New CMS results on B 0 K* 0 + decay studies Introduction Signal - - PowerPoint PPT Presentation

SLIDE 1

22/3/2017

Mauro Dinardo Università degli Studi di Milano Bicocca and INFN - Italy On behalf of the CMS collaboration

New CMS results on B0 ➝ K*0 μ+ μ− decay studies

Moriond 2017 EW Session Introduction Event selection Decay rate and total p.d.f. An interesting statistical problem … Signal evidence & fit validation Systematic uncertainties Preliminary results Summary

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*PLB 753 (2016) 424: AFB, FL, dBF/dq2

μ− μ+ K+ π− μμ / K*0 θK θl ϕ B0

2

Introduction

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

J/ψ ψ(2S) B0 ➝ K*0 μ+ μ− described within Standard Model (SM) as flavour-changing neutral-current process Decay fully described as a function of three angles (θl, θK, Φ) and dimuon invariant mass squared, q2 (searched in its fully charged final state B0 ➝ K*0(K+ π−) μ+ μ−) Robust SM calculations of several angular parameters, e.g. forward-backward asymmetry of the muons, AFB, longitudinal polarisation fraction of the K*0, FL, P5’ (see next slides) are available for much of the phase space Discrepancy of the angular parameters vs q2 with respect to SM indicates new physics This talk is about extension of previous analysis* (same 2012 data set, 20.5 fb−1 (8 TeV)): new angular parameters, P1 and P5’

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B0 ➝ K*0 J/ψ B0 ➝ K*0 ψ(2S) Dedicated low mass displaced dimuon trigger during 2012 data taking Most important selections to discriminate signal and reduce trigger rate: single muon pT > 3.5 GeV dimuon pT > 6.9 GeV 1 < m(μμ) = q < 4.8 GeV L / σ > 3 w.r.t. beamspot Vtx CL > 10% 3 Both K+π− and K−π+ mass hypothesis are computed pT > 0.8 GeV DCA / σ > 2 w.r.t. beamspot |m(Kπ) − 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 B0 and B0bar mass hypothesis are computed: pT > 8 GeV |η| < 2.2 |m(Kπμμ) − m(B0)PDG| < 280 MeV for at least one of the two mass hypothesis

• Vtx. CL > 10%

L / σ > 12 w.r.t. beamspot cos(α) > 0.9994 angle in transverse plane between B0 momentum and B0 line of flight (w.r.t. beamspot) If more than one candidate ➜ choose best B0 vtx CL Two CP-states, B0 ➝ K*0 (K+ π−) μ+ μ− and B0bar ➝ K*0bar (K− π+) μ+ μ−, difficult to disentangle (no particle ID) ➜ CP- 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

Event selection

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

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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 θl = π / 2 Decay rate depends upon 6 angular parameters: Fs, As, FL: fixed to published CMS measurements on same data set (Φ integrated out) P1, P5’: measured parameters in this analysis (Φ dependent) A5s: nuisance parameter (Φ dependent)

4

The decay rate

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

S-wave and S&P-wave interference P-wave 1 dΓ/dq2 d4Γ dq2d cos qld cos qKdf = 9 8p ⇢2 3 h

(FS + AS cos qK)

• 1 cos2 ql

+ A5

S

p 1 cos2 qK p 1 cos2 ql cos f i

+ (1 FS)

⇥ 2FL cos2 qK

• 1 cos2 ql
• + 1

2 (1 FL)

• 1 cos2 qK

1 + cos2 ql + 1 2P1(1 FL)

(1 cos2 qK)(1 cos2 ql) cos 2f + 2P0

5 cos qK

q FL (1 FL) p 1 cos2 qK p 1 cos2 ql cos f io

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Mistag fraction

PDF(m, qK, ql, f) = YC

S

 SC(m) Sa(qK, ql, f) eC(qK, ql, f)

+

f M 1 f M SM(m) Sa(qK, ql, f) eM(qK, ql, f)

