The expected confident intervals for triple gauge coupling parameter Zhijun Liang Academia Sinica ,Taiwan 5/5/2018 The expected confident intervals for triple gauge coupling parameter

The expected confident intervals for triple gauge coupling parameter Introduction Section 1 :Comparison of Bayesian approach and Frequentist approach in setting limit on triple gauge coupling parameter Bayesian approach or Frequentist approach ? Section 2 : W γ channel radiation zero discovery potential analysis , hypothesis test or consistency test ? 5/5/2018 The expected confident intervals for triple gauge coupling parameter

The expected confident intervals for triple gauge coupling parameter W γ physics Testing SM model Triple gauge coupling vertex . Measure magnetic dipole moment and electric quadruple moment of W Irreducible background 5/5/2018 The expected confident intervals for triple gauge coupling parameter

The expected confident intervals for triple gauge coupling parameter Generator level plots of W γ events with different coupling parameter setup Lambda and kappa are highly correlated with event kinematic Try to set limit in triple gauge coupling parameter by doing a counting experiment in event kinematic distribution 5/5/2018 The expected confident intervals for triple gauge coupling parameter

W γ events Full simulation result(300 pb-1) High Pt bin is more sensitive to coupling parameter . 5/5/2018 The expected confident intervals for triple gauge coupling parameter

Anomalous Triple gauge coupling study Try to use number of events in each bin of photon Pt distribution (n_i) to infer the triple gauge coupling parameter (lambda and kappa) n_i : is observed numbers events in ith pt bin S_i :is expected signal events in ith pt bin is Prior of s_i in given λ obtained from BAUR NLO MC Probability of measured n_i events in ith Pt bin for given expected signal (s_i ) and background (b_i) Assume π(b_i) follow poison , and π(λ ) is flat . Final PDF function of λ given obersered pt distribution is : 5/5/2018 The expected confident intervals for triple gauge coupling parameter

PDF distribution of λ and Δκ in Bayesian approach P(Δκ |data) P(λ |data) Δκ λ 5/5/2018 The expected confident intervals for triple gauge coupling parameter

2D PDF distribution of λ and Δκ (300 pb-1) Confident interval Δκ Δκ λ λ 5/5/2018 The expected confident intervals for triple gauge coupling parameter

Diboson CSC note method (Frequentist approach ) Construct likelihood function by convolved two Gaussian nuisance parameter with Poisson model . N is number of observed events v_s ,v_b : expected signal and background events f_s,f_b : fractional standard deviation of error, Assume signal systematic uncertainty is 10% , background uncertainty is 20% , that is σ_s=10% , σ_b=20% The final likelihood function is : More details could be found in Alan’s talk in SM meeting 13 ,Sep ,2007 where 5/5/2018 The expected confident intervals for triple gauge coupling parameter

Log likelihood distribution (300 pb-1) Δκ λ Table :ΔL corresponseing o a coverage probability Coverage probability 1 dimension 2 dimension 68% 0.5 1.15 95% 1.92 2.3 Confidence region is Log(Δκ)>=Log L_max –ΔL. ΔL=1.92 corresponse to 95% confident level for 1 dimensional case 5/5/2018 The expected confident intervals for triple gauge coupling parameter

2D Log likelihood distribution (300 pb-1) 2D Log likelihood as a function of λ and Δκ Confident intervals Δκ Δκ λ λ 5/5/2018 The expected confident intervals for triple gauge coupling parameter

The expected confident intervals for triple gauge coupling parameter Confident interval of λ In 300 pb -1 data Bayesian CSC note approach 68% CL (-0.06,0.07) (-0.04,0.05) 95% CL (-0.09,0.1) (-0.07,0.08) Confident interval of Δκ In 300 pb -1 data Bayesian CSC note approach 68% CL (-0.50,0.60) (-0.31,0.49) 95% CL (-0.89,1.02) (-0.58,0.73) 5/5/2018 The expected confident intervals for triple gauge coupling parameter

Section 2 : Theory prediction of radiation zero(RAZ) Destructed interference between S ,t ,u channel will cause a zero in angular distribution of W gamma system (Geobel,Halzen and Leveille,PRD 23:2682,1981) This zero point is in cos(theta)=(Q_u+Q_d)/ (Q_u-Q_d)=-1/3 for W+ In ATLAS case , theory predict that Eta(e)-Eta(γ) distribution have a dip in 0 . ATLAS TDR plot Eta(e)-Eta(γ) 5/5/2018 The expected confident intervals for triple gauge coupling parameter radiation zero

eta(γ)-eta(e) distribution Theoretical predictions have uncertainty , background will also mass up this radiation zero dip discovery . Hard to model both signal and background in this delta eta distribution , not easy to do consistency test . Hypothesis test could be performed to see whether the dip is significant . Generator level Central bin bin2 bin3 Central bin bin2 bin3 Full simulation 5/5/2018 The expected confident intervals for triple gauge coupling parameter

The expected confident intervals for triple gauge coupling parameter RAZ dip Significant Define that D1 is number s of events in central bin and D2 is number of events in Minimum neighbor bin . s1 ,b1 is truth signal and background events numbers in central bin respectively , s2 ,b2 is truth signal and background events numbers in Minimum neighbor bin( bin 2 or bin3) Our hypothesis test about whether there is a dip in central bin is that H0 :s1<s2 ,H1:s1>=s2 What we would like to know is given D1,D2, what is probability of H0 P(H0|D1,D2) Central bin bin2 Bin 3 5/5/2018 The expected confident intervals for triple gauge coupling parameter

Hypothesis test for RAZ P(H0)/ (P(H0)+P(H1)) 1 2 And H0: s1<s2 H1:s1>=s2 In order to get H0, we need to do integration on s1 and s2, b1,b2 but only in region where s1 <s2 3 5/5/2018 The expected confident intervals for triple gauge coupling parameter

The expected confident intervals for triple gauge coupling parameter 300pb-1 data: 82% probability for H0:s1<s2 1 fb -1 data : 96% probability for H0:s1<s2 In order to get H0, we need to do integration on s1 and s2, b1,b2 but only in region where s1 <s2 Which is s2/s1>1 P( s2/s1| D1,D2) H1 H0 H0 5/5/2018 The expected confident intervals for triple gauge coupling parameter

The expected confident intervals for triple gauge coupling parameter Summary The expected 95% confidence intervals for anomalous triple gauge-boson coupling are Bayesian approach : -0.09<λ<0.1 , -0.89<Δκ<1.02 Frequentist approach : -0.07< λ <0.08 , -0.58< Δκ <0.73 Frequentist approach could give a tighter limit . Radiation zero (RAZ)discovery potential was studied using Bayesian Hypothesis test . Expect to see 2 sigma significant for RAZ discovery in the first 1fb -1 data . 5/5/2018 The expected confident intervals for triple gauge coupling parameter