# Neutrino mixing and $R_K$ anomaly in $U(1)_X$ models: a bottom-up approach

## TL;DR

This paper proposes a class of $U(1)_X$ models that simultaneously explain the $R_K$ anomaly and neutrino mixing patterns by assigning specific lepton charges, introducing minimal new particles, and analyzing experimental constraints.

## Contribution

It introduces a bottom-up method to determine $X$-charges in $U(1)_X$ models that address both $R_K$ anomaly and neutrino masses with minimal new particles.

## Key findings

- Identifies parameter space consistent with meson mixing and decay constraints.
- Predicts a $Z'$ boson potentially observable at the LHC.
- Provides a framework linking lepton flavor violation and neutrino physics.

## Abstract

We identify a class of $U(1)_X$ models which can explain the $R_K$ anomaly and the neutrino mixing pattern, by using a bottom-up approach. The different $X$-charges of lepton generations account for the lepton universality violation required to explain $R_K$. In addition to the three right-handed neutrinos needed for the Type-I seesaw mechanism, these minimal models only introduce an additional doublet Higgs and a singlet scalar. While the former helps in reproducing the quark mixing structure, the latter gives masses to neutrinos and the new gauge boson $Z^\prime$. Our bottom-up approach determines the $X$-charges of all particles using theoretical consistency and experimental constraints. We find the parameter space allowed by the constraints from neutral meson mixing, rare $b\to s$ decays and direct collider searches for $Z^\prime$. Such a $Z^\prime$ may be observable at the ongoing run of the Large Hadron Collider with a few hundred fb$^{-1}$ of integrated luminosity.