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

Mattia Atzori Corona; Matteo Cadeddu; Nicola Cargioli; Paolo Finelli; Matteo Vorabbi

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

Mattia Atzori Corona, Matteo Cadeddu, Nicola Cargioli, Paolo Finelli, Matteo Vorabbi

Abstract

The only available electroweak measurement of the $^{208}\mathrm{Pb}$ neutron skin, $ΔR_{\rm{np}}$, 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, $ΔR_{\rm{np}}^{\mathrm{th}}\approx 0.13-0.19\ \mathrm{fm}$, and using it as a prior in the fit, we find a weak mixing angle value about $1.2σ$ 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.

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

Abstract

The only available electroweak measurement of the

neutron skin,

, 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,

, and using it as a prior in the fit, we find a weak mixing angle value about

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.

Paper Structure (11 equations, 4 figures)

This paper contains 11 equations, 4 figures.

Figures (4)

Figure 1: Favored regions in the $\sin^2\theta_W$ vs $\Delta R_{\rm{np}}(^{208}\mathrm{Pb})$ plane given by our reanalysis of the PREX-II data. The gray, brown and red shaded areas represent the 1, 2 and 3$\sigma$ confidence level contours. The red horizontal bar shows the PREX-II result PhysRevLett.126.172502 for $s^{2\ \rm{SM}}_W$ (blue line). The green vertical band corresponds to the theoretical prediction, $\Delta R^{\rm{th}}_{\rm{np}}(^{208}\mathrm{Pb})$.
Figure 2: Combined fit results of APV(Pb)+PREX-II (dashed orange and dark red contours) and APV(Pb)+PREX-II+theory (solid cyan and blue contours, with their corresponding best fits (orange square and cyan star, respectively), shown in the $\sin^2\theta_W$ vs $\Delta R_{\rm{np}}(^{208}\mathrm{Pb})$ plane at 1$\sigma$ and 3$\sigma$ confidence levels. The side panels show the one-dimensional marginalizations (red line for APV(Pb)+PREX-II, cyan line for APV(Pb)+PREX-II+theory) for both the fits. The red horizontal bar shows the PREX-II result PhysRevLett.126.172502 for $s^{2\ \rm{SM}}_W$(blue line).
Figure 3: Summary of the PREX-only (grey long dashed), combined (orange dashed) and combined+theory (cyan solid) 1$\sigma$ confidence level contours in the $\sin^2\theta_W$ vs $\Delta R_{\rm{np}}(^{208}\mathrm{Pb})$ plane. The orange square and the cyan star points are the best fits of combined and combined+theory, respectively. The green vertical band shows $\Delta R_{\rm np}^{\rm th}$, while the red dot the PREX-II result PhysRevLett.126.172502 for $s^{2\ \rm{SM}}_W$(blue line).
Figure 4: Weak mixing angle running with the energy scale $Q$. The SM prediction (solid blue curve) is compared with some experimental determinations (black dots) Wood:1997zqDzuba:2012kxTanabashi:2018ocaZyla:2020zbsAndroic:2018kniAnthony:2005pm, and future measurements (purple dots) Becker:2018gglDev:2021otbBenesch:2014bas. The orange dashed and the cyan solid points come from the combined and the combined+theory fits, respectively. The cyan result is shifted towards lower energies for illustrative purposes, as indicated by the arrows. The vertical arrows indicate the momentum transfer for APV(Pb), PREX-II and CREX, while the green dashed curve represents the modified running of $\sin^2\theta_W$ in a scenario involving a new mediator Cadeddu:2021dqx.