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 C1q, \, C2q, and C3q. At low scales, the corrections to C1q and C3q could be as large as $5%$ were a dark photon to exist. In DIS at very high Q², of relevance to HERA or the EIC, the dark photon could induce substantial corrections to C2q, 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.