Top electroweak couplings study using di-leptonic state at s = 500 GeV, ILC with the Matrix Element Method

Transcription

1 Top electroweak couplings study using di-leptonic state at s = 500 GeV, ILC with the Matrix Element Method AWLC017, SLAC Yo Sato A Akimasa Ishikawa A, Emi Kou B, Francois Le Diberder B, Hitoshi Yamamoto A, Junping Tian C, Keisuke Fujii D, Tohoku University A, LAL B, University of Tokyo C, KEK D AWLC017 1

2 Outline Motivation Kinematical reconstruction of top quark Strategy of kinematical reconstruction Fraction of wrong assignment of b-jets Helicity angles computation Matrix element method analysis Fit of CP-Conserving form factors Fit of CP-Violating form factors Summary AWLC017

3 Top EW Couplings Study Top quark is the heaviest particle in the SM. Its large mass implies that it is strongly coupled to the mechanism of electroweak symmetry breaking (EWSB) Top EW couplings are good probes for New physics behind EWSB In new physics models, such as composite models, the predicted deviation of coupling constants, g Z Z L, g R (= F Z 1V from SM is typically 10 % F Z 1A ) AWLC017 3

4 Di-leptonic State of the top pair production Top pair production has three different final states: Fully-hadronic state e + e tt bbqqqq 46. % Semi-leptonic state e + e tt bbqqlν 43.5% Di-leptonic state e + e tt bblνlν 10.3% Advantage 9 helicity angles can be computed (details will be described later) Higher sensitivity to the form factors Difficulty Two missing neutrinos Difficult to reconstruct top quark. Develop the reconstruction process in realistic situation AWLC017 4

5 Set Up of Analysis Situation Full simulation of ILD Hadronization Gluon emission from top ISR/BS γγ hadrons bkg. events On / Off On On On On On Off (ongoing) Sample (Only signal) s Polarization (P e, P e +) Integrated luminosity Generator Detector Di-muonic state e + e bbμ + νμ ν 500 GeV (-0.8, +0.3) Left / (+0.8, -0.3) Right 500 fb -1 (50/50 between Left and Right) Whizard ILD_01_v05 (DBD ver.) AWLC017 5

6 Reconstruction Process Isolated leptons tagging Number of isolated leptons = & Opposite charge each of two Suppression of γγ hadrons kt algorithm (cf. the Semi-leptonic analysis, R = 1.5) b-jet reconstruction LCFI Plus (Durham algorithm) The b-charge measurement is not used Kinematical reconstruction of top quark AWLC017 6

7 Kinematical Reconstruction of top quark e + e tt bbμ + νμ ν Measurable Missing muon s : E μ +, θ μ +, φ μ +, E μ, θ μ, φ μ b-jet s : E b1, θ b1, φ b1, E b, θ b, φ b neutrino s : E ν, θ ν, φ ν, E ν, θ ν, φ ν => 6 unknowns ν μ μ μ ν μ To recover them, impose the kinematical constraints; Initial state constraints : s, P init. = 500, 0 Mass constraints : m t, m t, m W +, m W => 8 constraints ( in excess) We don t need E b1 and E b which are relatively difficult to reconstruct. Just use to decide the assignment of b-jets AWLC017 7

8 Kinematical Reconstruction of top quark To detect the solution, we solve the following equations. E W± rest frame μ ± θ t, φ t = m W ±/ (Red : μ +, Green : μ ) assignment A (correct), b1 = b, b = b assignment B (wrong), b1 = b, b = b B A B1 A1 Typically, 4 candidates exist for each event. We need to select the optimal solution from these candidates. AWLC017 8

9 Kinematical Reconstruction of top quark χ b (θ t, φ t ) E b θ t,φ t E b meas. σ E b meas. + E b θ t,φ t E b meas. σ E b meas. = (Blue) assignment A (correct), b1 = b, b = b assignment B (wrong), b1 = b, b = b B A B1 A1 The candidate A1 has the minimum χ b The assignment A is selected and the solution is θ t, φ t (0.5, 0.35) AWLC017 9

10 Kinematical Reconstruction of top quark Technically, to obtain the solution, we minimize χ tot ; χ tot θ t, φ t = χ μ θ t, φ t + χ b θ t, φ t where χ μ θ t, φ t E W + rest frame μ + θt,φ t m W +/ W σ E + rest frame μ + + E μ W rest frame θt,φ t m W / σ E μ W rest frame χ μ is dominant to determine θ t, φ t because σ E μ W rest frame σ E b χ tot distribution AWLC017 10

