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

TL;DR

The paper investigates a minimal $U(1)'$ extension of the SM (the ABCD model) with a flavour-violating $Z'$ boson, whose couplings are controlled by four parameters $(M_{Z'}, g_{Z'}, \epsilon_1, \epsilon_2)$ after anomaly cancellation. By rotating fermion states, flavour-violating $Z'$ interactions arise, correlating quark and lepton observables; the analysis focuses on $b\to s\ell_1^-\ell_2^+$ transitions, LFV leptonic decays, and $(g-2)_{e,\mu}$, exploring both lepton flavour conserving and violating modes. The study shows that, under $\Delta F=2$ constraints, NP contributions to $C_9^{\rm NP}$ and $C_{10}^{\rm NP}$ are at the ~10% level of SM values for $\ell=\mu,\tau$, while LFV $B$ decays are tightly constrained by purely leptonic LFV processes, reducing branching fractions to ${\cal O}(10^{-13})$ in some cases. The work highlights nontrivial correlations between quark and lepton sectors that can guide future searches at planned facilities, and demonstrates that leptonic bounds progressively tighten the allowed LFV $B$ decay rates, with the muon channels providing the strongest constraints. Overall, the ABCD framework remains compatible with current data while offering testable predictions for LFV beauty decays and leptonic processes.

Abstract

We consider an abelian extension of the Standard Model (SM) comprising a new gauge group $U(1)^\prime$, with the neutral gauge boson $Z^\prime$ having flavour violating couplings to quarks and leptons. The fermion content is the same as in SM except for the addition of three right-handed neutrinos. The model, proposed in \cite{Aebischer:2019blw}, describes the couplings of $Z^\prime$ to fermions in terms of three rational parameters $ε_{1,2,3}$ that sum to zero imposing the cancellation of the gauge anomalies. Each $ε_i$ is common to all fermions in a generation, a feature producing correlations among quark and lepton observables. We focus on $b \to s \ell_1^- \ell_2^+$ transitions for the lepton flavour conserving $\ell_1=\ell_2$ and lepton flavour violating case $\ell_1 \neq \ell_2$. Small deviations with respect to the SM predictions are found in the first case, which reflects a feature of the model where quark and lepton sectors prevent each other to manifest large discrepancies with respect to SM. We investigate the correlations between rare $B$ and $B_s$ decays and the leptonic processes $τ^- \to μ^- μ^+ μ^-$, $μ^- \to e^- γ$, $μ^- \to e^- e^+ e^-$ and the $ μ^- \to e^-$ conversion in nuclei. We show that the current experimental upper bounds on these four channels play an increasingly important role in constraining the branching fractions of lepton flavour violating $B$ and $B_s$ decays. While the present bound on $τ^- \to μ^- μ^+ μ^-$ does not impose significant restrictions, the other three modes set progressively more stringent limits, an important information for the planned new experimental facilities.

Figures (23)

• Figure 1: Kinematics of the decay $\bar{B}^0 \to \bar{K}^{*0}(K \pi) \ell_1^- \ell_2^+$.
• Figure 2: Allowed region in the $(\epsilon_1,\,\epsilon_2)$ plane after imposing $\Delta F=2$ constraints, for $M_{Z^\prime}=1$ TeV (left panel) and $M_{Z^\prime}=3$ TeV (right panel).
• Figure 3: Allowed region in the $|V_{cb}|,\,|V_{ub}|$ plane after imposing the $\Delta F=2$ constraints (dark blue points) for $M_{Z^\prime}=1$ TeV and $3$ TeV. The light shaded area corresponds to the ranges \ref{['VcbVubRanges']}.
• Figure 4: Correlation between real and imaginary parts of the $Z^\prime$ contributions to the Wilson coefficients $C_9$ (left panels) and $C_{10}$ (right panels) for the LFC $b \to s \mu^- \mu^+$ (top panels) and LFV $b \to s \mu^- \tau^+$ transition (bottom panels). The $Z^\prime$ mass is set to $M_{Z^\prime}=1$ TeV.
• Figure 5: Correlation between real and imaginary parts of the $Z^\prime$ contributions to the Wilson coefficients $C_9$ and $C_{10}$ as in Fig. \ref{['Wilson1000']}, for $M_{Z^\prime}=3$ TeV.