Exploring the lepton flavor violating decay modes $b \to s \mu ^{\pm} \tau ^{\mp}$ in SMEFT approach

Abstract

We perform an analysis of the consequences of various new physics operators on the lepton flavor violating (LFV) decay modes mediated through $b \to s \ell _1 \ell _2$ transitions. We scrutinize the imprints of the (pseudo)scalar and axial(vector) operators on the exclusive LFV decay channels $ B_{(s)} \rightarrow (\phi, K^{*}, K_{2}^{*})\ell_{1}\ell_{2}$ and $\Lambda_{b}\rightarrow \Lambda \ell_{1}\ell_{2}$, where $\ell_{1}, \ell_{2}$ represent $\mu$ or $\tau$. The new physics parameters are constrained by using the upper limits of the branching fractions of the $B \to \tau \mu$ and $B \to K \tau \mu$ processes, assuming the new physics couplings to be real. We then explore the key observables such as the branching fraction, the forward-backward asymmetry, and the longitudinal polarisation fraction of the $B \to (K^*, \phi, K_2^*) \tau ^{\pm} \mu ^{\mp}$ decays. In addition, we also investigate the impact of the new physics couplings on the baryonic $\Lambda _b \to \Lambda \tau ^{\pm} \mu ^{\mp}$ decay channels mediated by the $b \to s$ quark level transition. With the experimental prospects at LHCb upgrade and Belle II, we also predict the upper limits of the above-discussed observables, which could intrigue the new physics search in these channels.