Motivated by recent anomalies in observables associated with flavor-changing neutral current (FCNC) transitions, specifically $b \rightarrow s \ell^+ \ell^-$ processes, we present a comprehensive analysis of lepton flavor-violating (LFV) decay modes mediated by $b \rightarrow s \ell_1 \ell_2$ transitions with $\ell_1 \neq \ell_2$. While such LFV processes are forbidden within the Standard Model (SM), they naturally arise in several of its extensions, including models featuring additional vector-like fermions and extra $Z'$ bosons. Employing the most general effective Hamiltonian for $b \rightarrow s \ell_1 \ell_2$ transitions, we derive the angular distributions of the relevant decay modes. Adopting a model-independent framework, we systematically study the LFV decays $B \rightarrow K^* \ell_1 \ell_2$, $B_s \rightarrow \phi \ell_1 \ell_2$, $B \rightarrow K_2^* \ell_1 \ell_2$, and $\Lambda_b \rightarrow \Lambda \ell_1 \ell_2$. Although LFV mesonic decays have been widely explored, the corresponding baryonic decays remain comparatively under-investigated. We provide bounds on branching ratio ($\mathcal{ B}$), forward-backward asymmetry ($\mathcal{ A}_{ FB}$), and longitudinal lepton polarization fraction ($\mathcal{ F}_L$). Furthermore, considering the projected sensitivities of the LHCb upgrade and Belle II experiments, we estimate upper limits for these observables, offering promising avenues for probing new physics in these LFV channels.
Categories: hep-ph