Information Content of the Parity-Violating Asymmetry in $^{208}$Pb

The parity violating asymmetry $A_{PV}$ in $^{208}$Pb, recently measured by the PREX-2 collaboration, is studied using modern relativistic (covariant) and non-relativistic 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 $\alpha_D$ of $^{208}$Pb. We then add the quantified value of $A_{PV}$ together with $\alpha_D$ to our calibration dataset to optimize new functionals. Based on these results, we predict a neutron skin thickness in $^{208}$Pb $r_\mathrm{skin} =0.19\pm 0.02$\,fm and the symmetry-energy slope $L=54\pm 8$\,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.