Frugal $U(1{)}_X$ models with non-minimal flavor violation for $b\to s\ell \ell$ anomalies and neutrino mixing

Abstract

We analyze the class of models with an extra $U(1{)}_X$ gauge symmetry that can account for the $b\to s\ell \ell$ anomalies by modifying the Wilson coefficients $C_{9e}$ and $C_{9\mu }$ from their standard model values. At the same time, these models generate appropriate quark mixing, and give rise to neutrino mixing via the Type-I seesaw mechanism. Apart from the gauge boson $Z^{\prime }$, these frugal models only have three right-handed neutrinos for the seesaw mechanism, an additional $SU(2{)}_L$ scalar doublet for quark mixing, and a SM-singlet scalar that breaks the $U(1{)}_X$ symmetry. This set-up identifies a class of leptonic symmetries, and necessitates non-zero but equal charges for the first two quark generations. If the quark mixing beyond the standard model were CKM-like, all these symmetries would be ruled out by the latest flavor constraints on Wilson coefficients and collider constraints on $Z^{\prime }$ parameters. However, we identify a single-parameter source of non-minimal flavor violation that allows a wider class of $U(1{)}_X$ symmetries to be compatible with all data. We show that the viable leptonic symmetries have to be of the form $L_e\pm 3L_{\mu }-L_{\tau }$ or $L_e-3L_{\mu }+L_{\tau }$, and determine the $(M_{Z^{\prime }},g_{Z^{\prime }})$ parameter space that may be probed by the high-luminosity data at the LHC.

26 pages, 6 figures

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