Flavor Anomalies Accommodated in A Flavor Gauged Two Higgs Doublet Model

The $3.1\sigma$ $R_K$ anomaly after Moriond 2021 and $3.3\sigma$ $\Delta a_\mu$ from Fermilab Muon g-2 experiment implicate that the lepton flavor universality violation (LFUV) may play a role in the exploration of new physics. A Flavor Gauged Two-Higgs Doublet Model (FG2HDM) is proposed and investigated in this work. To get rid of the the redundancy in Yukawa coupling of 2HDM-III, a specific U(1) flavor symmetry is introduced. The charge difference between two scalar doublet forbid the appearance of pseudoscalar and hence there are only three particles (a charged and neutral heavy scalar together with a neutral gauge boson) adding to SM particle spectrum. The heavy neutral scalar-mediated flavor-changing interactions occur among down-type quarks. With obvious difference from 2HDM-II, the charged Higgs in FG2HDM can naturally explain $R_{D^{(\ast )}}$ anomaly. The heavy neutral vector boson $Z^{\mathrm{\prime }}$, changing flavor for down-type quark uniquely as well, provides a solution to $R_{K^{(\ast )}}$. The anomalous magnetic dipole moment (AMDM) of muon and electron, especially the new released $\mathrm{\Delta }{a}_{\mu }$, can further discriminate $Z^{\mathrm{\prime }}$ parameter space.