3 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

6.  SM Lagrangian is modified by quantum effect of new physics. Effective Lagrangian approach ★ W.Buchmuller and D.Wyler, NPB268(1986)621 Model Independent Analysis Model Dependent Analysis Complementary relation New fields are not in existence under  scale. New heavy particles are decoupled. Assumption : SU(3) X SU(2) X U(1) invariant Dim.6 operators : Energy scale of new physics : non-standard couplings II. Framework Page-4 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

7. Effective Operators for γγ→ t t ｔｔ  interaction ( Top EDM ) Top Quark Production ｔｔ  interaction ( Contact Interaction ) We found relations between EDM operators and Contact interaction operators. Page-5 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

8. Relations of Operators Bianchi identities and SM classical motion of equations for quark and vector bosons lead us to Page-6 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

9. Need not to consider Contact Interaction. × × ×× × × ×× × × × : No contribution

10. Effective Operators for  →(H)→t t  H interaction (Higgs property) Effective Operators for t → ｂ W ｔｂ W interaction Top Decay Page-7 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

11. Feynman rules for on-shell photos (1) C P-conserving tt  vertex (2) C P-violating tt  vertex (1) C P-conserving  H vertex (2) C P-violating  H vertex ★ Top Electric Dipole Moment interaction :   ★ Higgs Exchange interaction :  h Page-8 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

12. ★ Decay Vertex Page-9 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

13. Feynman Diagrams for  → ｔ ｔ S.Y.Choi and Hagiwara P.Poulos and S.D.Rindani PLB359(1995)369, PRD56(1997)6835, etc. In actual experiment, their mixed signals will be observed !! B.Grzadkowski and J.F.Gunion, PLB294(1992)316, G.J.Gounaris and G.P.Tsirigoti,PRD56(1997)3030, E.Asakawa, J.Kamoshita, A.Sugamoto and I.Watanabe,EPJC14(2000)335, E.Asakawa, S.Y.Choi,K.Hagiwara and J.S.Lee, PRD62(2000)115005, R.M.Godbole, S.D.Rindani and R.K.Shigh PRD67(2003)095009, etc. All possible non-standard interactions are taken into account. All possible non-standard interactions are taken into account. Page-10 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

14. III. Optimal Observable Analysis Method for estimating the precision of determination of relevant non-standard couplings. What is Optimal Observable Analysis ? How to estimate these precision ? J. F. Gunion, et.al, PRL77 (1996) 5172 Suppose following distribution: : final-state phase space : known functions ← Calculable : model-independent coefficients Cross section Page-11 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

15. Extract C i using appropriate weighting function Extract In general, different choice for the are possible. There is a unique choice which minimizes the resultant statistical uncertainty:  C i. Such function is given by Page-12 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

16. Inverse matrix of M ij : Statistical uncertainty of C i is given by Calculable : Total cross section : Event number Apply to analysis of final-lepton’s energy and angular distribution for. Page-13 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

17. Application Final-lepton’s energy and angular distribution EDM Higgs Decay Calculable e.g. Page-14 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

18. Matrix Element M ij where I,J=1, ‥,6 correspond to SM,  １,  ２, h 1, h 2 and d, respectively. Inverse EX. Page-15 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

19. Parameters of Photon collider : Degree of circular polarization of initial laser : Initial electron longitudinal polarization : Degree of linear polarization of initial laser with azimuthal angle High energy colliding beams of polarized photons are generated by Compton backscattering Page-16 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

20. Probing optimal photon beam polarizations Estimate the uncertainty of couplings Search for the combinations that make minimal, varying polarization parameters as Note Page-17 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

21. Unfortunately ! Our results for X ij are very unstable even a tiny fluctuation of M ij changes X ij s ignificantly ! All the couplings cannot be determined at the same time from only. Refrain from determining all the couplings at once. Assumption Some non-standard couplings C i have been measured in other processes e.g. Page-18 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

22. Result 5 and 4 parameters analyses lead to unstable solutions. 3 and 2 parameters analysis give stable solutions within 10% ambiguity Under the conditions:,, Some results are presented hereafter. 3 parameter case : 3 combinations are OK final lepton 1 final bottom 2 2 parameter case : 68 combinations are OK final lepton 39 final bottom 29 Page-19 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

23. : detection efficiency Results (3 parameter analysis) Charged-lepton detection Bottom-quark detection with (2 of 3) Not so small ! Page-20 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

24. Results (2 parameter analysis) There are 68 stable solutions. However All the stable solutions do not give us good statistical precisions. Two statistical uncertainties (, ) satisfy is minimal for each pair of and Page-21 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

25. Results (2 parameter analysis) m H =300 GeV Final lepton detection Page-22 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

26. Results (2 parameter analysis) m H =300 GeV Final bottom quark detection Page-23 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

27. Results (2 parameter analysis) Independent of Higgs mass Final lepton detection Note There are no combinations which make   2 small (   2 < 0.1). Page-24 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

28. Probe Optimal beam polarizations for New physics search To study non-standard Effect in top quark production, IV. Summary we focus on. Statistical uncertainties were estimated - CP conserving and violating tt  coupling :   1,   2 - CP conserving and violating  H coupling :  h 1,  h 2 - anomalous tbW coupling :  d using Optimal Observable method. Model independent analysis were performed using effective low-energy Lagrangian. Page-25 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

29. Adjusting beam polarization gives us good statistical precisions: in two parameter analysis - all non-standard couplings （ except for   2 ） could be determined with accuracy better than 0.1 with a integrated luminosity of 500 fb -1. - the statistical uncertainty of   2 is still large in this analysis. We look for anther processes to determine   2. It is useful to probe the proprieties of Higgs boson couplings. Page-26 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

30. Back up

31. Comparing ee and  colliders Top quark productions  collider ee collider It is possible to measure tt  coupling at both colliders. Within the framework of the effective Lagrangian, we can estimate   . Appendix 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

32. In the e e t t l / b X,   2 could not be measured. Note! In    t t l / b X,   2 could be measured though it’s not to be measured precisely. B.Grazkowski and Z. Hioki, NP B484 (1997) 17, NP B585 (2000) 3 L. Brzezinski, Grzadkowski and Z. Hioki, Int. J. Mod. Phys. A14 (1999) 1261 Appendix 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

33. 1 parameter Optimal Observable analysis    t t l X e e t t l X ee colliders will give us slightly good precision. Comparison of   1 measurement in e e and    colliders Appendix 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

34. Comparing e e and    colliders ee collider ( e e t t l / b X )  It seems to be slightly favored to measure   1.    2 could not measure in the process.  collider (  t t l / b X )    2 could be measured in the process. (precision is not good)  It seems to be very useful for testing the Higgs coupling. Looking for the processes or observable that make statistical sensitivity small for the measuring   2 is important !

35. Circular polarization Asymmetry (-)(-) (-)(-) Appendix 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

36. Linear polarization Asymmetry Appendix 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections

37. Results (2 parameter analysis) m H =300 GeV Final bottom quark detection Appendix 7/Oct./2005 Shonan Village 7th International Symposium on Radiative Corrections