11 F wrong : Fraction of the Wrong Assignment of b-jets F wrong (the fraction of the wrong assignment of b-jets) = % When we use samples not including ISR, F wrong = 8 % ISR significantly affects the assignment problem. We use two quantities to reduce F wrong χ tot (as mentioned) Δχ tot = χ tot,assignment A χ tot,assignment B AWLC017 11

12 F wrong : Fraction of the Wrong Assignment of b-jets We investigate F wrong and the efficiency varying the set of criteria for χ tot, Δχ tot The polar angle distribution of top is improved by the quality cut. Efficiency vs. F wrong χ tot <5, Δχ tot >6 (F wrong = 5.0 % total efficiency = 8 %) AWLC017 1

13 Helicity Angles Computation All final state particles including two neutrinos can be calculated. The 9 helicity angles which are related to the ttz/γ vertex are computed. t θ t, θ frame t W +, φ frame W +, θ W+ frame W μ +, φ + frame t μ +, θ frame t W, φ frame W, θ W frame μ, φ W frame μ (G. L. Kane, G. A. Ladinsky, C.-P. Yuan, Phys.Rev. D45 (199) ) eg) t frame cos θ W + χ tot <5, Δχ tot >6 cos θ W+ frame μ + AWLC017 13

14 Matrix Element Method Analysis Matrix element method is based on the maximum likelihood method. N event log L F = χ F = log M (Φ e, F) N F M : the full matrix element, Φ e : the 9 helicity angles, F : the form factors, N(F) : the expected number of events. The minimization of χ F automatically introduces the derivatives; e=1 1 M Φ e ω i Φ e = M Φ e F, Ω i = 1 N i F at SM N F i The results of fit are related with ω i Φ e and Ω i ; F at SM δf i (= F fit F SM ) <ω i Ω i > < ω i Ω i > covariance matrix, V ij ; V 1 ij = N event < ω i Ω i ω j Ω j > AWLC017 14

15 Fit of the CP-Conserving form factors Result of δf 1V γ fit (the others are fixed at SM) Before the quality cut (total efficiency 77%) δf 1V γ = 0.03 ± , χ test = % CL Left polarization The ω Ω distribution of the wrong assignment (Green) is shifted to positive bias blunter over estimates the precision The histogram of ω Ω for δf 1V γ (before quality cut) * χ test = δf i V 1 ij δf j : the chi-square test AWLC017 15

16 Fit of the CP-Conserving form factors Result of δf 1V γ fit (the others are fixed at SM) Before the quality cut (total efficiency 77%) δf 1V γ After the quality cut (χ tot δf 1V γ = 0.03 ± , χ test = % CL < 5 & Δχ tot > 6, total efficiency 8%) = ± , χ test = % CL Left polarization Good agreement between MC truth and Rec. The bias disappears. The error becomes larger (~ N) The histogram of ω Ω for δf 1V γ (after quality cut) AWLC017 16

17 The distributions of ω Ω (bef. the quality cut) Left polarization δf 1V γ Z γ δf 1V δf 1A Z γ δf 1A δf V Z δf V AWLC017 17

18 The distributions of ω Ω (aft. the quality cut) Left polarization δf 1V γ Z γ δf 1V δf 1A Z γ δf 1A δf V Z δf V AWLC017 18

19 Fit of the CP-Conserving form factors Results of 6 CPC form factors fit Before quality cut (total efficiency 77%) After quality cut (χ tot χ test = 166 ~0% CL < 5 & Δχ tot > 6, total efficiency 8%) χ test = % CL AWLC017 19

20 Fit of the CP-Violating form factors Result of ReδF A γ fit (the others are fixed at SM) Before the quality cut (total efficiency 77%) ReδF A γ = ± , χ test = % CL Left polarization The histogram of ω Ω for ReδF A γ (before quality cut) The ω Ω distribution of the wrong assignment (Green) is centered at 0 no apparent effect on the bias χ test is misleading if we use a CP-Violating sample, the wrong assignment will dilute the effect of CPV blunter over estimates the precision * χ test = δf i V 1 ij δf j : the chi-square test AWLC017 0

21 Fit of the CP-Violating form factors Result of ReδF A γ fit (the others are fixed at SM) Before the quality cut (total efficiency 77%) ReδF A γ After the quality cut (χ tot ReδF γ A = ± , χ test = % CL < 5 & Δχ tot > 6, total efficiency 8%) = ± 0.087, χ test = % CL Left polarization Good agreement between MC truth and Rec. The error is estimated correctly. The histogram of ω Ω for ReδF A γ (after quality cut) AWLC017 1

22 The distributions of ω Ω (bef. the quality cut) Left polarization ReδF A γ Z ReδF A ImδF A γ Z ImδF A AWLC017

23 The distributions of ω Ω (aft. the quality cut) Left polarization ReδF A γ Z ReδF A ImδF A γ Z ImδF A AWLC017 3

24 Fit of the CP-Violating form factors Results of 4 CPV form factors fit Before quality cut (total efficiency 77%) χ test = 5.0 9% CL After quality cut (χ tot < 5 & Δχ tot > 6, total efficiency 8%) χ test = % CL AWLC017 4

