Microscopic calculation of two-particle-two-hole meson-exchange currents in $^{40}$Ar and asymmetric scaling properties for neutrino and electron scattering

Abstract: We present a microscopic calculation of two particle-two hole meson exchange current response functions in asymmetric nuclei, with particular emphasis on the $^{40}$Ar nucleus. Employing a relativistic mean-field and relativistic Fermi gas framework, we compute the nuclear response for $^{40}$Ar and compare it with that of the symmetric $^{40}$Ca nucleus, analyzing the role of proton-neutron imbalance. The model incorporates distinct proton and neutron Fermi momenta to accurately capture the nuclear dynamics of systems with $Z \neq N$. Our results indicate that using $^{40}$Ca as a proxy for $^{40}$Ar leads to a systematic error of approximately 10\%. Additionally, we propose an asymmetric scaling formula to obtain the 2p2h response for arbitrary nuclei from the $^{12}$C response, improving the description of asymmetric nuclei. Finally, we benchmark our predictions against inclusive electron scattering and neutrino cross sections.