Prospects for Measuring $CP$-Violation in $B_s^0\to \varphi {\mu }^{+}{\mu }^{-}$ via Time-Dependent Angular Analysis

Abstract

This work investigates the prospects for performing a time-dependent angular analysis of $B_s^0\to \varphi {\mu }^{+}{\mu }^{-}$ decays at hadron colliders, and introduces new optimised angular observables associated with $B_s^0$-mixing in the decay rate. The time-dependent normalised decay rate and corresponding probability density function is presented both for when the flavour of the $B_s^0$ meson at production is tagged and when it is untagged. The normalised angular terms linked to $B_s^0$-mixing in the tagged (untagged) case are denoted ${\mathcal{Z}}_i$ (${\mathcal{H}}_i$), and their optimised counterparts as $Q_i$ (${\mathcal{M}}_i$). The expected sensitivities of these observables at the end of Run 3, Run 4, and Run 5 of the LHC are determined using pseudoexperiments generated with a decay-time resolution, background level, and signal yield similar to those reported by the LHCb collaboration. It is found that all observables can be extracted with Run 3 statistics, and that the ${\mathcal{H}}_i$ and ${\mathcal{Z}}_i$ observables have similar sensitivity, despite the former being suppressed by mixing terms. Moreover, the angular observables only accessible via flavour tagging, such as the equivalent of $P_5^{\prime }$ in the $B_s^0$ system, are found to exhibit sensitivities comparable to current measurements in $B^0\to K^{\ast 0}{\mu }^{+}{\mu }^{-}$ decays once Run 5 datasets are available. Fits to the observables to extract the Wilson coefficients show a significant increase in precision when either the observables accessible via time-dependent analysis, or flavour tagging, are included. A marked increase in sensitivity to $CP$-violating short-distance effects is observed for a subset of the new optimised $M_i$ and $Q_i$ observables.