First constraint on the weak mixing angle using direct detection experiments

Current ton-scale dark matter direct detection experiments have reached an important milestone with the detection of solar neutrinos. In this paper, we show that these data can be used to determine a critical parameter of the Standard Model in particle physics, across an energy regime that has never been probed before. In particular, we show that the value of the weak mixing angle ($\theta_W$) which relates the mass of the $W$ and $Z$ bosons can be derived from 1) the recent measurements of coherent neutrino-nucleus scattering by PandaX-4T and XENONnT in the sub-GeV energy range -- a regime which is usually only probed by low energy neutrino experiments -- and from 2) XENONnT electron recoil data through neutrino-electron scattering at energy scale $\simeq 0.1 ~ \rm{ MeV}$, corresponding to a momentum transfer region over an order of magnitude smaller than that explored by atomic parity violation experiments. Now that an indicative measurement of the weak mixing angle exists at these lowest energy frontier, the challenge for the next generation of such experiments will be to provide a more precise measurement in the keV-MeV energy range.