Constraining Nuclear Models and Equation of State with Parity-violating Asymmetry of $^{208}$Pb and $^{48}$Ca

Neutron skin of $^{48}$Ca and $^{208}$Pb have been known to provide important information about the symmetry energy of nuclear matter. Previous skin measurements involving strong integration probes might be subject to various systematic errors. Purely electro-weak probes such as parity-violating asymmetry of $^{48}$Ca (CREX) and $^{208}$Pb (PREX) in elastic electron scattering are particularly valuable. We generate a few hundred thousand energy density functional and calculate finite nuclear properties, infinite nuclear matter properties as well as neutron star properties. Our joint analysis of PREX and CREX data flavor energy density functional with a large bulk symmetry energy $S_v$ and a small slope $L$, which is in 2-$sigma$ (95\%) tension with nuclei masses and charge radii. This tension leads to a strong constraint on symmetry energy slope $L=42^{+15}_{-17}$ MeV. The posterior distribution is dominated by CREX data since CREX ruled out large $L$ while PREX likelihood has a big tail which is compatible with small $L$. Joint analyses with astronomical constraints including maximum mass, tidal deformability, and radius observation slightly tighten the lower bound $L=43^{+15}_{-11}$ MeV. Furthermore, we found the result agree nicely with previous neutron skin experiment, dipole probabilities as well as ab-initial calculation. \