CMS-PAS-BPH-23-004

CMS-PAS-BPH-23-004
Measurement of time-dependent $CP$ violation in $B_s^0 \to \mathrm{J}/\psi\, \phi(1020)$ decays with the CMS detector
CMS Collaboration
8 April 2024

Abstract: A study of $CP$ violation in $B_s^0 \to \mathrm{J}/\psi\, \phi(1020)$ decays is presented, based on the data collected by the CMS experiment at the LHC. The measurement is based on a data sample of roughly 491 000 reconstructed signal events corresponding to an integrated luminosity of 96.5 fb $^{-1}$ , collected in proton-proton collisions at 13 TeV in 2017-2018. A time- and flavor-dependent angular analysis of the $\mu^+ \mu^-\,\mathrm{K}^+ \mathrm{K}^-$ final state is performed to extract the values of the $CP$ -violating phase $\phi_s$ , the decay width difference ( $\Delta\Gamma_s$ ), and absolute mass difference ( $\Delta m_s$ ) between the light and heavy $B_s^0$ mass eigenstates, their average decay width $\Gamma_s$ , and the direct $CP$ violation parameter $\|\lambda\|$ . The analysis utilizes a pioneering inclusive flavor tagging framework based on state-of-the-art machine learning techniques, achieving exceptional performance by exploiting both opposite-side and same-side information. The measurement yields $\phi_s = -$ 73 $\pm$ 23 (stat) $\pm$ 7 (syst) mrad, $\Delta\Gamma_s =$ 0.0761 $\pm$ 0.0043 (stat) $\pm$ 0.0019 (syst) ps $^{-1}$ , $\Delta m_s =$ 17.757 $\pm$ 0.035 (stat) $\pm$ 0.017 (syst) $\ \hslash$ ps $^{-1}$ , $\Gamma_s =$ 0.6613 $\pm$ 0.0015 (stat) $\pm$ 0.0028 (syst) ps $^{-1}$ , and $\|\lambda\| =$ 1.011 $\pm$ 0.014 (stat) $\pm$ 0.012 (syst). These results exhibit a level of precision on par with the most precise single measurements to date and agree with the standard model predictions. A combination with the previous CMS results obtained at 8 TeV is also performed, yielding $\phi_s = -$ 74 $\pm$ 23 mrad and $\Delta\Gamma_s =$ 0.0780 $\pm$ 0.0045 ps $^{-1}$ . The weak phase $\phi_s$ is found different from zero by 3.2 standard deviations, indicating evidences for $CP$ violation in $B_s^0 \to \mathrm{J}/\psi\, \mathrm{K}^+ \mathrm{K}^-$ decays.
Links: CDS record (PDF) ; Physics Briefing ; CADI line (restricted) ; These preliminary results are superseded in this paper, Submitted to PRL. The superseded preliminary plots can be found here.

Figures & Tables	Summary	Additional Figures	References	CMS Publications

Figures
png pdf	Figure 1: Definition of the three angles $\theta_{T}$ , $\psi_{T}$ , and $\varphi_{T}$ describing the $\mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi \to \mu^{+}\mu^{-}\,\mathrm{K^+}\mathrm{K^-}$ decay.
png pdf	Figure 2: The distributions for the input observables of the selected candidates and the projections from the fit for the standard trigger category (2018).
png pdf	Figure 2-a: The distributions for the input observables of the selected candidates and the projections from the fit for the standard trigger category (2018).
png pdf	Figure 2-b: The distributions for the input observables of the selected candidates and the projections from the fit for the standard trigger category (2018).
png pdf	Figure 2-c: The distributions for the input observables of the selected candidates and the projections from the fit for the standard trigger category (2018).
png pdf	Figure 2-d: The distributions for the input observables of the selected candidates and the projections from the fit for the standard trigger category (2018).
png pdf	Figure 2-e: The distributions for the input observables of the selected candidates and the projections from the fit for the standard trigger category (2018).
png pdf	Figure 2-f: The distributions for the input observables of the selected candidates and the projections from the fit for the standard trigger category (2018).
png pdf	Figure 2-g: The distributions for the input observables of the selected candidates and the projections from the fit for the standard trigger category (2018).
png pdf	Figure 3: The two-dimensional one, two, and three standard deviations contours in the $\phi_s$ - $\Delta\Gamma_s$ plane for the combined results. The contours take into account both statistical and systematic uncertainties. The SM prediction is represented by the black rectangle, with the central value indicated with the black diamond [2,3,63]. The dashed line indicates the $\phi_s =$ 0 value, corresponding to no CPV in the $\mathrm{B}_{s}^{0}$ meson decay/mixing interference.

