Semiempirical formula for electroweak response functions in the two-nucleon emission channel in neutrino-nucleus scattering

Abstract

A semi-empirical formula for the electroweak response functions in the two-nucleon emission channel is proposed. The method consists in expanding each one of the vector-vector, axial-axial and vector-axial responses as sums of six sub-responses. These corresponds to separating the meson-exchange currents as the sum of three currents of similar structure, and expanding the hadronic tensor, as the sum of the separate contributions from each current plus the interferences between them. For each sub-response we factorize the coupling constants, the electroweak form factors, the phase space and the delta propagator, for the delta forward current. The remaining spin-isospin contributions are encoded in coefficients for each value of the momentum transfer, $q$. The coefficients are fitted to the exact results in the relativistic mean field model of nuclear matter, for each value of $q$. The dependence on the energy transfer, $ω$ is well described by the semi-empirical formula. The $q$-dependency of the coefficients of the sub-responses can be parameterized or can be interpolated from the provided tables. The description of the five theoretical responses is quite good. The parameters of the formula, the Fermi momentum, number of particles relativistic effective mass, vector energy the electroweak form factors and the coupling constants, can be modified easily. This semi-empirical formula can be applied to the cross-section of neutrinos, antineutrinos and electrons.