Using the model independent average neutron rms radius of $^{ 133}\text{ Cs}$ and $^{ 127}\text{ I}$ obtained from the analysis of the coherent elastic neutrino-nucleus scattering data of the COHERENT experiment, we remove the long-standing $1.5\,\sigma$ tension between the Standard Model prediction and the weak mixing angle measurement from the atomic parity violation (APV) in caesium. The updated APV result becomes $\sin^2 \vartheta_{ \textrm{ W}}=0.239{ }^{ +0.006}_{ -0.007}$, to be compared with the Standard Model prediction at low momentum transfer, $\sin^2 \vartheta_{ \text{ W}}^{ \textrm{ SM}} = 0.23857(5)$. Moreover, exploiting the fact that the APV result is highly sensitive to the caesium neutron rms radius, $R_{ n}$, and assuming that the Standard Model is correct, we combine the APV and the COHERENT measurements in order to get a better determination of $R_{ n}$. The value of $R_{ n}=5.42\pm 0.31\,\textrm{ fm}$ is obtained, improving significantly the current uncertainty. This result allows to infer a meaningful value of the caesium neutron skin, the difference between the neutron and proton distribution radii, equal to $\Delta R_{ np}=0.62\pm 0.31\,\text{ fm}$, showing for the first time a $2\, \sigma$ deviation from zero.
Categories: hep-ph nucl-th