A consistent neutrino determination of the low-energy weak mixing angle

The weak mixing angle, ${\sin }^2{\theta }_W$, is a fundamental parameter of the Standard Model and a sensitive probe of electroweak physics across various energy scales. At low momentum transfer, the Standard Model prediction approaches a well-defined low-energy plateau, providing a target for precision tests of the electroweak theory. At the lowest momentum transfer, atomic parity violation (APV) in cesium provides one of the most precise determinations of the weak mixing angle. Here, we review and update the status of this determination and compare it with other available probes. We then consistently reanalyze low-energy neutrino scattering data and combine the resulting determinations from coherent elastic scattering (CE$\nu$NS) and neutrino-electron scattering. The complementary sensitivity of these processes to electroweak couplings enables a neutrino-based determination of the low-energy weak mixing angle, accounting for electroweak radiative corrections and relevant theoretical uncertainties. Our global analysis yields ${\sin }^2{\theta }_W^{\mathrm{l}\mathrm{o}\mathrm{w}}(\nu \text{data})=0.233_{-0.006}^{+0.007}$. We assess the consistency and relative impact of the individual neutrino measurements and discuss the prospects for future CE$\nu$NS and neutrino-electron scattering experiments to improve the precision of this determination. Our analysis provides an independent test of the Standard Model at low momentum transfer, complementary to that provided by atomic parity violation.