25 Relation of the helicity angles of μ ± and ω Ω δf V γ Left polarization When we don t use the φ W± μ ± or (φ W± μ ±, θ W± μ ± ), the ω Ω distribution becomes sharper, hence the sensitivity becomes lower. (φ W± μ ±, θ W± μ ± ) has a sensitivity to the ttz/γ. ReδF A γ Left polarization AWLC017 5

26 Summary Di-leptonic state analysis produces the 9 helicity angles which are sensitive to the form factors. Reconstruct top quark imposing the kinematical constraints ISR significantly affects the assignment problem of b-jets The quality cut improves the fraction of wrong assignment of b-jets, hence the angular distributions. Fit the form factors with the Matrix element method CPC : After quality cut, results are consistent with SM. CPV : The wrong fraction has no effects on the bias, but it will dilute the CPV effects if we use a CPV sample. AWLC017 6

27 Back up AWLC017 7

28 Suppression of γγ hadrons & b-jet reconstruction Particles from γγ hadrons are mostly emitted along the beam direction. The direction of the b-jet is affected by these particles. Suppress these particles using the kt algorithm (R=1.5). The direction of the b-jet is improved. A The polar angle distribution b-jets. A: without the suppression of γγ hadrons, B: with the suppression of γγ hadrons AWLC017 8 B

29 Scalar product, η t,mc η t,rec. AWLC017 9

30 Kinematical reconstruction of top To select the optimal solution, we compare E b and E b between calculated by θ t, φ t and measured by the b-jet reconstruction. E b (θ t, φ t ) in the case of assignment A χ b (θ t, φ t ) = E b θ t, φ t E b meas. σ E b meas. + E b θ t, φ t E b meas. σ E b meas. Compute χ b for each candidate Pick one which has the smallest χ b AWLC017 30

31 Luminosity spectrum Because we impose the initial state constraints, the events which have low s are badly reconstructed. Luminosity spectrum Black : Total events, Red : After quality cut Ratio of luminosity spectrum (Red/Black) The quality cut reduces low s events, but there are still a tail. AWLC017 31

32 Luminosity spectrum Tried to fit the energy of ISR photon along beam direction; Another parameter, K e + e bbμ + νμ ν + γ ISR K = E γ /50, hence s = K If γ is emitted in the e e + direction, K is positive (negative). Then one minimizes χ tot (θ t, φ t, K); χ tot θ t, φ t, K = χ tot θ t, φ t, K log PDF K K Reconstructed s don t correlate MC truth. The constraints are not enough. Now we fix K = 0 (i.e. use χ tot (θ t, φ t ) ) s (MC Truth vs. Rec.) AWLC017 3

33 F Z V fit (The simplest case) Other ways to reduce the bias Convolve the M with the resolution function of the helicity angles M = M cov. The deviation of each helicity angles Use other quantities for the quality cut. eg) χ tot,casea1 B1 χ tot,casea B AWLC017 33

34 F Z V Fit (The simplest case) (Fix the other form factors at the SM) Before quality cut δf Z V = ± 0.033, χ test = 1.6 (confidence level = 0.03%) χ vs Efficiency χ vs F wrong After quality cut (χ tot δf Z V < 5 & Δχ tot > 6, efficiency 36%) = ± 0.055, χ test = 3.0 (confidence level = 8.3%) AWLC017 34

35 6 CPC form factors fit Fit 6 form factors F γ 1V, F Z 1V, F γ 1A, F Z 1A, F γ Z V, F V Before quality cut < σ F > = 0.01, χ = 141 (confidence level ~ 0 %) χ vs Efficiency χ vs F wrong After quality cut (χ tot < 5 & Δχ tot > 6, efficiency 36%) < σ F > = 0.035, χ = 10.5 (confidence level = 11 %) Workshop on top physics at the LC

36 4 CP Violating Form Factors Fit Fit 4 form factors ReF γ A, ReF Z A, ImF γ Z A, ImF A Before quality cut < σ F >= 0.06, χ = 8.6 (confidence level = 7. %) χ vs Efficiency χ vs F wrong After quality cut (χ tot < 5 & Δχ tot > 6, efficiency 35%) < σ F >= 0.038, χ = 3.7 (confidence level = 45 %) AWLC017 36

37 The distributions of ω Ω (bef. the quality cut) Left polarization Right polarization AWLC017 37

38 The distributions of ω Ω (bef. the quality cut) Left polarization Right polarization AWLC017 38