Dark photon in parity-violating electron scatterings

We proposed that parity-violating electron scattering (PVES) offers a powerful tool to probe the hypothetical dark photon. We calculated the dark photon contributions to PVES asymmetries in both elastic and deep-inelastic scattering (DIS). These contributions are characterised by the corrections to the standard model couplings $C_{1q}, \, C_{2q}$, and $C_{3q}$. At low scales, the corrections to $C_{1q}$ and $C_{3q}$ could be as large as $5\%$ were a dark photon to exist. In DIS at very high $Q^2$, of relevance to HERA or the EIC, the dark photon could induce substantial corrections to $C_{2q}$, suggesting as large as $10\%$ uncertainties in the extraction of valence parton distribution functions. We also extracted the favoured regions of the dark photon parameter space by fitting the parity violation data and the CDF $W$ boson mass, which prefer a heavy dark photon with mass above the $Z$-boson mass.