Prospects for angular analyses of $B_s^0 \rightarrow \phi \mu^+\mu^-$ decays at hadron colliders

Rare decays of beauty hadrons to strange hadrons and dilepton pairs provide powerful probes of the Standard Model (SM), where long-standing tensions between experimental measurements and theoretical predictions persist. This talk presents the prospects for performing time-dependent angular analyses of $B_s^0 \rightarrow \phi \mu^+\mu^-$ decays at hadron colliders, explicitly formulating the full time-dependent angular probability density function for this decay. Additionally, key observables are identified that can be accessed only in the $B_s^0$ system, owing to the $CP$-eigenstate nature of the final state, and have reduced sensitivity to hadronic form-factors. The expected sensitivities to these observables are estimated using realistic pseudoexperiments for various milestones of data taking at a dedicated flavour-physics experiment at a hadron collider. The results are interpreted as constraints on short-distance Wilson coefficients describing potential New Physics effects.