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
The $CP$ violating weak phase $\phi_{\text{s}}$, and the decay width difference $\Delta\Gamma_{\text{s}}$ between the light and heavy $\mathrm{B_s}$ mass eigenstates are measured with the CMS detector at the LHC in a sample of reconstructed $\mathrm{B}_s \to \mathrm{J}/\psi\,\phi(1020) \to \mu^+\mu^-\,\mathrm{K}^+\mathrm{K}^-$ decays. The measurement is based on a data set corresponding to an integrated luminosity of $96.4\;\mathrm{fb}^{-1}$, collected in proton-proton collisions at a center-of-mass energy of $13\;\mathrm{TeV}$ in 2017-2018. To extract the values of $\phi_{\text{s}}$ and $\Delta\Gamma_{\text{s}}$, a time-dependent and flavor-tagged angular analysis of the $\mu^+\mu^-\,\mathrm{K}^+\mathrm{K}^-$ final state is performed. The analysis employs a novel opposite-side muon flavor tagger based on machine learning techniques, which, in conjunction with a dedicated tagging trigger, allowed to reach an unprecedented tagging power. The measurement yields $\phi_{\text{s}} = -0.011 \pm 0.050\,\mathrm{(stat)} \pm 0.010\,\mathrm{(syst)}\;\mathrm{rad}$, and $\Delta\Gamma_{\text{s}} = 0.114 \pm 0.014\,\mathrm{(stat)} \pm 0.007\,\mathrm{(syst)}\;\mathrm{ps}^{-1}$, in agreement with the standard model predictions. When combined with our previous measurement at a center-of-mass energy of 8 TeV, the following values are obtained: $\phi_{\text{s}} = -0.021 \pm 0.045\;\mathrm{rad}$, $\Delta\Gamma_{\text{s}} = 0.1074 \pm 0.0097\;\mathrm{ps}^{-1}$, a significant improvement over the 8 TeV result.
Results of the fit to the data at 13 TeV. Statistical uncertainties are obtained from the increase in $-\log{\mathcal{L}}$ by 0.5.
Values of parameter obtained combining the 13 TeV results with those obtained by CMS at 8 TeV.
Statistical correlation matrix of the physics parameters of interest, as obtained from the fit to data at 13 TeV.
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