• + YB Bm(m) BqK(qK) Bql(ql) Bf(f),

p.d.f.(m,θK,θl,Φ)

Correctly tagged events Mistagged events 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 Fit performed in two steps:

• 1. Fit sidebands to determine background shape
• 2. Fit whole mass spectrum, 5 free parameters:

signal (YS) and background (YB) yields P1, P5’, and A5s angular parameters Use unbinned extended maximum likelihood estimator Measurement performed 7 times (one in each q2 bin)

5

The probability density function

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

q2 bin index m2(μμ) (GeV2) 1st 1 − 2 2nd 2 − 4.3 3rd 4.3 − 6 4th 6 − 8.68 5th 10.9 − 12.86 6th 14.18 − 16 7th 16 − 19

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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

6

Efficiency function

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

2nd q2 bin

Closure test for correctly tagged events

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The decay rate can become negative for certain values of the angular parameters (P1, P5’, A5s) 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 P1 and P5’ is computed by: discretise the bi-dimensional space P1-P5’ maximise the likelihood as a function of YS, YB, and A5s at fixed values of P1, P5’ fit the likelihood distribution with a 2D-gaussian function the maximum of this function inside the physically allowed region is the best estimate

7

An interesting statistical problem …

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

Color code Log Likelihood (LL):

• yellow = 0 to 0.5 LL
• green = 0.5 to 2 LL

Coloured paths:

• Profile likelihood for P1
• Profile likelihood for P5’

To ensure correct coverage for the uncertainties of P1 and P5’, the Feldman-Cousins method is used in a simplified form: the confidence interval’s construction is performed only along two 1D paths determined by profiling the 2D-gaussian description of the likelihood inside the physically allowed region

2nd q2 bin

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Signal evidence

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

B0 ➝ K*0 ψ(2S) B0 ➝ K*0 J/ψ

• Total fit
• Signal, correctly tagged events
• Signal, mistagged events
• Background

Legend ➜

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Direct from simulation Treat simulation like data

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Fit validation

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

Several validation steps are performed with simulation: with statistically precise MC signal sample: compare fit results with input values to the simulation (simulation mismodeling) with 200 data-like MC signal+background samples: compare average fit results with fit to the statistically precise MC signal sample (fit bias) with pseudo-experiments Validation with data control channels: Fit performed with FL free to vary The difference of FL with respect to PDG value is propagated to the signal q2 bins as systematic uncertainty (efficiency)

B0 ➝ K*0 J/ψ

SLIDE 10

Kπ mistagging: mistag fraction free to vary in control channel B0 ➝ K*0 J/ψ ➜ discrepancy with respect to simulation is propagated to angular parameters FL, Fs, and As uncertainty propagation: Generate a statistically precise, O(100 × data), pseudo-experiments (one per q2 bin) Fit with all 6 angular parameters free to vary Fit with FL, Fs, and As fixed Ratio of uncertainties between free and partially-fixed fit is used to compute the systematic uncertainty

Systematic uncertainty P1(103) P0

5(103)

Simulation mismodeling 1–33 10–23 Fit bias 5–78 10–119 MC statistical uncertainty 29–73 31–112 Efficiency 17–100 5–65 Kπ mistagging 8–110 6–66 Background distribution 12–70 10–51 Mass distribution 12 19 Feed-through background 4–12 3–24 FL, FS, AS uncertainty propagation 0–126 0–200 Angular resolution 2–68 0.1–12 Total systematic uncertainty 60–220 70–230

☞ ☞ ☞ ☞ ☞

MC statistical uncertainty: fit data with 100 new efficiency distributions generated according to the simulation statistical uncertainty ➜ effect of the different efficiency functions on final result is used to estimate the systematic uncertainty

☞

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Systematic uncertainties

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

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Preliminary results: 2nd q2 bin

