CMSPASBPH22001  
Measurement of the $ \mathrm{B}^0_\mathrm{s} $ effective lifetime in the decay $ \mathrm{B}^0_\mathrm{s}\to\mathrm{J}/\psi\,\mathrm{K}^0_\mathrm{S} $ from pp collisions at $ \sqrt{s} = $ 13 TeV  
CMS Collaboration  
28 March 2024  
Abstract: The effective lifetime of the $ \mathrm{B}^0_\mathrm{s} $ meson in the decay $ \mathrm{B}^0_\mathrm{s}\to\mathrm{J}/\psi \, \mathrm{K}^0_\mathrm{S} $ is measured using data collected during 20162018 with the CMS detector in $ \sqrt{s}= $ 13 TeV protonproton collisions at the LHC, corresponding to an integrated luminosity of 140 fb$ ^{1} $. The effective lifetime is determined by performing a twodimensional unbinned maximum likelihood fit to the $ \mathrm{B}^0_\mathrm{s}\to\mathrm{J}/\psi\, \mathrm{K}^0_\mathrm{S} $ meson invariant mass and proper decay time distributions. The resulting value is 1.59 $ \pm $ 0.07 (stat) $ \pm $ 0.03 (syst) ps, where the first uncertainty represents the statistical uncertainty and the latter corresponds to the systematic uncertainty.  
Links: CDS record (PDF) ; CADI line (restricted) ; 
Figures  
png pdf 
Figure 1:
The treelevel (left) and penguin (right) diagrams for the decay $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\mathrm{K^0_S} $. 
png pdf 
Figure 1a:
The treelevel (left) and penguin (right) diagrams for the decay $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\mathrm{K^0_S} $. 
png pdf 
Figure 1b:
The treelevel (left) and penguin (right) diagrams for the decay $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\mathrm{K^0_S} $. 
png pdf 
Figure 2:
Distributions of the $ \mathrm{J}/\psi\mathrm{K^0_S} $ invariant mass (left) and proper decay time (right) from data (points) and the results from the 2D UML fit. The plots show the complete data set from 20162018. The vertical bars on the data points indicate the statistical uncertainty. The dashed, dotteddashed, dotted lines and solid lines show the $ \mathrm{B}_{s}^{0} $ signal, $ {\mathrm{B}^0} $ control channel, combinatorial background, and total fit contributions, respectively. 
png pdf 
Figure 2a:
Distributions of the $ \mathrm{J}/\psi\mathrm{K^0_S} $ invariant mass (left) and proper decay time (right) from data (points) and the results from the 2D UML fit. The plots show the complete data set from 20162018. The vertical bars on the data points indicate the statistical uncertainty. The dashed, dotteddashed, dotted lines and solid lines show the $ \mathrm{B}_{s}^{0} $ signal, $ {\mathrm{B}^0} $ control channel, combinatorial background, and total fit contributions, respectively. 
png pdf 
Figure 2b:
Distributions of the $ \mathrm{J}/\psi\mathrm{K^0_S} $ invariant mass (left) and proper decay time (right) from data (points) and the results from the 2D UML fit. The plots show the complete data set from 20162018. The vertical bars on the data points indicate the statistical uncertainty. The dashed, dotteddashed, dotted lines and solid lines show the $ \mathrm{B}_{s}^{0} $ signal, $ {\mathrm{B}^0} $ control channel, combinatorial background, and total fit contributions, respectively. 
png pdf 
Figure 3:
The proper decay time distribution from data (points) for events in the $ \mathrm{B}_{s}^{0} $ signal region with $ \mathrm{J}/\psi\mathrm{K^0_S} $ invariant mass in the range 5.345.42 GeV. The vertical bars on the data points indicate the statistical uncertainty. The dashed, dotteddashed, dotted lines and solid lines show the $ \mathrm{B}_{s}^{0} $ signal, $ {\mathrm{B}^0} $ control channel, combinatorial background, and total fit contributions, respectively. 
png pdf 
Figure 4:
The signal efficiency as a function of the decay time for the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ (left) and $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ (right) decays from simulation for each of the three datataking years. The vertical bars indicate the statistical uncertainty, and the horizontal bars give the bin width. The curves show the projections of the fit to the simulated event samples. 
png pdf 
Figure 4a:
The signal efficiency as a function of the decay time for the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ (left) and $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ (right) decays from simulation for each of the three datataking years. The vertical bars indicate the statistical uncertainty, and the horizontal bars give the bin width. The curves show the projections of the fit to the simulated event samples. 
