New CMS results on B 0 ➝ K* 0 μ + μ − decay studies Introduction Signal evidence & fit validation Event selection Systematic uncertainties Decay rate and total p.d.f. Preliminary results An interesting statistical problem … Summary Mauro Dinardo Università degli Studi di Milano Bicocca and INFN - Italy Moriond 2017 EW Session 22/3/2017 On behalf of the CMS collaboration
Introduction ϕ K + B 0 ➝ K* 0 μ + μ − described within Standard Model μ − (SM) as flavour-changing neutral-current process θ K Decay fully described as a function of three angles ( θ l , θ K , Φ ) and dimuon invariant mass squared, q 2 μμ / K *0 B 0 θ l ( searched in its fully charged final state B 0 ➝ K* 0 (K + π − ) μ + μ − ) Robust SM calculations of several angular μ + parameters, e.g. forward-backward asymmetry of π − the muons, A FB , longitudinal polarisation fraction of the K *0 , F L , P5’ (see next slides) are available for ψ (2S) much of the phase space J/ ψ Discrepancy of the angular parameters vs q 2 with respect to SM indicates new physics This talk is about extension of previous analysis * * PLB 753 (2016) 424: A FB , F L , d BF /dq 2 (same 2012 data set, 20.5 fb − 1 (8 TeV)): new angular parameters, P 1 and P 5 ’ 2 Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN
Event selection Dedicated low mass displaced dimuon trigger during 2012 data taking Most important selections to discriminate signal and reduce trigger rate: single muon p T > 3.5 GeV dimuon p T > 6.9 GeV Both K + π − and K − π + mass hypothesis are computed 1 < m( μμ ) = q < 4.8 GeV p T > 0.8 GeV L / σ > 3 w.r.t. beamspot DCA / σ > 2 w.r.t. beamspot Vtx CL > 10% |m(K π ) − m(K *0PDG )| < 90 MeV at least one of the two mass hypothesis must lie in the window m(KK) > 1.035 ( Φ (1020) particle rejection) Both B 0 and B 0bar mass hypothesis are computed: p T > 8 GeV | η | < 2.2 CMS Preliminary − 1 20.5 fb (8 TeV) Entries / (0.014 GeV) |m(K πμμ ) − m(B 0 ) PDG | < 280 MeV for at least one of the two mass hypothesis 4 10 Vtx. CL > 10% 3 10 L / σ > 12 w.r.t. beamspot cos( α ) > 0.9994 angle in transverse plane between B 0 2 10 momentum and B 0 line of flight (w.r.t. beamspot) If more than one candidate ➜ choose best B 0 vtx CL 10 B 0 ➝ K *0 J/ ψ B 0 ➝ K *0 ψ (2S) 1 Two CP-states , B 0 ➝ K* 0 (K + π − ) μ + μ − and B 0bar ➝ K* 0bar 1 1.5 2 2.5 3 3.5 4 4.5 5 (K − π + ) μ + μ − , difficult to disentangle (no particle ID) ➜ CP- − m( + ) (GeV) µ µ state assignment based on mass hypothesis closer to K* 0 PDG mass (mistag rate ~14%) Signal and control samples are treated identically Signal candidates obtained by J/ ψ and ψ (2S) rejections 3 Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN
The decay rate Two channels can contribute to the final state K + π − μ + μ − : P-wave resonant channel, K + π − from the meson vector resonance K* 0 decay S-wave non-resonant channel, K + π − don’t come from any resonance We have to parametrise both decay rates ➜ 14 parameters ➜ given the number events in 2012 data set , we need to reduce number of free angular parameters to allow the fit to converge ➜ exploit the odd symmetry of trigonometric functions, i.e. fold decay rate around Φ = 0 and θ l = π / 2 S-wave and S&P-wave interference d 4 Γ � + A 5 ⇢ 2 1 d q 2 d cos q l d cos q K d f = 9 h 1 � cos 2 q l p 1 � cos 2 q K � ( F S + A S cos q K ) S d Γ /d q 2 8 p 3 i 2 F L cos 2 q K 1 � cos 2 q l p 1 � cos 2 q l cos f ⇥ � � + ( 1 � F S ) � + 1 + 1 1 � cos 2 q K 1 + cos 2 q l � � � 2 P 1 ( 1 � F L ) 2 ( 1 � F L ) q ( 1 � cos 2 q K )( 1 � cos 2 q l ) cos 2 f + 2 P 0 F L ( 1 � F L ) 5 cos q K io p 1 � cos 2 q K p 1 � cos 2 q l cos f P-wave Decay rate depends upon 6 angular parameters: F s , A s , F L : fixed to published CMS measurements on same data set ( Φ integrated out) P 1 , P 5 ’ : measured parameters in this analysis ( Φ dependent) A 5s : nuisance parameter ( Φ dependent) 4 Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN
