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The $CP$-violating weak phase $\phi_\mathrm{s}$ and the decay widthdifference $\Delta\Gamma_\mathrm{s}$ between the light and heavyB$^0_\mathrm{s}$ mass eigenstates are measured with the CMS detector at the LHCin a sample of 48 500 reconstructed B$^0_\mathrm{s}$ $\to$ J$/\psi\,\phi$(1020) $\to$ $\mu^+\mu^-$K$^+$K$^-$ events. The measurement is based on adata sample corresponding to an integrated luminosity of 96.4 fb$^{-1}$,collected in proton-proton collisions at $\sqrt{s} =$ 13 TeV in 2017-2018. Toextract the values of $\phi_\mathrm{s}$ and $\Delta\Gamma_\mathrm{s}$, atime-dependent and flavor-tagged angular analysis of the $\mu^+\mu^-$K$^+$K$^-$final state is performed. The analysis employs a dedicated tagging trigger anda novel opposite-side muon flavor tagger based on machine learning techniques.The measurement yields $\phi_\mathrm{s} = -$11 $\pm$ 50 (stat) $\pm$ 10 (syst)mrad and $\Delta\Gamma_\mathrm{s} =$ 0.114 $\pm$ 0.014 (stat) $\pm$ 0.007(syst) ps$^{-1}$, in agreement with the standard model predictions. Whencombined with the previous CMS measurement at $\sqrt{s} =$ 8 TeV, the followingvalues are obtained: $\phi_\mathrm{s} = -$21 $\pm$ 44 (stat) $\pm$ 10 (syst)mrad, $\Delta\Gamma_\mathrm{s} =$ 0.1032 $\pm$ 0.0095 (stat) $\pm$ 0.0048(syst) ps$^{-1}$, a significant improvement over the 8 TeV result.

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Measurement of the $CP$-violating phase $\phi_\mathrm{s}$ in the  B$^0_\mathrm{s}$ $\to$ J$/\psi\, \phi$(1020) $\to$ $\mu^+\mu^-$K$^+$K$^-$  channel in proton-proton collisions at $\sqrt{s} =$ 13 TeV