png pdf 
Figure 4b:
The signal efficiency as a function of the decay time for the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ (left) and $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ (right) decays from simulation for each of the three datataking years. The vertical bars indicate the statistical uncertainty, and the horizontal bars give the bin width. The curves show the projections of the fit to the simulated event samples. 
png pdf 
Figure 4c:
The signal efficiency as a function of the decay time for the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ (left) and $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ (right) decays from simulation for each of the three datataking years. The vertical bars indicate the statistical uncertainty, and the horizontal bars give the bin width. The curves show the projections of the fit to the simulated event samples. 
png pdf 
Figure 4d:
The signal efficiency as a function of the decay time for the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ (left) and $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ (right) decays from simulation for each of the three datataking years. The vertical bars indicate the statistical uncertainty, and the horizontal bars give the bin width. The curves show the projections of the fit to the simulated event samples. 
png pdf 
Figure 4e:
The signal efficiency as a function of the decay time for the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ (left) and $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ (right) decays from simulation for each of the three datataking years. The vertical bars indicate the statistical uncertainty, and the horizontal bars give the bin width. The curves show the projections of the fit to the simulated event samples. 
png pdf 
Figure 4f:
The signal efficiency as a function of the decay time for the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ (left) and $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ (right) decays from simulation for each of the three datataking years. The vertical bars indicate the statistical uncertainty, and the horizontal bars give the bin width. The curves show the projections of the fit to the simulated event samples. 
png pdf 
Figure 5:
Distributions of the $ \mathrm{J}/\psi\mathrm{K^0_S} $ invariant mass (left) and decay time (right) from data (points), along with the projections from the 2D UML fit for each year of data taking. The vertical bars on the data points indicate the statistical uncertainty. The dashed, dotteddashed, dotted and solid lines represent the signal, control channel, combinational background, and total fit contributions respectively. 
png pdf 
Figure 5a:
Distributions of the $ \mathrm{J}/\psi\mathrm{K^0_S} $ invariant mass (left) and decay time (right) from data (points), along with the projections from the 2D UML fit for each year of data taking. The vertical bars on the data points indicate the statistical uncertainty. The dashed, dotteddashed, dotted and solid lines represent the signal, control channel, combinational background, and total fit contributions respectively. 
png pdf 
Figure 5b:
Distributions of the $ \mathrm{J}/\psi\mathrm{K^0_S} $ invariant mass (left) and decay time (right) from data (points), along with the projections from the 2D UML fit for each year of data taking. The vertical bars on the data points indicate the statistical uncertainty. The dashed, dotteddashed, dotted and solid lines represent the signal, control channel, combinational background, and total fit contributions respectively. 
png pdf 
Figure 5c:
Distributions of the $ \mathrm{J}/\psi\mathrm{K^0_S} $ invariant mass (left) and decay time (right) from data (points), along with the projections from the 2D UML fit for each year of data taking. The vertical bars on the data points indicate the statistical uncertainty. The dashed, dotteddashed, dotted and solid lines represent the signal, control channel, combinational background, and total fit contributions respectively. 
png pdf 
Figure 5d:
Distributions of the $ \mathrm{J}/\psi\mathrm{K^0_S} $ invariant mass (left) and decay time (right) from data (points), along with the projections from the 2D UML fit for each year of data taking. The vertical bars on the data points indicate the statistical uncertainty. The dashed, dotteddashed, dotted and solid lines represent the signal, control channel, combinational background, and total fit contributions respectively. 
png pdf 
Figure 5e:
Distributions of the $ \mathrm{J}/\psi\mathrm{K^0_S} $ invariant mass (left) and decay time (right) from data (points), along with the projections from the 2D UML fit for each year of data taking. The vertical bars on the data points indicate the statistical uncertainty. The dashed, dotteddashed, dotted and solid lines represent the signal, control channel, combinational background, and total fit contributions respectively. 
png pdf 
Figure 5f:
Distributions of the $ \mathrm{J}/\psi\mathrm{K^0_S} $ invariant mass (left) and decay time (right) from data (points), along with the projections from the 2D UML fit for each year of data taking. The vertical bars on the data points indicate the statistical uncertainty. The dashed, dotteddashed, dotted and solid lines represent the signal, control channel, combinational background, and total fit contributions respectively. 
