CMS-BPH-21-006

CMS-BPH-21-006 ; CERN-EP-2022-270
Measurement of the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decay properties and search for the ${\mathrm{B}^0} \to \mu^{+}\mu^{-}$ decay in proton-proton collisions at $\sqrt{s}=$ 13 TeV
CMS Collaboration
20 December 2022
Phys. Lett. B 842 (2023) 137955
Abstract: Measurements are presented of the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ branching fraction and the $\mathrm{B}_{s}^{0}$ effective lifetime, as well as results of a search for the ${\mathrm{B}^0} \to \mu^{+}\mu^{-}$ decay in proton-proton collisions at $\sqrt{s}=$ 13 TeV at the LHC. The analysis is based on data collected with the CMS detector in 2016-2018 corresponding to an integrated luminosity of 140 fb $^{-1}$ . The branching fraction of the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decay and the effective $\mathrm{B}_{s}^{0}$ meson lifetime are the most precise single measurements to date. No evidence for the ${\mathrm{B}^0} \to \mu^{+}\mu^{-}$ decay has been found. All results are found to be consistent with the standard model predictions and previous measurements.
Links: e-print arXiv:2212.10311 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; Physics Briefing ; CADI line (restricted) ;

Figures & Tables	Summary	Additional Figures	References	CMS Publications

Figures
png pdf	Figure 1: Distributions of the $d_{\text{MVA}}$ output for the 2016a (left), 2016b (center), and 2017-2018 (right) data and the corresponding MC samples. The blue squares represent the weighted simulated distributions using the XGBOOST reweighting method. In the lower panel, the blue squares and red points are the ratio of the data to weighted and not weighted simulated distribution respectively. The MC distributions are normalized to the total number of events in data.
png pdf	Figure 1-a: Distributions of the $d_{\text{MVA}}$ output for the 2016a data and the corresponding MC samples. The blue squares represent the weighted simulated distributions using the XGBOOST reweighting method. In the lower panel, the blue squares and red points are the ratio of the data to weighted and not weighted simulated distribution respectively. The MC distributions are normalized to the total number of events in data.
png pdf	Figure 1-b: Distributions of the $d_{\text{MVA}}$ output for the 2016b data and the corresponding MC samples. The blue squares represent the weighted simulated distributions using the XGBOOST reweighting method. In the lower panel, the blue squares and red points are the ratio of the data to weighted and not weighted simulated distribution respectively. The MC distributions are normalized to the total number of events in data.
png pdf	Figure 1-c: Distributions of the $d_{\text{MVA}}$ output for the 2017-2018 data and the corresponding MC samples. The blue squares represent the weighted simulated distributions using the XGBOOST reweighting method. In the lower panel, the blue squares and red points are the ratio of the data to weighted and not weighted simulated distribution respectively. The MC distributions are normalized to the total number of events in data.
png pdf	Figure 2: The distribution of the ${\mathrm{B}}$ meson $p_{\mathrm{T}}$ after the sPlot background subtraction in data (points with error bars) and simulation (hatched histogram) for ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ (left) and $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ (right) events. The MC distributions are normalized to the total number of events in data.
png pdf	Figure 2-a: The distribution of the ${\mathrm{B}}$ meson $p_{\mathrm{T}}$ after the sPlot background subtraction in data (points with error bars) and simulation (hatched histogram) for ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ events. The MC distributions are normalized to the total number of events in data.
png pdf	Figure 2-b: The distribution of the ${\mathrm{B}}$ meson $p_{\mathrm{T}}$ after the sPlot background subtraction in data (points with error bars) and simulation (hatched histogram) for $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ events. The MC distributions are normalized to the total number of events in data.
png pdf	Figure 3: The projections on the dimuon mass axis of the fit to the branching fraction for the $d_{\text{MVA}} >$ 0.99 (left) and 0.99 $> d_{\text{MVA}} >$ 0.90 (right) categories. The solid blue curves represent the corresponding projections of the final fit model, while the individual components of the fit are represented by the dashed curves (backgrounds) and hatched histograms (signals).
png pdf	Figure 3-a: The projection on the dimuon mass axis of the fit to the branching fraction for the $d_{\text{MVA}} >$ 0.99 category. The solid blue curves represent the corresponding projections of the final fit model, while the individual components of the fit are represented by the dashed curves (backgrounds) and hatched histograms (signals).
png pdf	Figure 3-b: The projection on the dimuon mass axis of the fit to the branching fraction for the 0.99 $> d_{\text{MVA}} >$ 0.90 category. The solid blue curves represent the corresponding projections of the final fit model, while the individual components of the fit are represented by the dashed curves (backgrounds) and hatched histograms (signals).
png pdf	Figure 4: The profile likelihood as a function of $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ (left) and ${\mathrm{B}^0} \to \mu^{+}\mu^{-}$ (middle) decay branching fractions in 1D (top and middle plots) and in 2D (lower plot). The contours in 2D enclose the regions with 1-5 $\sigma$ coverage, where 1, 2, and 3 $\sigma$ regions correspond to 68.3, 95.4, and 99.7% confidence levels, respectively.
png pdf	Figure 4-a: The profile likelihood as a function of the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decay branching fraction in 1D.
png pdf	Figure 4-b: The profile likelihood as a function of the ${\mathrm{B}^0} \to \mu^{+}\mu^{-}$ decay branching fraction in 1D.
png pdf	Figure 4-c: The profile likelihood as a function of $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ and ${\mathrm{B}^0} \to \mu^{+}\mu^{-}$ decay branching fractions in 2D. The contours enclose the regions with 1-5 $\sigma$ coverage, where 1, 2, and 3 $\sigma$ regions correspond to 68.3, 95.4, and 99.7% confidence levels, respectively.
png pdf	Figure 5: The upper limits on the ${\mathrm{B}^0} \to \mu^{+}\mu^{-}$ decay branching fraction using the $\text{CL}_\text{s}$ method. The dashed line represents the expected median value of the quantity 1 $-$ CL for the background-only hypothesis, while the solid line shows the observed value. The shaded region indicates the $\pm$ 1 $\sigma$ band.
png pdf	Figure 6: The UML fit projection on the decay time axis for the signal region 5.28 $< m_{\mu^{+}\mu^{-}} <$ 5.48 GeV.