Tables
png pdf	Table 1: Angular and time-dependent terms of the $\mathrm{B}_{s}^{0}$ signal model. The terms for the decay of the $\overline{\mathrm{B}}_{s}^{0}$ meson are obtained by inverting the signs of the $c_i$ and $d_i$ terms.
png pdf	Table 2: Calibrated flavor tagging performance as measured in the $\mathrm{B}_{s}^{0}$ data sample. The effective dilution is obtained from the measured $\varepsilon_{\text{tag}}$ and $P_{\text{tag}}$ . The uncertainties are statistical only.
png pdf	Table 3: Summary of the systematic uncertainties. The dashes ( $\text{---}$ ) mean that the corresponding uncertainty is not assigned. The total systematic uncertainty is obtained as the quadratic sum of the individual contributions.
png pdf	Table 4: Results of the fit to data for the main physics parameters.

Summary

The

$CP$ violating phase

$\phi_s$ is measured by analyzing a total of 491 270

$\pm$ 950

$\mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) \to \mu^{+}\mu^{-}\,\mathrm{K^+}\mathrm{K^-}$ signal events, recorded by the CMS experiment at the LHC in proton-proton collisions at

$\sqrt{s} =$ 13 TeV, representing an integrated luminosity of 96.5 fb

$^{-1}$ . The study employs an innovative inclusive flavor tagging framework that relies on cutting-edge machine learning methods. This novel framework achieves excellent performance by leveraging information from both opposite-side and same-side techniques, corresponding to a tagging power of

${\approx}$ 5.6%. The CPV phase

$\phi_s$ is measured to be

$-$ 73

$\pm$ 23 (stat)

$\pm$ 7 (syst) mrad. In addition, the decay width and absolute mass differences

$\Delta\Gamma_s$ and

$\Delta m_s$ between the light and heavy

$\mathrm{B}_{s}^{0}$ mass eigenstates, their average decay width

$\Gamma_s$ , and the direct

$CP$ violation parameter

$|\lambda|$ , have been measured. All measured values are in agreement with their theoretical predictions and world-average values. The results presented in this Note are combined our previous measurement at

$\sqrt{s} =$ 8 TeV [11], yielding

$\phi_s = -$ 74

$\pm$ 23 mrad, consistent with the SM prediction and indicating evidences for CPV in

$\mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\mathrm{K^+}\mathrm{K^-}$ . The combined results superseed those from the previous CMS measurements and are comparable in precision to the world's most precise single measurements, reported by the LHCb Collaboration [17].

