Penguin $b\to s{\ell }^{\prime +}{\ell }^{\prime -}$ and $B$-meson anomalies in a gauged $L_{\mu }-L_{\tau }$

Abstract

The $Z^{\prime }$-gauge boson in an $U(1{)}_{L_{\mu }-L_{\tau }}$ gauge symmetry has two interesting features: one is its vector couplings to the charged leptons, and the other is the decoupling from the electron. Based on these properties, we investigate the feasibility to simultaneously resolve the $R_{K^{(\ast )}}=BR(B\to K^{(\ast )}{\mu }^{+}{\mu }^{-})/BR(B\to K^{(\ast )}{e}^{+}{e}^{-})$ and $R_{D^{(\ast )}}=BR(\bar{B}\to D^{(\ast )}\tau {\bar{\nu }}_{\tau })/BR(\bar{B}\to D^{(\ast )}\ell {\bar{\nu }}_{\ell })$ anomalies in an $U(1{)}_{L_{\mu }-L_{\tau }}$ model, where the former is expected to arise from the $Z^{\prime }$-penguin-induced $b\to s{\mu }^{+}{\mu }^{-}$ process and the latter from the tree-level $b\to c\tau {\bar{\nu }}_{\tau }$ decay. In order to achieve the intended purpose, we employ one vector-like doublet lepton and one singlet scalar leptoquark (LQ), in which the new particles all carry the $U(1{)}_{L_{\mu }-L_{\tau }}$ charges; the $b\to s{Z}^{\prime }$ effective interaction is generated from the vector-like lepton and LQ loop, and the $b\to c\tau {\bar{\nu }}_{\tau }$ decay is induced from the LQ. When the constraints from the $b\to s\gamma$, $B^{+}\to K^{+}\nu \bar{\nu }$, $B_c^{-}\to \tau {\bar{\nu }}_{\tau }$, $\Delta F=2$, and $\tau \to \mu \ell \bar{\ell }$ processes are included, it is found that $R_D$ and $R_{D^{\ast }}$ can be enhanced to fit the experimental data, and the Wilson coefficient $C_9$ from the LQ-loop can reach $C_9^{LQ,\mu }\sim -1$, which can explain the $R_K$ and $R_{K^{\ast }}$ anomalies. In addition, in this simple model, the Higgs lepton-flavor violating $h\to \mu \tau$ decay can occur at the tree level, and its branching ratio can be as large as the current experimental upper limit.

Comments: 21 pages, 6 figures, 1 table, version published in PLB