png pdf 
Figure 6:
The 2D UML fit projection on the decay time axis for mass range 5.17 $ < m < $ 5.22 GeV for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 6a:
The 2D UML fit projection on the decay time axis for mass range 5.17 $ < m < $ 5.22 GeV for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 6b:
The 2D UML fit projection on the decay time axis for mass range 5.17 $ < m < $ 5.22 GeV for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 6c:
The 2D UML fit projection on the decay time axis for mass range 5.17 $ < m < $ 5.22 GeV for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 7:
The 2D UML fit projection on the decay time axis for mass range 5.22 $ < m < $ 5.34 GeV for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 7a:
The 2D UML fit projection on the decay time axis for mass range 5.22 $ < m < $ 5.34 GeV for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 7b:
The 2D UML fit projection on the decay time axis for mass range 5.22 $ < m < $ 5.34 GeV for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 7c:
The 2D UML fit projection on the decay time axis for mass range 5.22 $ < m < $ 5.34 GeV for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 8:
The 2D UML fit projection on the decay time axis for mass range 5.42 $ < m < $ 5.57 GeV for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 8a:
The 2D UML fit projection on the decay time axis for mass range 5.42 $ < m < $ 5.57 GeV for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 8b:
The 2D UML fit projection on the decay time axis for mass range 5.42 $ < m < $ 5.57 GeV for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 8c:
The 2D UML fit projection on the decay time axis for mass range 5.42 $ < m < $ 5.57 GeV for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 9:
The 2D UML fit projection plots on the mass axis for decay time range 0.2 $ < t < $ 2.5 ps for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 9a:
The 2D UML fit projection plots on the mass axis for decay time range 0.2 $ < t < $ 2.5 ps for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 9b:
The 2D UML fit projection plots on the mass axis for decay time range 0.2 $ < t < $ 2.5 ps for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 9c:
The 2D UML fit projection plots on the mass axis for decay time range 0.2 $ < t < $ 2.5 ps for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 10:
The 2D UML fit projection plots on the mass axis for decay time range 2.5 $ < t < $ 3.5 ps for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 10a:
The 2D UML fit projection plots on the mass axis for decay time range 2.5 $ < t < $ 3.5 ps for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 10b:
The 2D UML fit projection plots on the mass axis for decay time range 2.5 $ < t < $ 3.5 ps for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 10c:
The 2D UML fit projection plots on the mass axis for decay time range 2.5 $ < t < $ 3.5 ps for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 11:
The 2D UML fit projection plots on the mass axis for decay time range 3.5 $ < t < $ 10 ps for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 11a:
The 2D UML fit projection plots on the mass axis for decay time range 3.5 $ < t < $ 10 ps for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 11b:
The 2D UML fit projection plots on the mass axis for decay time range 3.5 $ < t < $ 10 ps for 2016, 2017 and 2018 respectively. 
png pdf 
Figure 11c:
The 2D UML fit projection plots on the mass axis for decay time range 3.5 $ < t < $ 10 ps for 2016, 2017 and 2018 respectively. 
Tables  
png pdf 
Table 1:
Sources of systematic uncertainties in the $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ effective lifetime measurement and their estimated values, along with the total systematic uncertainty. 
Summary 
The effective lifetime of the $ \mathrm{B}_{s}^{0} $ meson in the $ \mathrm{J}/\psi\mathrm{K^0_S} $ decay channel is measured using the data collected during 20162018 by the CMS detector in protonproton collision events at a centerofmass energy of 13 TeV, corresponding to an integrated luminosity of 140 fb$ ^{1} $. Throughout the analysis, the decay $ {\mathrm{B}^0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ with larger event yield is used as a reference at multiple stages validating analysis method. The measured effective lifetime is found to be 1.59 $ \pm $ 0.07 (stat) $ \pm $ 0.03 (syst) ps. This measurement is compatible within 2.1$ \sigma $ with a previous measurement conducted by the LHCb experiment and shows strong agreement with the SM prediction of 1.62 $ \pm $ 0.02 ps. 
