A pioneering machine-learning-based flavor-tagging algorithm combining same-side and opposite-side tagging is used to obtain the equivalent of 27$\,$000 tagged B$^0_\mathrm{s}$$\to$ J/$\psi\, \phi$(1020) decays from pp collisions at $\sqrt{s} =$ 13 TeV, collected by the CMS experiment and corresponding to an integrated luminosity of 96.5 fb$^{-1}$. A time- and flavor-dependent angular analysis of the $\mu^+\mu^-$K$^+$K$^-$ final state is used to measure parameters of the $\mathrm{B}^0_\mathrm{s}$-$\overline{\mathrm{B}}^0_\mathrm{s}$ system. The weak phase is measured to be $\phi_\mathrm{s}$ = $-$73 $\pm$ 23 (stat) $\pm$ 7 (syst) mrad, which, combined with a $\sqrt{s}$ = 8 TeV CMS result, gives $\phi_\mathrm{s}$ = $-$74 $\pm$ 23 mrad. This value differs from zero by 3.2 standard deviations, providing evidence for $CP$ violation in B$^0_\mathrm{s}$$\to$ J/$\psi\,\phi$(1020) decays. All measured physics parameters are found to agree with standard model predictions where available.
Measured values and uncertainties of the main parameters of interest, as obtained from the analysis to data at 13 TeV.
Values and uncertainties of the physics parameters obtained from the combination of the CMS 8 TeV and 13 TeV results using the BLUE method. The uncertainty includes both statistical and systematic sources.
Matrix of the correlations of the statistical uncertainties between pairs of physics parameters, as obtained from the analysis to data at 13 TeV.
The effective lifetime of the B$^0_\mathrm{s}$ meson in the decay B$^0_\mathrm{s}$$\to$ J/$\psi$K$^0_\mathrm{S}$ is measured using data collected during 2016-2018 with the CMS detector in $\sqrt{s}$ = 13 TeV proton-proton collisions at the LHC, corresponding to an integrated luminosity of 140 fb$^{-1}$. The effective lifetime is determined by performing a two-dimensional unbinned maximum likelihood fit to the B$^0_\mathrm{s}$ meson invariant mass and proper decay time distributions. The resulting value of 1.59 $\pm$ 0.07 (stat) $\pm$ 0.03 (syst) ps is the most precise measurement to date and is in good agreement with the expected value.
The measured effective lifetime for the $\mathrm{B}^{0}_{\mathrm{s}} \to \mathrm{J}/{\psi}\,\mathrm{K}^{0}_{\mathrm{S}}$ decay
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