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

TL;DR

This paper uses neutrino scattering data to refine the measurement of the weak mixing angle from atomic parity violation in cesium, resolving previous discrepancies and providing new insights into neutron distribution within the atom.

Contribution

It introduces a model-independent neutron radius measurement from COHERENT data to reinterpret atomic parity violation results, reducing uncertainties and revealing a neutron skin in cesium.

Findings

The weak mixing angle measurement aligns with Standard Model predictions.

A new neutron radius for cesium is determined with improved precision.

A 2-sigma indication of neutron skin in cesium is reported.

Abstract

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.