Explaining $g_{\mu}-2$ and $R_{K^{(*)}}$ using the light mediators of $U(1)_{T3R}$

Scenarios in which right-handed light Standard Model fermions couple to a new gauge group, $U(1)_{T3R}$ can naturally generate a sub-GeV dark matter candidate. But such models necessarily have large couplings to the Standard Model, generally yielding tight experimental constraints. We show that the contributions to $g_\mu-2$ from the dark photon and dark Higgs largely cancel out in the narrow window where all the experimental constraints are satisfied, leaving a net correction which is consistent with recent measurements from Fermilab. These models inherently violate lepton universality, and UV completions of these models can include quark flavor violation which can explain $R_{K^{(\ast)}}$ anomalies as observed at the LHCb experiment after satisfying constraints on $Br(B_s\rightarrow\mu\mu)$ and various other constraints in the allowed parameter space of the model. This scenario can be probed by FASER, SeaQuest, SHiP, LHCb, Belle, etc.