Tables
png pdf	Table 1: Selection requirements for the three decay channels used in the signal yield and normalization fits. Addition selection requirements are applied for the ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ control sample used in systematic studies.
png pdf	Table 2: Efficiency corrections for the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decays derived using two different methods: the efficiency ratio between data and simulation, and the XGBOOST reweighting in ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ events. The quoted uncertainties are statistical only.
png pdf	Table 3: Summary of the systematic uncertainties for the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ and ${\mathrm{B}^0} \to \mu^{+}\mu^{-}$ branching fraction measurements.
png pdf	Table 4: Summary of the systematic uncertainties in the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ effective lifetime measurement (in ps) in four data-taking periods.
png pdf	Table 5: The expected event yields for $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ ( $N(\mathrm{B}_{s}^{0})$ ), ${\mathrm{B}^0} \to \mu^{+}\mu^{-}$ ( $N({\mathrm{B}^0})$ ), the combinatorial background ( $N$ (comb) ), the peaking background ( $N$ (peak)), and the semileptonic background ( $N$ (semi)) are summarized for each category (post-fit). The total expected and observed event yields are given in $N$ (total) and Data column, respectively. Regions 0 and 1 refer to the ranges of 0.0-0.7 and 0.7-1.4, respectively, for the $\|\eta\|$ of the most forward muon. The uncertainties are statistical only.

Summary

Measurements of the branching fraction (

$\mathcal{B}$ ) of the

$\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decay and the effective

$\mathrm{B}_{s}^{0}$ meson lifetime in this decay based on a data set of proton-proton collisions at

$\sqrt{s} =$ 13 TeV corresponding to an integrated luminosity of 140 fb

$^{-1}$ have been presented and found to be:

$\mathcal{B} ( \mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-} ) =$ [ 3.83

$^{+0.38}_{-0.36}$ (stat)

$^{+0.19}_{-0.16}$ (syst)

$^{+0.14}_{-0.13}$ (

$f_\mathrm{s}/f_\mathrm{u}$ ) ]

$\times$ 10

$^{-9}$ ,

$\tau =$ 1.83

$^{+0.23}_{-0.20}$ (stat)

$^{+0.04}_{-0.04}$ (syst) ps.

Both measurements are the most precise single measurements to date and consistent with the standard model (SM) predictions and previous measurements within one standard deviation. The relative total uncertainty in

$\mathcal{B}$ is reduced from 23 to 11% compared with the previous CMS measurement [6], based on 2011-2012 and partial 13 TeV data sets, while the central value is found to be somewhat higher. The new analysis applied to the 2016 data used in Ref. [6] yields a central value similar to the original measurement, indicating that the shift in the central value is driven mostly by the new data. The search for the

${\mathrm{B}^0} \to \mu^{+}\mu^{-}$ decay has not revealed a significant event excess with respect to the dominant combinatorial background prediction. The 95% confidence level upper limit on the branching fraction is found to be

$\mathcal{B} ( {\mathrm{B}^0} \to \mu^{+}\mu^{-} ) <$ 1.9

$\times$ 10

$^{-10}$ at 95% CL.