Additional Figures
png pdf	Additional Figure 1: The $ct$ uncertainty calibration fits for the 2018 data sample. The measured effective $ct$ resolution is reported on the $y$ -axis, while the average value of $\sigma_{ct}$ in the various bins is reported on the $x$ -axis. The fit results are shown with a solid red line. The error bars in the x-axis represent the bins' edges and are not used in the fit.
png pdf	Additional Figure 2: Proper decay length distribution in prompt events for the 2018 data sample. The solid blue line represents the fit to data used to calibrate the PDL resolution. The long-lived components are shown in red, while the components of the resolution function are shown in green. The resolution is modeled with two gaussian distributions.
png pdf	Additional Figure 3: PDL efficiency in the muon-tagging (left) and standard (right) trigger categories for 2018 data. The red line represents the efficiency function fit. All corrections are applied.
png pdf	Additional Figure 3-a: PDL efficiency in the muon-tagging (left) and standard (right) trigger categories for 2018 data. The red line represents the efficiency function fit. All corrections are applied.
png pdf	Additional Figure 3-b: PDL efficiency in the muon-tagging (left) and standard (right) trigger categories for 2018 data. The red line represents the efficiency function fit. All corrections are applied.
png pdf	Additional Figure 4: Results of the mistag probability calibration fit for the OS-muon tagger on ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+}$ decays from data. The solid red line shows the calibration fit to data (solid markers). The left plot refers to the muon-tagging trigger category (2018), while the right plot to standard one (2018).
png pdf	Additional Figure 4-a: Results of the mistag probability calibration fit for the OS-muon tagger on ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+}$ decays from data. The solid red line shows the calibration fit to data (solid markers). The left plot refers to the muon-tagging trigger category (2018), while the right plot to standard one (2018).
png pdf	Additional Figure 4-b: Results of the mistag probability calibration fit for the OS-muon tagger on ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+}$ decays from data. The solid red line shows the calibration fit to data (solid markers). The left plot refers to the muon-tagging trigger category (2018), while the right plot to standard one (2018).
png pdf	Additional Figure 5: Results of the mistag probability calibration fit for the OS-electron tagger on ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+}$ decays from 2018 data. The solid red line shows the calibration fit to data (solid markers).
png pdf	Additional Figure 6: Results of the mistag probability calibration fit for the OS-jet tagger on ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+}$ decays from 2018 data. The solid red line shows the calibration fit to data (solid markers).
png pdf	Additional Figure 7: Results of the mistag probability calibration fit for the Same-Side tagger on ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+}$ decays from 2018 data. The solid red line shows the calibration fit to data (solid markers). Events with score between 0.46 and 0.54 are considered untagged and not used for the calibration.
png pdf	Additional Figure 8: Comparison of the calibration curves before (black, ${\mathrm{B}^{+}}$ ) and after (red, $\mathrm{B}_{s}^{0}$ ) the application of the corrections from simulation to the calibration obtained in ${\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+}$ decays. The plot refers to 2018 data. The red function is the one used as calibration for the CPV measurement.
png pdf	Additional Figure 9: The ${\mathrm{B}^0}$ mixing asymmetry as a function of the proper decay length as measured in the ${\mathrm{B}^0} \to \mathrm{J}/\psi\,\mathrm{K}^{*}(892)^{0}$ control data sample as a validation to the tagging framework.
png pdf	Additional Figure 10: The ${\mathrm{B}^0}$ mixing asymmetry as a function of the proper decay length as measured in the ${\mathrm{B}^0} \to \mathrm{J}/\psi\,\mathrm{K}^{*}(892)^{0}$ control data sample in the different tagging categories. Top row, from left to right: only OS muon (muon-tagging trigger category), only OS muon (standard trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only Same Side, SS + OS muon, SS + OS electron, and SS + OS jet. All categories are mutually exclusive.
