Muonic Force Behind Flavor Anomalies

We develop an economical theoretical framework for combined explanations of the flavor physics anomalies involving muons: $(g-2)_\mu$, $R_{K^{(*)}}$, and $b \to s \mu^+ \mu^-$ angular distributions and branching ratios, that was first initiated by some of us in Ref. [1]. The Standard Model (SM) is supplemented with a lepton-flavored $\mathrm{U}(1)_X$ gauge group. The $\mathrm{U}(1)_X$ gauge boson with the mass of $\mathcal{O}(0.1)$ GeV resolves the $(g-2)_\mu$ tension. A TeV-scale leptoquark, charged under the $\mathrm{U}(1)_X$, carries a muon number and mediates $B$-decays without prompting charged lepton flavor violation or inducing proton decay. We explore the theory space of the chiral, anomaly-free $\mathrm{U}(1)_X$ gauge extensions featuring the above scenario, and identify many suitable charge assignments for the SM$+3\nu_R$ fermion content with the integer charges in the range $X_{F_i} \in [-10,10]$. We then carry out a comprehensive phenomenological study of the muonic force in representative benchmark models. Interestingly, we found models which can resolve the tension without conflicting the complementary constraints, and all of the viable parameter space will be tested in future muonic resonance searches. Finally, the catalog of the anomaly-free lepton-non-universal charge assignments motivated us to explore different directions in model building. We present a model in which the muon mass and the $(g-2)_\mu$ are generated radiatively from a common short-distance dynamics after the $\mathrm{U}(1)_X$ breaking. We also show how to charge a vector leptoquark under $\mathrm{U}(1)_{\mu - \tau}$ in a complete gauge model.