[Paper Review] Information content of the parity-violating asymmetry in $^{208}$Pb

P.‐G. Reinhard, X. Roca-Maza+1 more|PubMed|May 31, 2021

Nuclear physics research studies44 references6 citations

TL;DR

This study re-evaluates the parity-violating asymmetry $A_{\rm PV}$ in $^{208}$Pb using a diverse set of relativistic and non-relativistic energy density functionals, incorporating experimental $A_{\rm PV}$ and dipole polarizability $\alpha_{\rm D}$ data to calibrate new functionals. It finds a neutron skin thickness of $r_{\rm skin} = 0.19 \pm 0.02$ fm and symmetry-energy slope $L = 54 \pm 8$ MeV—significantly lower than prior estimates—while predicting $A_{\rm PV} = 2400 \pm 60$ ppb for $^{48}$Ca to be tested by the CREX experiment.

ABSTRACT

The parity-violating asymmetry A_{PV} in ^{208}Pb, recently measured by the PREX-2 Collaboration, is studied using modern relativistic (covariant) and nonrelativistic energy density functionals. We first assess the theoretical uncertainty on A_{PV} which is intrinsic to the adopted approach. To this end, we use quantified functionals that are able to accommodate our previous knowledge on nuclear observables such as binding energies, charge radii, and the dipole polarizability α_{D} of ^{208}Pb. We then add the quantified value of A_{PV} together with α_{D} to our calibration dataset to optimize new functionals. Based on these results, we predict a neutron skin thickness in ^{208}Pb r_{skin}=0.19±0.02 fm and the symmetry-energy slope L=54±8 MeV. These values are consistent with other estimates based on astrophysical data and are significantly lower than those recently reported using a particular set of relativistic energy density functionals. We also make a prediction for the A_{PV} value in ^{48}Ca that will be soon available from the CREX measurement.

Motivation & Objective

• To assess the theoretical uncertainty in $A_{\rm PV}$ predictions using modern relativistic and non-relativistic energy density functionals (EDFs).
• To resolve tensions between the PREX-2 measured $A_{\rm PV}$ and other observables like $\alpha_{\rm D}$ by calibrating new EDFs with both $A_{\rm PV}$ and $\alpha_{\rm D}$ data.
• To provide improved, model-consistent predictions for $r_{\rm skin}$ and the symmetry-energy slope $L$ in $^{208}$Pb, consistent with astrophysical constraints.
• To predict the $A_{\rm PV}$ value for $^{48}$Ca at CREX kinematics to guide upcoming experimental measurements.

Proposed method

• Employed quantified relativistic and non-relativistic EDFs calibrated on binding energies, charge radii, and $\alpha_{\rm D}$ of $^{208}$Pb to estimate intrinsic theoretical uncertainty in $A_{\rm PV}$.
• Extended calibration to include the PREX-2 measured $A_{\rm PV}$ at $q = 0.3978$ fm$^{-1}$, enabling new EDF optimization with combined $A_{\rm PV}$ and $\alpha_{\rm D}$ constraints.
• Used statistical analysis (Dobaczewski et al., 2014) to quantify model uncertainties and correlations between $A_{\rm PV}$, $r_{\rm skin}$, $L$, and $\alpha_{\rm D}$ across different EDF families.
• Modified the Dirac partial-wave code elsepa to include parity-violating potentials and accounted for Coulomb distortions and PREX-2 acceptance function in $A_{\rm PV}$ calculations.
• Evaluated the correlation between $A_{\rm PV}$ and $r_{\rm skin}$ via statistical analysis, finding a 99.9% correlation coefficient in SV and RMF-PC EDFs.
• Predicted $A_{\rm PV}$ for $^{48}$Ca at $Q^2 = 0.03$ GeV$^2$ using the best-fitting EDFs, with uncertainty propagation based on model variance.

Experimental results

Research questions

• RQ1 Does the PREX-2 measurement of $A_{\rm PV}$ in $^{208}$Pb create a fundamental tension with other nuclear data when analyzed with diverse EDFs?
• RQ2 What is the theoretical uncertainty in $A_{\rm PV}$ predictions arising from the choice of EDF, and how does it compare to the PREX-2 experimental uncertainty?
• RQ3 How do the $A_{\rm PV}$ and $\alpha_{\rm D}$ data jointly constrain the neutron skin thickness and symmetry-energy slope $L$ in $^{208}$Pb?
• RQ4 Can the observed correlation between $A_{\rm PV}$ and $r_{\rm skin}$ be used to improve model calibration and reduce uncertainty in nuclear matter properties?
• RQ5 What is the predicted $A_{\rm PV}$ value for $^{48}$Ca at CREX kinematics, and how does it compare to current experimental estimates of $\alpha_{\rm D}$?

Key findings

• The neutron skin thickness in $^{208}$Pb is predicted to be $r_{\rm skin} = 0.19 \pm 0.02$ fm, significantly lower than the $0.283 \pm 0.071$ fm reported in previous studies.
• The symmetry-energy slope $L$ is determined to be $54 \pm 8$ MeV, in agreement with astrophysical and chiral effective field theory estimates, but substantially lower than the $106 \pm 37$ MeV reported in Reed et al. (2021).
• The theoretical uncertainty in $A_{\rm PV}$ predictions is estimated at 6–7 ppb, comparable to the PREX-2 systematic error of 8 ppb, supporting its use as a calibration observable.
• A strong correlation of 99.9% exists between $A_{\rm PV}$ and $r_{\rm skin}$ across EDF families, confirming $A_{\rm PV}$ as a sensitive probe of neutron skin structure.
• The predicted $A_{\rm PV}$ for $^{48}$Ca at CREX kinematics is $2400 \pm 60$ ppb, providing a benchmark for upcoming experimental measurements.
• The model-averaged symmetry energy $J$ is estimated at $32 \pm 1$ MeV, consistent with recent astrophysical and chiral EFT constraints, and lower than the $38.1 \pm 4.7$ MeV reported in Reed et al. (2021).