Possibly heteroclite electron Yukawa coupling and small $\triangle a_μ$ in a hidden Abelian gauge model for neutrino masses

Abstract: We attempt to simultaneously explain the neutrino oscillation data and the observed $(g-2){e,\mu}$ in a hidden gauge $U(1)_X$ model where all the Standard Model(SM) fields are $U(1)_X$ singlets. The minimal version of this model calls for four exotic scalars and two pairs of vector fermions, and all are charged under $U(1)_X$. We carefully consider the experimental limits on charge lepton flavor violation without assuming any flavor symmetry and explore the viable model parameter space. The model can accommodate the neutrino oscillation data for both the normal and the inverted mass ordering while explaining the central value of $\triangle a_e$ by adopting the fine structure constant determined by using either Cesium or Rubidium atoms. However, mainly constrained by the current experimental bound on ${\cal B}(\tau\rightarrow \mu \gamma)$, this model predicts $\triangle a\mu <5.5(8.0)\times 10^{-10}$ for the normal(inverted) neutrino ordering. Moreover, while the muon Yukawa coupling is close to the SM one, we find the magnitude of the electron Yukawa coupling could be one order of magnitude larger than the SM prediction. This abnormal electron Yukawa could be probed in the future FCC-ee collider and plays an essential role in testing flavor physics.