Analysis of the semileptonic $B_c\to D_s^*\mu^+ \mu^-$ decay mode in the effective field theory approach

Discrepancies have been noted between experimental measurements and Standard Model predictions for various observables related to the $B\to(K, K^*,\phi) ll$ processes. Recently, the Belle-II Collaboration observed a $2.8\sigma$ deviation from Standard Model predictions in the branching ratio of the $B \to K \nu_l \bar{\nu_l}$ decay mode. In this context, we investigate the exclusive semileptonic $B_c\to D_s^{*}\mu^+ \mu^-$ decay mode, mediated by $b\to s$ quark level transition, using Effective Field Theory formalism. We perform a global fit to the new parameters using existing experimental data on $b \to s \mu^+ \mu^-$. We then estimate the branching ratio and other observables such as forward-backward asymmetry, lepton polarisation asymmetry, and the lepton non-universality parameter of the $B_c\to D_s^{(*)}\mu^+ \mu^-$ process. Although this process has not yet been detected experimentally, we offer predictions and discuss the observables for $B_c\to D_s^{*}\mu^+ \mu^-$ in both the Standard Model and potential new physics scenarios.