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

Representative fit results: vertical bars give the statistical uncertainties, horizontal bars the bin width (fits to all other q2 bins are in backup slides)

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〉 SM-DHMV 〈 〉 SM-HEPfit 〈 CMS LHCb Belle-preliminary

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〉 SM-DHMV 〈 〉 SM-HEPfit 〈 CMS LHCb

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Preliminary results

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

Both SM-DHMV and SM-HEPfit uses the same form- factors, and light-cone sum rule predictions are combined with lattice determinations at high q2 to yield more precise determinations of the form factors over the full q2 range SM-DHMV the hadronic charm-loop contribution is derived from calculations SM-HEPfit the hadronic contribution is derived from LHCb data SM-DHMV: JHEP 01 (2013) 048, JHEP 05 (2013) 137 SM-HEPfit: JHEP 06 (2016) 116, arXiv:1611.04338

J/ψ

Inner vertical bars ➜ statistical uncertainty Outer vertical bars ➜ total uncertainty Horizontal bars ➜ bin widths Statistical uncertainty is the dominant contribution but in 5th and 6th q2 bins were it is comparable to systematic uncertainty LHCb: JHEP 02 (2016) 104 Belle-preliminary: arXiv:1612.05014

ψ(2S) ψ(2S) J/ψ

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Using proton-proton collision data recorded at sqrt(s) = 8 TeV with the CMS detector at the LHC, corresponding to an integrated luminosity of 20.5 fb−1, an angular analysis has been carried out on the decay B0 ➝ K*0(K+ π−) μ+ μ− The data used for this analysis include 1397 signal decays For each q2 bin, unbinned maximum-likelihood fits were performed to the distributions of the K+ π− μ+ μ− invariant mass and the three decay angles, to

• btain values of the P1 and P5’ parameters

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Summary

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

The results are among the most precise to date The two SM predictions are seen to be in agreement with the CMS results, although the agreement with SM-DHMV is somewhat better

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Backup

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

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±

d b W − s d µ− µ+ Z0/γ

Bd K∗0

u/c/t d b s d µ− µ+ Z0/γ

Bd K∗0

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Figure 2: Dominant Standard Model Feynman diagrams for the decay B0 ! K⇤0µ+µ.

New phenomena (NP), beyond SM, observed directly or indirectly, through their influence on other physics processes B0 ➝ K*0 μ+ μ− described within SM as flavour-changing neutral-current process Within the reach of CMS: (a) decay rate has small theoretical uncertainties (b) new physics predictions that differ from SM (c) experimental accessible (fully charged final state (K*0 ➝ K+ π−) with easy-to- trigger muons) Good candidate for indirect searches for NP

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Physics case

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

s a m e l

• w

e s t

• r

d e r F e y n m a n d i a g r a m s a s f

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t h e Bs ➝ μ+ μ− d e c a y

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0.00 0.05 0.10 0.15

q2 HGeV2L A9

GMSSMII

SM

GMSSMI

A9

1 2 3 4 5 6

• 0.10
• 0.05

0.00 0.05 0.10 0.15

q2 HGeV2L S3

GMSSMII GMSSMI

SM

S3

1 2 3 4 5 6

• 0.3
• 0.2
• 0.1

0.0 0.1 0.2

q2 HGeV2L S6

s

SM FBMSSMIII FBMSSMI FBMSSMII

S6 (= −4/3 • AFB)

SM vs plausible SM-extensions (JHEP 01 (2009) 019)

• General MSSM
• Flavour Blind MSSM

Dramatic change of trends versus q2

16

Physics case

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

SLIDE 17

K

θ cos

• 1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1

a.u.

20 40 60 80 100 120 140 160 180 CMS Simulation

8 TeV

2

< 4.30 GeV

2

2.00 < q

L

θ cos

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

a.u.

20 40 60 80 100 120 140 160 180 200 220 CMS Simulation

8 TeV

2

< 4.30 GeV

2

2.00 < q

φ

0.5 1 1.5 2 2.5 3

a.u.