More data will be required to establish its existence and compare the result with the SM predictions. Compared with the latest LHCb measurement [8]

$\mathcal{B} ( \mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-} ) =$ (3.09

$^{+0.46}_{-0.43}$ (stat)

$^{+0.15}_{-0.11}$ (syst) )

$\times$ 10

$^{-9}$ , our result with the combined systematic uncertainty

$\mathcal{B} ( \mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-} ) =$ (3.83

$^{+0.38}_{-0.36}$ (stat)

$^{+0.24}_{-0.21}$ (syst) )

$\times$ 10

$^{-9}$ , is about 1.2 standard deviations higher. These two measurements will shift the world average from its current value of

$\mathcal{B}(\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}) =$ ( 2.69

$^{+0.37}_{-0.35}$ )

$\times$ 10

$^{-9}$ [9] to a larger value, more consistent with the SM prediction, thus reducing the overall tension. The new measurement of the

$\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ branching fraction is an important input to the global fits to the flavor data (e.g., Ref. [23]) in light of the reported

$\mathrm{b} \to \mathrm{s}\ell^+\ell^-$ anomalies (where lepton

$\ell =$ e or

$\mu$ ). The uncertainties in the branching fraction and effective lifetime measurements are dominated by the statistical component, which means that significant improvements can be expected in the precision of future measurements with the LHC Run 3 data. The effective

$\mathrm{B}_{s}^{0}$ meson lifetime measurement in the

$\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decay has achieved a precision comparable with the lifetime difference between the heavy and light

$\mathrm{B}_{s}^{0}$ meson mass eigenstates, thus offering sensitivity to potential beyond-the-SM physics effects in the effective lifetime.