png pdf	Additional Figure 10-a: The ${\mathrm{B}^0}$ mixing asymmetry as a function of the proper decay length as measured in the ${\mathrm{B}^0} \to \mathrm{J}/\psi\,\mathrm{K}^{*}(892)^{0}$ control data sample in the different tagging categories. Top row, from left to right: only OS muon (muon-tagging trigger category), only OS muon (standard trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only Same Side, SS + OS muon, SS + OS electron, and SS + OS jet. All categories are mutually exclusive.
png pdf	Additional Figure 10-b: The ${\mathrm{B}^0}$ mixing asymmetry as a function of the proper decay length as measured in the ${\mathrm{B}^0} \to \mathrm{J}/\psi\,\mathrm{K}^{*}(892)^{0}$ control data sample in the different tagging categories. Top row, from left to right: only OS muon (muon-tagging trigger category), only OS muon (standard trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only Same Side, SS + OS muon, SS + OS electron, and SS + OS jet. All categories are mutually exclusive.
png pdf	Additional Figure 10-c: The ${\mathrm{B}^0}$ mixing asymmetry as a function of the proper decay length as measured in the ${\mathrm{B}^0} \to \mathrm{J}/\psi\,\mathrm{K}^{*}(892)^{0}$ control data sample in the different tagging categories. Top row, from left to right: only OS muon (muon-tagging trigger category), only OS muon (standard trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only Same Side, SS + OS muon, SS + OS electron, and SS + OS jet. All categories are mutually exclusive.
png pdf	Additional Figure 10-d: The ${\mathrm{B}^0}$ mixing asymmetry as a function of the proper decay length as measured in the ${\mathrm{B}^0} \to \mathrm{J}/\psi\,\mathrm{K}^{*}(892)^{0}$ control data sample in the different tagging categories. Top row, from left to right: only OS muon (muon-tagging trigger category), only OS muon (standard trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only Same Side, SS + OS muon, SS + OS electron, and SS + OS jet. All categories are mutually exclusive.
png pdf	Additional Figure 10-e: The ${\mathrm{B}^0}$ mixing asymmetry as a function of the proper decay length as measured in the ${\mathrm{B}^0} \to \mathrm{J}/\psi\,\mathrm{K}^{*}(892)^{0}$ control data sample in the different tagging categories. Top row, from left to right: only OS muon (muon-tagging trigger category), only OS muon (standard trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only Same Side, SS + OS muon, SS + OS electron, and SS + OS jet. All categories are mutually exclusive.
png pdf	Additional Figure 10-f: The ${\mathrm{B}^0}$ mixing asymmetry as a function of the proper decay length as measured in the ${\mathrm{B}^0} \to \mathrm{J}/\psi\,\mathrm{K}^{*}(892)^{0}$ control data sample in the different tagging categories. Top row, from left to right: only OS muon (muon-tagging trigger category), only OS muon (standard trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only Same Side, SS + OS muon, SS + OS electron, and SS + OS jet. All categories are mutually exclusive.
png pdf	Additional Figure 10-g: The ${\mathrm{B}^0}$ mixing asymmetry as a function of the proper decay length as measured in the ${\mathrm{B}^0} \to \mathrm{J}/\psi\,\mathrm{K}^{*}(892)^{0}$ control data sample in the different tagging categories. Top row, from left to right: only OS muon (muon-tagging trigger category), only OS muon (standard trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only Same Side, SS + OS muon, SS + OS electron, and SS + OS jet. All categories are mutually exclusive.
png pdf	Additional Figure 10-h: The ${\mathrm{B}^0}$ mixing asymmetry as a function of the proper decay length as measured in the ${\mathrm{B}^0} \to \mathrm{J}/\psi\,\mathrm{K}^{*}(892)^{0}$ control data sample in the different tagging categories. Top row, from left to right: only OS muon (muon-tagging trigger category), only OS muon (standard trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only Same Side, SS + OS muon, SS + OS electron, and SS + OS jet. All categories are mutually exclusive.
png pdf	Additional Figure 11: Results of the fits when using only one of the four flavor tagging algorithms with respect to the reference fit. Only parameters sensitive to the flavor information are shown. Only statistical uncertainties are considered. The grey area represents the statistical uncertainty of the full fit.
png pdf	Additional Figure 12: The two-dimensional 68.3% CL contours in the $\phi_s$ - $\Delta\Gamma_s$ plane for the combined 8+13 TeV CMS (red), ATLAS (blue) [23], and LHCb (green) [17] results. The LHCb results refer only to $\mathrm{B}_{s}^{0} \to \mathrm{J}/\psi \mathrm{K^+}\mathrm{K^-}$ measurements in the $m(\mathrm{K^+}\mathrm{K^-})$ region of the $\phi(1020)$ resonance. The contours account for both statistical and systematic uncertainties. The SM prediction is represented by the black rectangle [2,3,63]

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