Muon Efficiency and Fake Rate Two Dimension Fit Exclusive B->JPsiMuMu Analysis in CMSSW_3_1_2 1

outline Muon Efficiency and Fake rate new MC data sample comparison of three kinds muons’ efficiency muon to pi/K fake rate Two Dimension Fit CDF J/ψ meson 2D fit David’s Note BtoJPsiK 2D fit To do list 2

Mu efficiency and fake rate MC Data Sample: Single Muon events Single Pion events Single Kaon events Muon type: Glb Ξ Global Muon Trk Ξ Track Muon Trk’ Ξ Track Muon with χ 2 11 Muon efficiency: Muon fake: Using Single Pion and Kaon MC Datasample. Here, we correct our mistake about double counting of muons With Pt =[3,65] GeV 3

Muon Efficiency I. At low pt <  5GeV, Endcap muon can get highest efficiency, barrel + endcap lower, and barrel the lowest. But at high pt range, the contrary in the case. II. At high pt range,Global muon can get 96% efficiency, Tracker muon 97%,and Tracker muon with cuts 96%, and at low pt range Tracker muon can get highest effieiency 77.5%, Tracker muon with cuts 75.5% and Global muon only 63%. In a word, at high pt Global and Tracker muon efficiency almost the same, but in low pt Tracker muon can gain 12% higher efficiency than Global muon. Barrel+Endcap Barrel Endcap Barrel+Endcap Barrel Endcap Barrel+Endcap Barrel Endcap 4

Comparison of fake rate Pi After correctdouble counting, using new Single Pi MC sample Barrel+Endcap Barrel Endcap 5

Comparison of fake rate K After correct double counting, using new Single Kaon MC sample Barrel+Endcap Barrel Endcap 6

Two Dimension Fit for J/ψ (CDF) Unbinned extended maximum likelihood fit  N is total number of events in the mass range 2.85GeV<m μμ <3.55GeV f Sig is the fraction of signal J/ψ events, F Sig and F Bkg are the PDLS of Signal and BKG. M Sig and M Bkg is the mass spectrum for Signal and BKG. parameters Signal PDL: f B,s 2 M : f 2, M,D,σ M,r2 5 BKG PDL: f +,f -,f sym, λ +,λ -,λ sym 6 M : M slope 1 lnL : fsig 1 total 15 7

Fit results of CDF 8

Two Dimension Fit for BtoJPsiK (David Note) Unbinned extended maximum likelihood fit Five components of B + -> J/ψ K + datasample: Signal, B + ->J/ψπ +, prompt J/ψ, combinatorial bbar(BB), feeddown bbar(B 0 -> J/ψ K *0,B ± -> J/ψ K *± ) Extended likelihood function: where i = [1…5], n i and P i is the yield and PDF of each component separately, j is the event No. of the fit. 9

PDF of B mass and c  MBMB cc Component FunctionParameterFunctionparameter Signal G1+G2+G3 {μi,σi}{μi,σi} (G1+G2) e -ct/ λ {μi,σi,λ}{μi,σi,λ} J/ψπ G1+G2+G3 {μi,σi}{μi,σi} (G1+G2) e -ct/ λ {μi,σi,λ}{μi,σi,λ} Peak B G1+G2+e - αMB {μi,σi,α}{μi,σi,α} G (e -ct/ λ1 + e -ct/ λ1 ){σ,λ1,λ2}{σ,λ1,λ2} Comb B e - αMB {α}{α} (G1+G2) e -ct/ λ {μi,σi,λ}{μi,σi,λ} Prompt J/ψ e - αMB {α}{α}{μi,σi,λ}{μi,σi,λ} Same with Signal 10

Fit Procedure First fit each component with p T > 9GeV MC truth match data sample to determine the best values of λs(except Signal) and all parameters. 11 PDL MASS

Fit Procedure Then fix λ s(except Signal) and all parameters, and fit all pt bins sample of S+B to determine the B lifetime λ B and yield for each component. (4 yields + λ B ) T he last, fix all λ s and all parameters, and fit data sample(S+B) for yields in each bins of P T. 12

To do list Perform the two dimension fit referring to David’s Note. Code skeleton was ready, but parameters need to be optimized QCD BKG may introduce new variables when we fit the real data. 13