The probability density function PDF ( m , q K , q l , f ) = Y C S C ( m ) S a ( q K , q l , f ) e C ( q K , q l , f ) p.d.f.(m, θ K , θ l , Φ ) Correctly tagged events S f M � Mistag fraction 1 � f M S M ( m ) S a ( � q K , � q l , f ) e M ( q K , q l , f ) + Mistagged events + Y B B m ( m ) B q K ( q K ) B q l ( q l ) B f ( f ) , Background Signal contribution: mass shape (double gaussian), decay rate, and 3D efficiency function Background contribution: mass shape (exponential) and factorised polynomial functions for each angular variable q 2 bin index m 2 ( μμ ) (GeV 2 ) Fit performed in two steps: 1 st 1 − 2 1. Fit sidebands to determine background shape 2 nd 2 − 4.3 2. Fit whole mass spectrum, 5 free parameters: 3 rd 4.3 − 6 signal ( Y S ) and background ( Y B ) yields 4 th 6 − 8.68 P 1 , P 5 ’ , and A 5s angular parameters 5 th 10.9 − 12.86 Use unbinned extended maximum likelihood estimator 6 th 14.18 − 16 Measurement performed 7 times (one in each q 2 bin) 7 th 16 − 19 5 Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN
Efficiency function Numerator and denominator of efficiency are separately described with nonparametric technique implemented with a kernel density estimator on unbinned distributions Final efficiency distributions in the p.d.f. obtained from the ratio of 3D histograms derived from the sampling of the kernel density estimators Closure test: compute efficiency with half of the MC simulation and use it to correct the other half same test performed both for correctly and mistagged events independently CMS Simulation CMS Simulation CMS Simulation 8 TeV 8 TeV 8 TeV 140 a.u. a.u. a.u. 200 350 Closure test for 2 2 2 2 2 2 2.00 < q < 4.30 GeV 2.00 < q < 4.30 GeV 2.00 < q < 4.30 GeV correctly tagged events 180 120 300 Generation × ε 160 100 140 250 Reconstruction 120 Efficiency 80 200 ε ∈ Efficiency 100 ε 0.025 2 nd q 2 bin ∈ 0.045 60 0.02 0.04 150 80 0.035 0.015 0.03 ε ∈ 60 40 0.025 0.03 100 0.01 0.02 0.025 0.015 40 Efficiency 0.005 0.01 20 0.02 50 0.005 0 20 0 0.5 1 1.5 2 2.5 3 0.015 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 cos 0.01 0 0 -1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 2.5 3 0.005 cos cos θ θ φ 0 -1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 K L cos θ 6 Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN
An interesting statistical problem … The decay rate can become negative for certain values of the angular parameters ( P 1 , P 5 ’ , A 5s ) The presence of such a physically allowed region greatly complicates the numerical maximisation process of the likelihood by MINUIT and especially the error determination by MINOS , in particular next to the boundary between physical and unphysical regions The best estimate of P 1 and P 5 ’ is computed by: discretise the bi-dimensional space P 1 -P 5 ’ maximise the likelihood as a function of Y S , Y B , and A 5s at fixed values of P 1 , P 5 ’ fit the likelihood distribution with a 2D-gaussian function the maximum of this function inside the physically allowed region is the best estimate 20.5 fb − 1 (8 TeV) -1 CMS Preliminary L = 20.5 fb (8 TeV) 5 P' 2 nd q 2 bin 0.4 To ensure correct coverage for the Color code Log 0.2 uncertainties of P 1 and P 5 ’ , the Likelihood (LL): Feldman-Cousins method is used in a 0 • yellow = 0 to 0.5 LL simplified form: the confidence • green = 0.5 to 2 LL -0.2 interval’s construction is performed only -0.4 + along two 1D paths determined by Coloured paths: -0.6 • Profile likelihood for P 1 profiling the 2D-gaussian description of -0.8 • Profile likelihood for P 5 ’ the likelihood inside the physically Best -1 estimate allowed region -1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 P 1 7 Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN
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