Incorporating the weak mixing angle dependence to reconcile the neutron skin measurement on 208Pb by PREX-II

TL;DR

This paper investigates how incorporating the weak mixing angle dependence affects the neutron skin measurement of lead-208 by PREX-II, suggesting that accounting for this dependence can reconcile the measurement with theoretical predictions and other experiments.

Contribution

It explicitly models the dependence of the PREX-II neutron skin measurement on the weak mixing angle and uses atomic parity violation data to reduce tension with theoretical predictions.

Findings

The measurement is degenerate with the weak mixing angle.

Using atomic parity violation data slightly reduces the neutron skin estimate.

A smaller weak mixing angle at low energy could reconcile PREX-II with theory.

Abstract

The only available electroweak measurement of the $^{208}\mathrm{Pb}$ neutron skin, $\Delta R_{\rm{np}}$, performed by the PREX-II Collaboration through polarized electron-lead scattering, shows a mild tension with respect to both the theoretical nuclear-model predictions and a host of measurements. However, the dependence on the weak mixing angle should be incorporated in the calculation, since its low-energy value is experimentally poorly known. We first repeat the PREX-II analysis confirming their measurement by fixing the weak mixing angle to its standard model value. Then, we show the explicit dependence of the PREX-II measurement on the weak mixing angle, obtaining that it is fully degenerate with the neutron skin. To break this degeneracy, we exploit the weak mixing angle measurement from atomic parity violation on lead, obtaining a slightly thinner neutron skin but with about doubled uncertainties, possibly easing the PREX tension. Relying on the theoretical prediction, $\Delta R_{\rm{np}}^{\mathrm{th}}\approx 0.13-0.19\ \mathrm{fm}$, and using it as a prior in the fit, we find a weak mixing angle value about $1.2\sigma$ smaller than the standard model prediction. Thus, we suggest a possible solution of the PREX-II tension by showing that, considering its underlying dependence on the weak mixing angle, the PREX-II neutron skin determination could be in agreement with the other available measurements and predictions if the weak mixing angle at the proper energy scale is smaller than the standard model prediction.