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

Understand

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.