References  
1  K. De Bruyn et al.  Branching ratio measurements of $ \mathrm{B}_{s}^{0} $ decays  PRD 86 (2012) 014027  
2  CMS Collaboration  Measurement of the B$ ^0_\mathrm{S} \to \mu^+\mu^ $ decay properties and search for the B$ ^0 \to \mu^+\mu^ $ decay in protonproton collisions at $ \sqrt{s} $ = 13 TeV  PLB 842 (2023) 137955  CMSBPH21006 2212.10311 
3  CMS Collaboration  Measurement of properties of B$ ^0_\mathrm{s}\to\mu^+\mu^ $ decays and search for B$ ^0\to\mu^+\mu^ $ with the CMS experiment  JHEP 04 (2020) 188  CMSBPH16004 1910.12127 
4  CMS Collaboration  Combination of the ATLAS, CMS and LHCb results on the B$ ^0_\mathrm{s}\to\mu^+\mu^ $ decays  LHCbCONF2020002, ATLASCONF2020049, 2020  CMSPASBPH20003 
5  LHCb Collaboration  Measurement of the B$ ^0_\mathrm{s}\to\mu^+\mu^ $ decay properties and search for the B$ ^0\to\mu^+\mu^ $ and B$ ^0_\mathrm{s}\to\mu^+\mu^\gamma $ decays  PRD 105 (2022) 012010  2108.09283 
6  ATLAS Collaboration  Study of the rare decays of $ B^0_s $ and $ B^0 $ mesons into muon pairs using data collected during 2015 and 2016 with the ATLAS detector  JHEP 04 (2019) 098  1812.03017 
7  LHCb Collaboration  Measurement of the $ B_s $ effective lifetime in the $ J/\psi f_0(980) $ final state  PRL 109 (2012) 152002  1207.0878 
8  LHCb Collaboration  Measurement of the effective $ B_s^0 \rightarrow K^+ K^ $ lifetime  PLB 716 (2012) 393  1207.5993 
9  K. De Bruyn, R. Fleischer, and P. Koppenburg  Extracting $ \gamma $ and penguin topologies through CP violation in $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\mathrm{K^0_S} $  EPJC 70 (2010)  1010.0089 
10  R. Fleischer  Extracting $ \gamma $ from $ {\mathrm{B}^0} $ (s/d) $ \to \mathrm{J}/\psi\mathrm{K^0_S} $ and $ {\mathrm{B}^0} $ (d/s) $ \to $ D$ ^+ $(d/s) D$ ^ $(d/s)  EPJC 10 (1999)  hepph/9903455 
11  Particle Data Group Collaboration  Review of particle physics  Prog. Theor. Exp. Phys. 2022 (2022) 083C01  
12  LHCb Collaboration  Measurement of the effective $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\mathrm{K^0_S} $ lifetime  NPB 873 (2013)  1304.4500 
13  CMS Collaboration  Description and performance of track and primaryvertex reconstruction with the CMS tracker  JINST 9 (2014) P10009  CMSTRK11001 1405.6569 
14  CMS Tracker Group Collaboration  The CMS phase1 pixel detector upgrade  JINST 16 (2021) P02027  2012.14304 
15  CMS Collaboration  Track impact parameter resolution for the full pseudo rapidity coverage in the 2017 dataset with the CMS phase1 pixel detector  CMS Detector Performance Summary CMSDP2020049, 2020 CDS 

16  CMS Collaboration  The CMS experiment at the CERN LHC  JINST 3 (2008) S08004  
17  CMS Collaboration  Performance of the CMS Level1 trigger in protonproton collisions at $ \sqrt{s} = $ 13 TeV  JINST 15 (2020) P10017  CMSTRG17001 2006.10165 
18  CMS Collaboration  The CMS trigger system  JINST 12 (2017) P01020  CMSTRG12001 1609.02366 
19  CMS Collaboration  Precision luminosity measurement in protonproton collisions at $ \sqrt{s}= $ 13 TeV in 2015 and 2016 at CMS  EPJC 81 (2021) 800  CMSLUM17003 2104.01927 
20  CMS Collaboration  CMS luminosity measurement for the 2017 datataking period at $ \sqrt{s} = $ 13 TeV  CMS Physics Analysis Summary, 2018 link 
CMSPASLUM17004 
21  CMS Collaboration  CMS luminosity measurement for the 2018 datataking period at $ \sqrt{s} = $ 13 TeV  CMS Physics Analysis Summary, 2019 link 
CMSPASLUM18002 
22  T. Sjöstrand et al.  An introduction to PYTHIA 8.2  Comput. Phys. Commun. 191 (2015) 159  1410.3012 
23  D. J. Lange  The EvtGen particle decay simulation package  NIM A 462 (2001) 152  
24  GEANT4 Collaboration  GEANT 4  a simulation toolkit  NIM A 506 (2003) 250  
25  CMS Collaboration  Performance of the CMS muon detector and muon reconstruction with protonproton collisions at $ \sqrt{s}= $ 13 TeV  JINST 13 (2018)  CMSMUO16001 1804.04528 
26  P. B. Rodríguez et al.  Calibration of the momentum scale of a particle physics detector using the ArmenterosPodolanski plot  JINST 16 (2021)  2012.03620 
27  L.G. Xia  Understanding the boosted decision tree methods with the weaklearner approximation  
28  N. L. Johnson  Systems of frequency curves generated by methods of translation  Biometrika 36 (1949) 149  
29  S. Jackman  Bayesian analysis for the social sciences  John Wiley & Sons, New Jersey, USA, 2009 link 
Compact Muon Solenoid LHC, CERN 