Correlating lepton flavor violating $b \to s$ and leptonic decay modes in a minimal abelian extension of the Standard Model

Abstract

We examine possible correlations between $b \to s \ell_1^- \ell_2^+$ transitions -- both in the lepton flavor conserving ($\ell_1=\ell_2$) and violating case ($\ell_1 \neq \ell_2$) -- and purely leptonic flavor violating decays within the ABCD model [1], a minimal abelian extension of the Standard Model (SM) introducing a new $\text{U}(1)'$ symmetry. The associated neutral $Z'$ boson has generation-dependent, flavor non-universal couplings to SM fermions, governed by three rational parameters $\epsilon_{1,2,3}$, which sum to zero to ensure gauge anomaly cancellation. Each $\epsilon_i$ is common to all fermions of a given generation, thus inducing correlations among quark and lepton observables. For lepton flavor conserving (LFC) processes, only small deviations from SM predictions were found [2], reflecting the mutual constraints between the quark and lepton sectors, which preclude large discrepancies. On the other hand, the model allows tree-level lepton flavor violating (LFV) decays, yielding correlations between LFV $b\to s$ transitions and charged lepton decays. The analysis of such correlations shows that the current experimental upper bounds for the rates of $\tau^- \to \mu^-\mu^+\mu^-$, \ $\mu^-\to e^- \gamma$, \ $\mu^- \to e^- e^+e^-$ and $\mu^- \to e^-$ conversion in nuclei constrain branching ratios of LFV $B_{(s)}$ decays in hierarchical order [2].