Reinterpreting the weak mixing angle from atomic parity violation in view of the Cs neutron rms radius measurement from COHERENT

Using the first model independent average neutron rms radius of ¹³³Cs and ¹²⁷I obtained from the analysis of the coherent elastic neutrino-nucleus scattering data of the COHERENT experiment, we show the effect on the weak mixing angle measurement from the atomic parity violation (APV) in cesium. Despite that the large uncertainty on the neutron skin measurement makes it difficult to draw statistically significant conclusions on the weak mixing angle, we exploit the fact that the APV result is highly sensitive to the cesium neutron rms radius, Rₙ, to combine the APV and the COHERENT measurements in order to get a better determination of Rₙ, assuming that the standard model is correct. The value of Rₙ=5.42±0.31 fm is obtained, improving significantly the current uncertainty. This result allows to infer a meaningful value of the cesium neutron skin, the difference between the neutron and proton distribution radii, equal to ΔRₙₚ=0.62±0.31 fm, showing for the first time a 2σ deviation from zero.