Additional Figures
png pdf	Additional Figure 1: Comparison of the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ branching fraction measurement with the most recent results and the Standard Model.
png pdf	Additional Figure 2: Comparison of the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ branching fraction measurement with the most recent results and the Standard Model.
png pdf	Additional Figure 3: Comparison of the ${\mathrm{B}^0} \to \mu^{+}\mu^{-}$ branching fraction measurement with the most recent results and the Standard Model.
png pdf	Additional Figure 4: Comparison of the ${\mathrm{B}^0} \to \mu^{+}\mu^{-}$ branching fraction measurement with the most recent results and the Standard Model.
png pdf	Additional Figure 5: Comparison of the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ effective lifetime measurement with the most recent results and the Standard Model.
png pdf	Additional Figure 6: Comparison of the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ effective lifetime measurement with the most recent results and the Standard Model.
png pdf	Additional Figure 7: The dimuon mass distribution projection for the branching fraction fit for high purity event category. The blue curves represent the corresponding projections of the final fit model.
png pdf	Additional Figure 8: Simulated ${\mathrm{B}}\to \mathrm{h}^+\mathrm{h}^-$ mass distribution using the nominal event selection.
png pdf	Additional Figure 9: The mass distribution of the ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ decays observed in Run2018 data for events where $\|\eta_{\mu}\| <$ 0.7. The blue curve shows the result of the unbinned maximum likelihood fit. The signal event yield, extracted from the fit, is used for normalization of the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ branching fraction. The selection requirements are optimized for the most precise estimation of the normalization.
png pdf	Additional Figure 10: The mass distribution of the ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ decays observed in Run2018 data for events where $\|\eta_{\mu 1}\| >$ 0.7 or $\|\eta_{\mu 2}\| >$ 0.7. The blue curve shows the result of the unbinned maximum likelihood fit. The signal event yield, extracted from the fit, is used for normalization of the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ branching fraction. The selection requirements are optimized for the most precise estimation of the normalization.
png pdf	Additional Figure 11: The mass distribution of the $\mathrm{B}_{s}^{0}\to\mathrm{J}/\psi\phi(1020)$ decays observed in Run2018 data for events where $\|\eta_{\mu}\| <$ 0.7. The blue curve shows the result of the unbinned maximum likelihood fit. The signal event yield, extracted from the fit, is used for normalization of the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ branching fraction. The selection requirements are optimized for the most precise estimation of the normalization.
png pdf	Additional Figure 12: The mass distribution of the $\mathrm{B}_{s}^{0}\to\mathrm{J}/\psi\phi(1020)$ decays observed in Run2018 data for events where $\|\eta_{\mu 1}\| >$ 0.7 or $\|\eta_{\mu 2}\| >$ 0.7. The blue curve shows the result of the unbinned maximum likelihood fit. The signal event yield, extracted from the fit, is used for normalization of the $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ branching fraction. The selection requirements are optimized for the most precise estimation of the normalization.
png pdf	Additional Figure 13: Ratios of the decay time efficiencies for the tight ( $d_{\text{MVA}} >$ 0.99) and loose ( $d_{\text{MVA}} >$ 0.90) selections observed in Run2016a Data and MC simulations for ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ decays. The difference between the two ratios is used to correct the decay time efficiency for $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decays.
png pdf	Additional Figure 14: Ratios of the decay time efficiencies for the tight ( $d_{\text{MVA}} >$ 0.99) and loose ( $d_{\text{MVA}} >$ 0.90) selections observed in Run2016b Data and MC simulations for ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ decays. The difference between the two ratios is used to correct the decay time efficiency for $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decays.
png pdf	Additional Figure 15: Ratios of the decay time efficiencies for the tight ( $d_{\text{MVA}} >$ 0.99) and loose ( $d_{\text{MVA}} >$ 0.90) selections observed in Run2017 Data and MC simulations for ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ decays. The difference between the two ratios is used to correct the decay time efficiency for $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decays.
png pdf	Additional Figure 16: Ratios of the decay time efficiencies for the tight ( $d_{\text{MVA}} >$ 0.99) and loose ( $d_{\text{MVA}} >$ 0.90) selections observed in Run2018 Data and MC simulations for ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ decays. The difference between the two ratios is used to correct the decay time efficiency for $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decays.
png pdf	Additional Figure 17: The pointing angle distribution for 2017--2018 data and corresponding MC simulation. The blue histogram represent the reweighted MC simulation using the XGBoost reweighting method.
png pdf	Additional Figure 18: The impact parameter significance distribution for 2017--2018 data and corresponding MC simulation. The blue histogram represent the reweighted MC simulation using the XGBoost reweighting method.
png pdf	Additional Figure 19: The impact parameter distribution for 2017--2018 data and corresponding MC simulation. The blue histogram represent the reweighted MC simulation using the XGBoost reweighting method.
png pdf	Additional Figure 20: 3D view of a $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ candidate in Run 2 data. The two red lines correspond to the two muons from the decay. Other curved lines represent charged tracks originating from the same primary vertex as the B candidate. Tracks from other interactions in the event have been removed for clarity.
png pdf	Additional Figure 21: The rho-phi projection of a $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ candidate in Run 2 data. The two red lines correspond to the two muons from the decay. Other curved lines represent charged tracks originating from the same primary vertex as the B candidate. Tracks from other interactions in the event have been removed for clarity.
png pdf	Additional Figure 22: The rho-phi projection of a $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ candidate in Run 2 data zoomed in on the inner tracker regions. The two red lines correspond to the two muons from the decay. Other curved lines represent charged tracks originating from the same primary vertex as the B candidate. Tracks from other interactions in the event have been removed for clarity.
png pdf	Additional Figure 23: The rho-phi proejction of a $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ candidate in Run 2 data zoomed in on the innermost detector regions. The two red lines correspond to the two muons from the decay. Other curved lines represent charged tracks originating from the same primary vertex as the B candidate. Tracks from other interactions in the event have been removed for clarity.
png pdf	Additional Figure 24: Comparison of the pointing angle distributions for ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ and $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decays in MC simulated data using the nominal event selection.
png pdf	Additional Figure 25: Comparison of the pointing angle distributions for ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ and $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decays in MC simulated data with the kaon $p_{\mathrm{T}} >$ 3.0 GeV.
png pdf	Additional Figure 26: Comparison of the pointing angle distributions for ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ and $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decays in MC simulated data with the kaon $p_{\mathrm{T}} <$ 1.5 GeV.
png pdf	Additional Figure 27: The ${\mathrm{B}^0} \to \mu^{+}\mu^{-}$ signal significance distribution for 1000 pseudo data experiments generated with the nominal fit configuration.
png pdf	Additional Figure 28: Comparison of the $d_{\text{MVA}}$ distributions for ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ and $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decays in MC simulated data treating ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ as background.
png pdf	Additional Figure 29: Comparison of the flight length significance distributions for ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ and $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decays in MC simulated data with the kaon $p_{\mathrm{T}} <$ 1.5 GeV.
png pdf	Additional Figure 30: Comparison of the flight length significance distributions for ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ and $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decays in MC simulated data with the kaon $p_{\mathrm{T}} <$ 1.5 GeV scaling the flight length significance by 1.6 for ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\mathrm{K^+}$ events.
png pdf	Additional Figure 31: Distribution of the dimuon mass uncertainty for $\mathrm{B}_{s}^{0} \to\mu^{+}\mu^{-}$ decays in MC simulated data. The first peak corresponds to events with both muons in the central part of the detector, the second one has one central and one forward muons and the last one corresponds to events where both muons are forward.

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