20 40 60 80 100 120 140 CMS Simulation

8 TeV

2

< 4.30 GeV

2

2.00 < q

ε × Generation Reconstruction

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

17

Efficiency function

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

2nd q2 bin

cos

• 1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1

ε

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 CMS Simulation

8TeV

2

< 4.30 GeV

2

2.00 < q

ε

Efficiency

θ cos

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ε

0.01 0.02 0.03 0.04 0.05 CMS Simulation

8TeV 2

< 4.30 GeV

2

2.00 < q

Efficiency

ε

φ

0.5 1 1.5 2 2.5 3

ε

0.005 0.01 0.015 0.02 0.025 0.03 CMS

2

< 4.30 GeV

2

2.00 < q

Efficiency

ε

Closure test for mistagged events

SLIDE 18

)

2

(GeV

2

q

2 4 6 8 10 12 14 16 18 20

1

P

1 − 0.8 − 0.6 − 0.4 − 0.2 − 0.2 0.4 0.6 0.8 1

Direct from simulation Treat simulation like data

CMS

Simulation

= 8 TeV s

• Input to simulation
• Fit results

) (GeV)

−

µ

+

µ

−

π

+

Κ ( m 5 5.1 5.2 5.3 5.4 5.5 Events / ( 0.028 GeV ) 0.5 1 1.5 2 2.5 3 3.5

3

10 ×

115 ± Signal yield: 10492

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

14.18 GeV − : 12.86

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

l

θ cos( 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Events / ( 0.05 ) 0.2 0.4 0.6 0.8 1 1.2

3

10 ×

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

14.18 GeV − : 12.86

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

Κ

θ cos(

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 Events / ( 0.1 ) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

3

10 ×

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

14.18 GeV − : 12.86

2

q Data Total fit Corr.tag sig. Mistag sig. Background

φ 0.5 1 1.5 2 2.5 3 Events / ( 0.15708 ) 0.2 0.4 0.6 0.8 1 1.2 1.4

3

10 ×

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

14.18 GeV − : 12.86

2

q Data Total fit Corr.tag sig. Mistag sig. Background

18

Fit validation

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

B0 ➝ K*0 ψ(2S)

SLIDE 19

19

Preliminary results

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

q2 (GeV2) Signal yield P1 P0

5

1.00–2.00 80 ± 12

+0.12+0.46

0.47 ± 0.06

+0.10+0.32

0.31 ± 0.12

2.00–4.30 145 ± 16

0.69+0.58

0.27 ± 0.09

0.57+0.34

0.31 ± 0.15

4.30–6.00 119 ± 14

+0.53+0.24

0.33 ± 0.18

0.96+0.22

0.21 ± 0.16

6.00–8.68 247 ± 21

0.47+0.27

0.23 ± 0.13

0.64+0.15

0.19 ± 0.14

10.09–12.86 354 ± 23

0.53+0.20

0.14 ± 0.14

0.69+0.11

0.14 ± 0.23

14.18–16.00 213 ± 17

0.33+0.24

0.23 ± 0.22

0.66+0.13

0.20 ± 0.19

16.00–19.00 239 ± 19

0.53+0.19

0.19 ± 0.13

0.56+0.12

0.12 ± 0.07

SLIDE 20

) (GeV)

−

µ

+

µ

−

π

+

Κ ( m 5 5.1 5.2 5.3 5.4 5.5 Events / ( 0.028 GeV ) 5 10 15 20 25 30 35

12 ± Signal yield: 80

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

2.00 GeV − : 1.00

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

l

θ cos( 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Events / ( 0.05 ) 5 10 15 20 25 30

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

2.00 GeV − : 1.00

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

Κ

θ cos(

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 Events / ( 0.1 ) 5 10 15 20 25 30 35 40 45

