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

TL;DR

The paper analyzes a minimal SM extension, the ABCD model, which adds a generation-dependent $U(1)^ extprime$ leading to a new $Z^\prime$ boson with flavour-violating couplings. Anomaly cancellation enforces relations among quark and lepton charges via rational parameters $\epsilon_i$, inducing correlations across quark and lepton observables and enabling tree-level LFV. Focusing on $b \to s \ell_1^+ \ell_2^-$ transitions, the study computes NP contributions to Wilson coefficients and explores LFV constraints, finding modest deviations in flavour-conserving channels ($\sim$10% in ${\rm Re}(C_9^{\rm NP})$, ${\rm Re}(C_{10}^{\rm NP})$) while LFV processes impose strong bounds that strongly constrain LFV B decays. The work highlights predictive correlations between LFC and LFV observables and between leptonic LFV processes and LFV $B$ decays, with clear experimental signatures for ongoing and future flavour experiments.

Abstract

We study $b \to s \ell_1^+ \ell_2^-$ 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 $U(1)^\prime$ component. The fermion $U(1)^\prime$ 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 $Z^\prime$ 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 $τ^- \to μ^- μ^+ μ^-$, $μ^- \to e^- γ$, $μ^- \to e^- e^+ e^-$ and the $ μ^- \to e^-$ conversion in nuclei play a hierarchical role in constraining the branching fractions of lepton flavour violating $B$ and $B_s$ decays.

Figures (4)

• Figure 1: Angular $P$-observables for the mode $\bar{B}^0 \to \bar{K}^{*0} (K \pi) \mu^+ \mu^-$. The black dots correspond to LHCb measurement LHCb:2020lmf.
• Figure 2: Correlation between the branching fractions ${\bar{\cal B}}(B_s \to \mu^+ \mu^-)$ and ${\bar{\cal B}}(B_s \to \tau^+ \mu^-)$ (left panel) and ${\cal B}(\bar{B}^0 \to \bar{K}^{*0} \mu^+ \mu^-)$ and ${\cal B}(\bar{B}^0 \to \bar{K}^{*0} \mu^+ \tau^-)$ (right panel) for $M_{Z^\prime}=1$ TeV, obtained after imposing $\Delta F=2$ constraints. The shaded vertical band corresponds to the experimental world averages Navas:PDG.
• Figure 3: Correlation between ${\bar{\cal B}}(B_s \to \tau^+ \mu^-)$ and ${\cal B}(\bar{B}^0 \to \bar{K}^{*0} \tau^+ \mu^-)$ when the constraints from LFV charged lepton decay modes are subsequently imposed as specified in the legenda, for $M_{Z^\prime}=1$ TeV (left panel) and $M_{Z^\prime}=3$ TeV (right panel).
• Figure 4: Correlation between ${\cal B}(\mu^- \to e^- e^+ e^-)$ and ${\cal B}(\mu^- \to e^- \gamma)$ (top panels) and between ${\cal B}(\mu^- \to e^- e^+ e^-)$ and ${\cal B}(\tau^- \to \mu^- \mu^+ \mu^-)$ (bottom panels), for $M_{Z^\prime}=1$ TeV (left panel) and $M_{Z^\prime}=3$ TeV (right panel). The gray band corresponds to the upper bound ${\cal B}(\mu^- \to e^- e^+ e^-)<1 \times 10^{-12}\,\, (\rm{at}\, 90\% \, {\rm CL})$SINDRUM1988Navas:PDG.