Solar neutrinos with CE$\nu$NS and flavor-dependent radiative corrections

We examine solar neutrinos in dark matter detectors including the effects of flavor-dependent radiative corrections to the CE$\nu$NS cross section. Working within a full three-flavor framework, and including matter effects within the Sun and Earth, detectors with thresholds $\lesssim 1$ keV and exposures of $\sim 100$ ton-year could identify contributions to the cross section beyond tree level. The differences between the cross sections for the flavors, combined with the difference in fluxes, would provide a new and unique method to study the muon and tau components of the solar neutrino flux. Flavor-dependent corrections induce a small day-night asymmetry of $< |3 \times10^{-4}|$ in the event rate, which if ultimately accessible would provide a novel probe of flavor oscillations.