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

2.00 GeV − : 1.00

2

q Data Total fit Corr.tag sig. Mistag sig. Background

φ 0.5 1 1.5 2 2.5 3 Events / ( 0.15708 ) 5 10 15 20 25 30 35

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

2.00 GeV − : 1.00

2

q Data Total fit Corr.tag sig. Mistag sig. Background

20

Preliminary results: 1st q2 bin

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

SLIDE 21

P1

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 P'5

• 1.2
• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2

Negative decay rate Positive decay rate P5’ P1 The decay rate can become negative for certain values of the angular parameters (P1, P5’, A5s) 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 P1 and P5’ is computed by: discretise the bi-dimensional space P1-P5’ maximise the likelihood as a function of YS, YB, and A5s at fixed values of P1, P5’ fit the likelihood distribution with a 2D-gaussian function the maximum of this function inside the physically allowed region is the best estimate

Grey lines: A5s range gradually increases, up to its maximum, while moving along the arrows 21

An interesting statistical problem …

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

1

P

• 1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1

5

P'

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4

(8 TeV)

• 1

L = 20.5 fb

CMS Preliminary

20.5 fb−1 (8 TeV)

+

Best estimate Color code Log Likelihood (LL):

• yellow = 0 to 0.5 LL
• green = 0.5 to 2 LL

Coloured paths:

• Profile likelihood for P1
• Profile likelihood for P5’

2nd q2 bin

SLIDE 22

P1

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 P'5

• 1.2
• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2

• 1
• 1.5

1

• 2 -1 0 1 2

P5’

Physically allowed region

a.u.

P1

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 P'5

• 1.2
• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2

Negative decay rate Positive decay rate P5’ P1

22

An interesting statistical problem …

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

Cross section

Grey lines: A5s range gradually increases, up to its maximum, while moving along the arrows

SLIDE 23

1

P

• 1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1

5

P'

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4

(8 TeV)

• 1

L = 20.5 fb

CMS Preliminary

20.5 fb−1 (8 TeV)

+

Best estimate

23

An interesting statistical problem …

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

To ensure correct coverage for the uncertainties of P1 and P5’, the Feldman-Cousins method is used in a simplified form: the confidence interval’s construction is performed only along the two 1D paths determined by profiling the 2D-gaussian description of likelihood inside the physically allowed region: generate 100 pseudo-experiments for each point of the path fit and rank according to the likelihood-ratio confidence interval bound is found when data likelihood-ratio exceeds the 68.3% of the pseudo-experiments Due to the limited number of pseudo-experiments statistical fluctuations are present To produce a robust result, the ranking of the data likelihood-ratio is plotted for several scan points The intersection is then computed using a linear fit

SLIDE 24

) (GeV)

−

µ

+

µ

−

π

+

Κ ( m 5 5.1 5.2 5.3 5.4 5.5 Events / ( 0.028 GeV ) 10 20 30 40 50

14 ± Signal yield: 119

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

6.00 GeV − : 4.30

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

l

θ cos( 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Events / ( 0.05 ) 10 20 30 40 50

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

6.00 GeV − : 4.30

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

Κ

θ cos(

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 Events / ( 0.1 ) 10 20 30 40 50

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

6.00 GeV − : 4.30

2

q Data Total fit Corr.tag sig. Mistag sig. Background

φ 0.5 1 1.5 2 2.5 3 Events / ( 0.15708 ) 10 20 30 40 50

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

6.00 GeV − : 4.30

2

q Data Total fit Corr.tag sig. Mistag sig. Background

24

Preliminary results: 3rd q2 bin

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

SLIDE 25

1

P

• 1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1

5

P'

• 1.3
• 1.2
• 1.1
• 1
• 0.9
• 0.8
• 0.7
• 0.6

(8 TeV)

• 1

L = 20.5 fb

CMS Preliminary

20.5 fb−1 (8 TeV)

