QED medium effects in (anti)neutrino-nucleus and electron-nucleus scattering: Elastic scattering on nucleons

Interpretation of current and future neutrino oscillation electron scattering experiments requires knowledge lepton-nucleon lepton-nucleus interactions at the percent level. We study exchange photons between charged particles nuclear medium for (anti)neutrino-, electron-, muon-induced reactions inside a large nucleus. While quantum electrodynamics (QED)-medium contributions are formally suppressed by two powers electromagnetic coupling constant α when compared to leading-order cross sections, low-energy modes size enhance effect orders magnitude. They require proper infrared regularization, which we implement as screening atomic length scales or above. provide approximate analytic expressions distortion (anti)neutrino-nucleus sections evaluate QED-medium effects realistic values scale on example elastic with nucleons find new permille- percent-level effects, were not considered in either electron-nucleus scattering.