Quark-lepton correlations in gauge anomaly free abelian extension of the Standard Model

Abstract: We study $b \to s \ell_1⁺ \ell_2<sup>-$ transitions, both for the lepton flavour conserving $\ell_1=\ell_2$ and violating case $\ell_1 \neq \ell_2$, in a minimal extension of the Standard Model proposed in [1]. In this framework, the Standard Model (SM) gauge group is enlarged by a new $U(1)<sup>\prime$ component. The fermion $U(1)<sup>\prime$ charges are assigned in a generation-dependent way, and involve three rational parameters $ε_{1,2,3}$ summing to zero by the condition of cancellation of the gauge anomalies. Each $ε_i$ is common to all fermions in a generation, which produces correlations among quark and lepton observables. The new neutral gauge boson $Z<sup>\prime$ has flavour violating couplings to quarks and leptons. For SM allowed processes, small deviations with respect to the SM predictions are found: this is a consequence of a feature of the model where quark and lepton sectors preclude each other large deviations from SM. Lepton flavour violating processes are allowed at tree-level. The experimental upper bounds for the rates of the processes $$τ^- \to μ^- μ⁺ μ<sup>-$$, $μ^- \to e^- γ$, $$μ^- \to e^- e⁺ e<sup>-$$ and the $μ^- \to e<sup>-$ conversion in nuclei play a hierarchical role in constraining the branching fractions of lepton flavour violating $B$ and $B_s$ decays.