+

Best estimate

25

An interesting statistical problem …

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

Due to the limited number of pseudo-experiments statistical fluctuations are present To produce a robust result, the ranking of the data likelihood-ratio is plotted for several scan points The intersection is then computed using a linear fit To ensure correct coverage for the uncertainties of P1 and P5’, the Feldman-Cousins method is used in a simplified form: the confidence interval’s construction is performed only along the two 1D paths determined by profiling the 2D-gaussian description of likelihood inside the physically allowed region: generate 100 pseudo-experiments for each point of the path fit and rank according to the likelihood-ratio confidence interval bound is found when data likelihood-ratio exceeds the 68.3% of the pseudo-experiments

SLIDE 26

) (GeV)

−

µ

+

µ

−

π

+

Κ ( m 5 5.1 5.2 5.3 5.4 5.5 Events / ( 0.028 GeV ) 20 40 60 80 100

21 ± Signal yield: 247

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

8.68 GeV − : 6.00

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

l

θ cos( 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Events / ( 0.05 ) 10 20 30 40 50 60

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

8.68 GeV − : 6.00

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

Κ

θ cos(

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 Events / ( 0.1 ) 20 40 60 80 100

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

8.68 GeV − : 6.00

2

q Data Total fit Corr.tag sig. Mistag sig. Background

φ 0.5 1 1.5 2 2.5 3 Events / ( 0.15708 ) 10 20 30 40 50 60 70 80

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

8.68 GeV − : 6.00

2

q Data Total fit Corr.tag sig. Mistag sig. Background

26

Preliminary results: 4th q2 bin

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

SLIDE 27

) (GeV)

−

µ

+

µ

−

π

+

Κ ( m 5 5.1 5.2 5.3 5.4 5.5 Events / ( 0.028 GeV ) 20 40 60 80 100 120 140

23 ± Signal yield: 354

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

12.86 GeV − : 10.09

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

l

θ cos( 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Events / ( 0.05 ) 20 40 60 80 100

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

12.86 GeV − : 10.09

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

Κ

θ cos(

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 Events / ( 0.1 ) 20 40 60 80 100

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

12.86 GeV − : 10.09

2

q Data Total fit Corr.tag sig. Mistag sig. Background

φ 0.5 1 1.5 2 2.5 3 Events / ( 0.15708 ) 20 40 60 80 100 120

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

12.86 GeV − : 10.09

2

q Data Total fit Corr.tag sig. Mistag sig. Background

27

Preliminary results: 5th q2 bin

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

SLIDE 28

) (GeV)

−

µ

+

µ

−

π

+

Κ ( m 5 5.1 5.2 5.3 5.4 5.5 Events / ( 0.028 GeV ) 0.5 1 1.5 2 2.5 3 3.5

3

10 ×

115 ± Signal yield: 10492

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

14.18 GeV − : 12.86

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

l

θ cos( 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Events / ( 0.05 ) 0.2 0.4 0.6 0.8 1 1.2

3

10 ×

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

14.18 GeV − : 12.86

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

Κ

θ cos(

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 Events / ( 0.1 ) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

3

10 ×

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

14.18 GeV − : 12.86

2

q Data Total fit Corr.tag sig. Mistag sig. Background

φ 0.5 1 1.5 2 2.5 3 Events / ( 0.15708 ) 0.2 0.4 0.6 0.8 1 1.2 1.4

3

10 ×

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

14.18 GeV − : 12.86

2

q Data Total fit Corr.tag sig. Mistag sig. Background

28

Preliminary results: ψ(2S) q2 bin

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

SLIDE 29

) (GeV)

−

µ

+

µ

−

π

+

Κ ( m 5 5.1 5.2 5.3 5.4 5.5 Events / ( 0.028 GeV ) 10 20 30 40 50 60 70

17 ± Signal yield: 213

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

16.00 GeV − : 14.18

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

l

θ cos( 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Events / ( 0.05 ) 10 20 30 40 50

