The Revival of $U(1)_{L_e-L_\mu}$: A Natural Solution for $(g-2)_\mu$ with a Sub-GeV Dark Matter

The experiments searching for a hidden gauge sector with a leptophilic neutral gauge boson have already ruled out $U(1)_{L_e-L_\mu}$ as a feasible extension of the Standard Model (SM) gauge group ($\mathcal{G}_{\rm SM}$) for explaining the observed discrepancy in $(g-2)_\mu$. The paper proposes a simple extension of the minimal particle content of $\mathcal{G}_{\rm SM}\otimes U(1)_{L_e-L_\mu}$ with a TeV-scale scalar leptoquark $S_1$. Due to the non-trivial transformation of $S_1$ under $U(1)_{L_e-L_\mu}$, the model generates additional one-loop contributions to $(g-2)_\mu$, reviving the considered gauge extension within the experimentally allowed regions of the parameter space. The model can also accommodate a viable Dark Matter (DM) candidate $\chi$ -- a vector-like SM-singlet fermion in the sub-GeV mass regime. The theory provides a natural framework to test the proposed DM phenomenology through electron excitation signals. Moreover, the DM-specific observables and $(g-2)_\mu$ being connected through the New Physics (NP) parameters, the future beam dump experiments hunting for light, feebly interacting particles and the DM direct detection experiments are complementary to each other for constraining/falsifying the model.