Investigating New Physics through the Observables of Semileptonic <i>Bs</i> → <i>K</i> *(→ <i>K</i> π) <i>μ</i> + <i>μ</i> − Decay

Abstract The rare 4-fold decay $B_s \rightarrow K^{*}(\rightarrow K\pi )\mu ^+\mu ^-$, governed by the flavor-changing neutral current transition $b \rightarrow d\mu ^+\mu ^-$, provides a sensitive probe for testing the Standard Model (SM) and investigating signatures of new physics (NP). This work presents a comprehensive model-independent analysis of the decay using the framework of the weak effective field theory. We compute a set of key physical observables, including the differential branching ratio, forward-backward asymmetry, longitudinal polarization fraction, and several normalized angular coefficients $\langle I_i\rangle$, as a function of the dilepton invariant mass squared $q^2$. The impact of NP is explored via both 1D and 2D scenarios involving NP Wilson coefficients $C_7^{\text{NP}}$, $C_9^{(\prime )\text{NP}}$, and $C_{10}^{(\prime )\text{NP}}$. Our findings reveal notable deviations from the SM predictions across multiple observables. Furthermore, we analyze the correlations between different observables and their 2D contour plots which would be useful to further constrain the parametric space of possible NP contributions. This study reinforces the potential of $B_s \rightarrow K^{*} \mu^{+} \mu^{-}$ decay as a complementary channel in the search for physics beyond the SM.