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

16.00 GeV − : 14.18

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

Κ

θ cos(

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 Events / ( 0.1 ) 10 20 30 40 50

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

16.00 GeV − : 14.18

2

q Data Total fit Corr.tag sig. Mistag sig. Background

φ 0.5 1 1.5 2 2.5 3 Events / ( 0.15708 ) 10 20 30 40 50 60

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

16.00 GeV − : 14.18

2

q Data Total fit Corr.tag sig. Mistag sig. Background

29

Preliminary results: 6th q2 bin

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

SLIDE 30

) (GeV)

−

µ

+

µ

−

π

+

Κ ( m 5 5.1 5.2 5.3 5.4 5.5 Events / ( 0.028 GeV ) 10 20 30 40 50 60 70 80

19 ± Signal yield: 239

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

19.00 GeV − : 16.00

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

l

θ cos( 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Events / ( 0.05 ) 10 20 30 40 50

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

19.00 GeV − : 16.00

2

q Data Total fit Corr.tag sig. Mistag sig. Background

)

Κ

θ cos(

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 Events / ( 0.1 ) 10 20 30 40 50

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

19.00 GeV − : 16.00

2

q Data Total fit Corr.tag sig. Mistag sig. Background

φ 0.5 1 1.5 2 2.5 3 Events / ( 0.15708 ) 5 10 15 20 25 30 35 40 45

CMS

Preliminary (8 TeV)

1 −

20.5 fb

2

19.00 GeV − : 16.00

2

q Data Total fit Corr.tag sig. Mistag sig. Background

30

Preliminary results: 7th q2 bin

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

SLIDE 31

|

mψPDG)| < ∆m, more precisely if m(µµ) < mJ/

ψPDG, then:

• |(m(Kπµµ) mB0PDG) (m(µµ) mJ/

ψPDG)| < 160 MeV

/c2;

• |(m(Kπµµ) mB0PDG) (m(µµ) mψ0PDG)| < 60 MeV

/c2; while if mJ/

ψPDG < m(µµ) < mψ0PDG, then:

• |(m(Kπµµ) mB0PDG) (m(µµ) mJ/

ψPDG)| < 60 MeV

/c2;

• |(m(Kπµµ) mB0PDG) (m(µµ) mψ0PDG)| < 60 MeV

/c2; and if m(µµ) > mψ0PDG, then:

• |(m(Kπµµ) mB0PDG) (m(µµ) mJ/

ψPDG)| < 60 MeV

/c2;

• |(m(Kπµµ) mB0PDG) (m(µµ) mψ0PDG)| < 30 MeV

/c2.

Events are rejected

• !

⇤

• The signal sample is required to pass the selection:
• m(µµ) < mJ/

ψPDG 3σm(µµ) or

• mJ/

ψPDG + 3σm(µµ) < m(µµ) < mψ0PDG 3σm(µµ) or

• m(µµ) > mψ0PDG + 3σm(µµ);

for the control channel B0 ! K⇤0(K+π)J/ψ(µ+µ) the requirement is:

• |m(µµ) mJ/

ψPDG| < 3σm(µµ).

while for the B0 ! K⇤0(K+π)ψ0(µ+µ) channel is:

• |m(µµ) mψ0PDG| < 3σm(µµ).

To further reject feed-through from control channels ➜

31

J/ψ and ψ(2S) rejection

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

SLIDE 32

32

J/ψ and ψ(2S) rejection

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

) (GeV)

−

µ

+

µ m( 1 1.5 2 2.5 3 3.5 4 ) (GeV)

−

µ

+

µ π m(K 5 5.1 5.2 5.3 5.4 5.5

• q2 bin
• 3σ cut
• m(Kπμμ) & m(μμ) cut

SLIDE 33

33

Physics constraints on the interference terms

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

The interference terms AS and A5S must vanish if either of the two interfering components

