First evidence for mixing-induced $CP$ violation in B${}_{\mathrm{s}}^0$ $\to$ J/$\psi \phi$(1020) decays in pp collisions at $\sqrt{s}=$ 13 TeV

A novel machine-learning-based flavor-tagging algorithm combining same-side and opposite-side tagging is used to obtain the equivalent of 27$$000 tagged B${}_{\mathrm{s}}^0$ $\to$ 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, consistent with a $\phi$(1020) $\to$ K${}^{+}$K${}^{-}$ decay, is used to measure parameters of the ${\mathrm{B}}_{\mathrm{s}}^0-{\bar{\mathrm{B}}}_{\mathrm{s}}^0$ system. The weak phase is measured to be ${\phi }_{\mathrm{s}}$ = $-$73 $\pm$ 22 (stat) $\pm$ 10 (syst) mrad, which, combined with the $\sqrt{s}$ $=$ 8 TeV CMS result, gives ${\phi }_{\mathrm{s}}$ = $-$75 $\pm$ 23 mrad. This value differs from zero by 3.2 standard deviations, providing the first evidence for mixing-induced $CP$ violation in B${}_{\mathrm{s}}^0$ $\to$ J/$\psi \phi$(1020) decays. All measured physics parameters are found to agree with standard model predictions where available.