Investigating New Physics through the Observables of Semileptonic $B_{s}\to K^{\ast}(\to K π)μ^{+}μ^{-}$ Decay

TL;DR

This work performs a comprehensive, model-independent analysis of the rare decay $B_s\to K^{*}(\to K\pi)\,\mu^+\mu^-$ within the weak effective theory framework for the quark transition $b\to d\mu^+\mu^-$. It computes differential observables such as the differential branching ratio, forward-backward asymmetry, longitudinal $K^{*}$ polarization, and normalized angular coefficients $\langle I_i\rangle$ using form factors from SSE fits to LCSR and lattice data, while exploring NP via 1D and 2D Wilson coefficient scenarios. The study emphasizes correlations and contour plots to constrain NP parameter space and demonstrates notable deviations from SM predictions across several observables, highlighting the potential of this channel as a complementary probe for new physics. By mapping observable sensitivities to NP WCs and providing semi-analytical expressions, the work offers a robust framework for interpreting upcoming measurements at Belle II and LHCb in the $b\to d$ sector.

Abstract

The rare four-fold decay $B_s \to K^*(\to Kπ)μ^+μ^- $, governed by the flavor-changing neutral current transition $b \to dμ^+μ^-$, 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 one-dimensional (1D) and two-dimensional (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 $B_s \to K^* μ^+ μ^-$ decay as a complementary channel in the search for physics beyond the SM.

Figures (13)

• Figure 1: Kinematics of the $B_{s}\to K^{\ast}(\to K\pi)l^{+}l^{-}$ decay.
• Figure 2: Different observables of $B_s \to K^*(\to K\pi)\mu^+\mu^-$ decay in the SM and in 1D NP scenarios. The first and the second columns show (from top to bottom) the differential branching ratio $\mathrm{d}B/\mathrm{d}q^2$, the $A_{\mathrm{FB}}$, $f_L$ as functions of the squared dilepton mass $q^2$$(\text{GeV}^2)$ and of WCs ($C_i=C_{9,10}^{(')NP}$), respectively. While the third column displays the variation in their values by different colors bar due to $1\sigma$ and $2\sigma$ parametric ranges of 1D NP WCs.
• Figure 3: The angular coefficients $\langle I_{1s} \rangle$, $\langle I_{1c} \rangle$, $\langle I_{2s} \rangle$, and $\langle I_{2c} \rangle$ for $B_s \to K^*(\to K\pi)\mu^+\mu^-$ where the remaining description is the same as describe in caption of Fig. \ref{['Fig1']}.
• Figure 4: The angular coefficients $\langle I_{3} \rangle$, $\langle I_{4} \rangle$, $\langle I_{5} \rangle$, and $\langle I_{6s} \rangle$ for $B_s \to K^*(\to K\pi)\mu^+\mu^-$ where the remaining description is the same as describe in the caption of Fig. \ref{['Fig1']}.
• Figure 5: Correlations between $A_{\text{FB}}$ and different observables of $B_s \to K^*(\to K\pi)\mu^+\mu^-$ decay in SM and in 1D NP scenarios.