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 (${\ell }_1\ne {\ell }_2$) -- and purely leptonic flavor violating decays within the ABCD model [1], a minimal abelian extension of the Standard Model (SM) introducing a new $\text{U}(1{)}^{\prime }$ symmetry. The associated neutral $Z^{\prime }$ boson has generation-dependent, flavor non-universal couplings to SM fermions, governed by three rational parameters ${ϵ}_{1,2,3}$, which sum to zero to ensure gauge anomaly cancellation. Each ${ϵ}_i$ 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].

Comments: LaTeX, 8 pages, 4 figures. Talk given at WIFAI 2025, Bari, November 11-14