Electroweak Radiative Corrections to Parity-Violating Electron-Nucleus Scattering

Parity-violating electron-scattering provides a largely model independent way of measuring neutron densities in nuclei that has important implications for the structure of nuclei and neutron stars. In this paper we calculate radiative corrections to the parity-violating asymmetry $A_{\rm pv}$ in electron-nucleus scattering including vertex and vacuum polarization contributions. We find large cancellations between the vertex corrections to the vector and axial-vector vertices. As a result the total radiative correction in 2nd Born approximation is dominated by vacuum polarization and is of order -0.5\%. Coulomb distortions have modest effects on radiative corrections for $^{12}$C and $^{48}$Ca nuclei. For $^{208}$Pb Coulomb distortions reduce the total radiative correction to only about 0.1\%. Therefore, these corrections are not important for the interpretation of the PREX and MREX experiments on $^{208}$Pb and for the CREX experiment on $^{48}$Ca. However, radiative corrections must be carefully included for a precision measurement of the weak charge of $^{12}$C.