Effective Lagrangian Approach to Top-Quark Production at PLC

Transcription

1 KEKPH06 Effective Lagrangian Approach to Top-Quark Production at PLC Kazumasa OHKUMA (Fukui Tech.) Based on JHEP 0511(2005) 029 PLB593(2004)189 & NPB698(2004)108 In collaboration with B. Grzadkowski (Warsaw Univ.) Z. Hioki (U. Tokushima) J. Wudka (UC. 4, Mar. 06

2 Plan of talk 1 Introduction Framework Effective Lagrangian Optimal Observable method Photon Linear Collider 5 Numerical Results 6 Summary 2006/3/4 KEKPH06@KEK Page-2

3 Plan of talk Introduction Effective Lagrangian Optimal Observable method Photon Linear Collider Numerical Results Summary 2006/3/4 Page-3

4 Introduction The Standard Model is highly successful model. BUT Neutrino experiment The SM has to be modified New Model is needed! Collider experiment The SM seems to work well How to search for new physics at collider 2006/3/4 Page-4

5 New Physics search at collider experiment Direct measurement of new particle High precision measurement Clear evidence of new physics. Light quark : no obvious deviation from the SM with high accuracy. Top quark : also no deviation but smaller accuracy. Window for new physics 2006/3/4 KEKPH06@KEK Page-5

6 New Physics search at collider experiment Direct measurement of new particle High precision measurement Effective Lagrangian approach is one of most promising approaches Model Independent Analysis Complementary relation Model Dependent Analysis 2006/3/4 Page-6

7 Using effective Lagrangian, we estimate Statistical Significance of non-standard Couplings and probe Optimal Beam Polarizations for New Physics Search. for the processes; at Photon Collider. Interesting option of ILC Initial CP parity is controllable!! Useful to search for CP-odd scalar particles 2006/3/4 Page-7

8 Plan of talk Introduction Effective Lagrangian Optimal Observable method Photon Linear Collider Numerical Results Summary 2006/3/4 Page-8

9 How to construct effective Lagrangian Assumption All non-standard particles are heavier than the lowest new physics scale in the low energy processes. non-standard particles are decupled only standard particles are appeared Non-standard effects are parameterized by coupling constant of effective operators. 2006/3/4 Page-9

10 Effective Lagrangian SU(3) X SU(2) X U(1) gauge invariant dim.6 operator Non-standard coupling The SM Lagrangian Scale of new physics 2006/3/4 KEKPH06@KEK Page-10

11 Effective Operator (Example) Left-handed quark doublet Right-handed quark Higgs doublet Gauge field strength Constructed by only standard particle. W.Buchmuller and D.Wyler, NPB268(1986) /3/4 Page-11

12 Top production Effective Operators for ttγ interaction (Top EDM) Effective Operators for γγh interaction (Higgs property) 2006/3/4 Page-12

13 Top decay Effective Operators for tbw interaction 2006/3/4 Page-13

14 Feynman rules for on-shell photos Top Electric Dipole Moment interaction : α γ (1) CP-conserving ttγ vertex (2) CP-violating ttγ vertex Higgs Exchange interaction : α h (1) CP-conserving γγh vertex (2) CP-violating γγh vertex 2006/3/4 KEKPH06@KEK Page-14

15 Decay Vertex 2006/3/4 Page-15

16 Plan of talk Introduction Effective Lagrangian Optimal Observable method Photon Linear Collider Numerical Results Summary 2006/3/4 Page-16

17 Optimal Observable Method What is Optimal Observable Method? Method for estimating the precision of determination of relevant non-standard couplings. How to estimate these precision? Suppose following distribution: J. F. Gunion, et.al, PRL77 (1996) 5172 : final-state phase space : known functions Calculable : model-independent coefficients Cross section 2006/3/4 KEKPH06@KEK Page-17

18 Extract function using appropriate weighting Extract In general, different choice for the are possible. There is a unique choice which minimizes the resultant statistical uncertainty: Such function is given by 2006/3/4 KEKPH06@KEK Page-18