• vanish. From (JHEP 05 (2013) 137), these constraints are implemented as:
• |AS| < √(12FS (1 − FS) FL) • R
• |A5S| < √(3FS (1 − FS) (1 − FL) (1 + P1)) • R

where R is a ratio related to the S-wave and P-wave line shapes, estimated to be 0.89 near the K*0 mass The constraint on AS is naturally satisfied since the measurement of the parameters FS, FL, and AS is inherited from the previous CMS analysis (PLB 753 (2016) 424)

SLIDE 34

34

Folding mechanism

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

If φ < 0, then φ ➜ −φ, and the new φ domain is [0, π] If θl > π / 2, then θl ➜ π − θl, and the new θl domain is [0, π / 2]

SLIDE 35

d4Γ[B0 → K∗0µ+µ−] dq2 d⃗ Ω = 9 32π

• i

Ii(q2)fi(⃗ Ω) d4¯ Γ[B0 → K∗0µ+µ−] dq2 d⃗ Ω = 9 32π

• i

¯ Ii(q2)fi(⃗ Ω)

Γ and Γbar: expression of the decay f(Ω ⃗): combinations of spherical harmonics I and Ibar: q2-dependent angular parameters (combinations of six complex decay amplitudes)

Decay rate involving b quark, i.e. B0bar meson Decay rate involving bbar quark, i.e. B0 meson

Assumptions / simplifications: CP-averaged measurement Massless limit, i.e. q2 ≫ 4m2μ 8 independent angular parameters

35

Decay rate

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN

1 d(Γ + ¯ Γ)/dq2 d4(Γ + ¯ Γ) dq2 d⃗ Ω = 9 32π 3 4(1 − FL) sin2 θK + FL cos2 θK + 1 4(1 − FL) sin2 θK cos 2θl − FL cos2 θK cos 2θl + S3 sin2 θK sin2 θl cos 2φ + S4 sin 2θK sin 2θl cos φ + S5 sin 2θK sin θl cos φ + 4 3AFB sin2 θK cos θl + S7 sin 2θK sin θl sin φ + S8 sin 2θK sin 2θl sin φ + S9 sin2 θK sin2 θl sin 2φ

SLIDE 36

1 Γ0

full

d4Γ dq2 dcos θK dcos θl dφ = 9 32π 3 4FT sin2 θK + FL cos2 θK +(1 4FT sin2 θK − FL cos2 θK) cos 2θl + 1 2P1FT sin2 θK sin2 θl cos 2φ + p FTFL ✓1 2P0

4 sin 2θK sin 2θl cos φ + P0 5 sin 2θK sin θl cos φ

◆ − p FTFL ✓ P0

6 sin 2θK sin θl sin φ − 1

2P0

8 sin 2θK sin 2θl sin φ

◆ +2P2FT sin2 θK cos θl − P3FT sin2 θK sin2 θl sin 2φ

• (1 − FS) +

1 Γ0

full

L L L L L L L

FL

dq2 dΩ dΓ4P-wave =

36

Decay rate parameterisation (JHEP 01 (2013) 048) For example P5’ =

S5 √FL (1 − FL)

Two channels can contribute to the final state K+ π− μ+ μ−: P-wave channel, K+ π− from the meson vector resonance K*0 decay S-wave channel, K+ π− not coming from any resonance We have to parametrise both decay rates ! Both S-wave and S&P- wave interference 6 independent parameters

dq2 dΩ dΓ4Total = (1 − Fs) dq2 dΩ dΓ4P-wave + dq2 dΩ dΓ4S/SP-wave

3 16π

• FS sin2 θℓ + AS sin2 θℓ cos θK + A4

S sin θK sin 2θℓ cos φ

+A5

S sin θK sin θℓ cos φ + A7 S sin θK sin θℓ sin φ + A8 S sin θK sin 2θℓ sin φ

• =

dq2 dΩ dΓ4S/SP-wave

Decay rate

Mauro Dinardo, Università degli Studi di Milano Bicocca and INFN