19 Inverse matrix of M ij : Calculable Statistical uncertainty of C i is given by : Event number : Total cross section Apply to analysis of final-lepton s energy and angular distribution for. 2006/3/4 KEKPH06@KEK Page-19

20 Application e.g. Final-lepton s energy and angular distribution EDM Non-SM coupling Higgs Decay 2006/3/4 KEKPH06@KEK Page-20

21 Application e.g. Final-lepton s energy and angular distribution EDM Calculable Higgs Decay 2006/3/4 KEKPH06@KEK Page-21

22 Matrix Element M ij Inverse EX. where I,J=1,,6 correspond to SM, γ1,γ2, h1, h2 and d, respectively. 2006/3/4 KEKPH06@KEK Page-22

23 Plan of talk Introduction Effective Lagrangian Optimal Observable method Photon Linear Collider Numerical Results Summary 2006/3/4 Page-23

24 Photon linear Collider High energy colliding beams of polarized photons are generated by Compton backscattering : Initial electron longitudinal polarization : Degree of circular polarization of initial laser : Degree of linear polarization of initial laser with azimuthal angle 2006/3/4 KEKPH06@KEK Page-24

25 Plan of talk Introduction Effective Lagrangian Optimal Observable method Photon Linear Collider Numerical Results Summary 2006/3/4 Page-25

26 Numerical Result Estimate the uncertainty of couplings Search for the combinations that make minimal, varying polarization parameters as Note 2006/3/4 Page-26

27 Unfortunately! Our results for Xij are very unstable even a tiny fluctuation of Mij changes Xij significantly! 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. 2006/3/4 KEKPH06@KEK Page-27

28 Result Under the conditions:,, 5 and 4 parameters analyses lead to unstable solutions. 3 and 2 parameters analysis give stable solutions within 10% ambiguity 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 Some results are presented hereafter. 2006/3/4 KEKPH06@KEK Page-28

29 Results (3 parameter analysis) (2 of 3) Charged-lepton detection Bottom-quark detection Not so small! with with : detection efficiency 2006/3/4 KEKPH06@KEK Page-29

30 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 for each pair of and is minimal 2006/3/4 KEKPH06@KEK Page-30

31 Results (2 parameter analysis) m H =300 GeV Final lepton detection 2006/3/4 KEKPH06@KEK Page-31

32 Results (2 parameter analysis) m H =300 GeV Final bottom quark detection 2006/3/4 KEKPH06@KEK Page-32

33 Results (2 parameter analysis) Independent of Higgs mass Final lepton detection Note There are no combinations which make Δα γ2 small (Δα γ2 < 0.1). 2006/3/4 Page-33

34 Plan of talk Introduction Effective Lagrangian Optimal Observable method Photon Linear Collider Numerical Results Summary 2006/3/4 Page-34

35 Summary To study non-standard Effect of top quark couplings, We focus on. Model independent analysis were performed using effective low-energy Lagrangian. Statistical uncertainties were estimated - CP conserving and violating ttγ coupling :α γ1,α γ2 - CP conserving and violating γγh coupling :α h1,α h2 - anomalous tbw coupling :α d using Optimal Observable method. Probe Optimal beam polarizations for New physics search. 2006/3/4 KEKPH06@KEK Page-35

36 Adjusting beam polarization gives us good statistical precisions: in two parameter analysis - all non-standard couplings (except for α γ2 ) could be determined with accuracy better than 0.1 with a integrated luminosity of 500 fb -1. It is useful to probe the Higgs boson couplings. - the statistical uncertainty of α γ2 is still large in this analysis. We look for anther processes to determine the α γ /3/4 KEKPH06@KEK Page-36

37 Back up

38 Top production Effective Operators for ttγ interaction (Top EDM) ttγγ interaction (Contact Interaction) We found relations between EDM operators and contact interaction operators. 2006/3/4 Page-38

39 Relations of Operators Bianchi identities and SM classical motion of equations for quark and vector bosons lead us to 2006/3/4 Page-39

40 : No contribution Need not to consider contact interaction. 2006/3/4 Page-40

41 Linear polarization Asymmetry 2006/3/4 Page-41