Relativistic model of 2p-2h meson exchange currents in (anti)neutrino scattering

TL;DR

This paper develops a relativistic meson-exchange current model for neutrino-nucleus interactions, extending previous electromagnetic models to the weak sector and analyzing the response functions and relativistic effects.

Contribution

The paper introduces a relativistic model of charged meson-exchange currents for neutrino interactions, incorporating axial contributions and extending electromagnetic models to the weak sector.

Findings

The model accurately reproduces electromagnetic MEC contributions to electron scattering.

Relativistic effects significantly influence the response functions.

Axial currents play a crucial role in neutrino scattering responses.

Abstract

We develop a model of relativistic, charged meson-exchange currents (MEC) for neutrino-nucleus interactions. The two-body current is the sum of seagull, pion-in-flight, pion-pole and $\Delta$-pole operators. These operators are obtained from the weak pion-production amplitudes for the nucleon derived in the non-linear $\sigma$-model together with weak excitation of the $\Delta(1232)$ resonance and its subsequent decay into $N\pi$. With these currents we compute the five 2p-2h response functions contributing to $(\nu_l,l^-)$ and $(\overline{\nu}_l,l^+)$ reactions in the relativistic Fermi gas model. The total current is the sum of vector and axial two-body currents. The vector current is related to the electromagnetic MEC operator that contributes to electron scattering. This allows one to check our model by comparison with the results of De Pace {\em et al.,} Nuclear Physics A 726 (2003) 303. Thus our model is a natural extension of that model to the weak sector with the addition of the axial MEC operator. The dependences of the response functions on several ingredients of the approach are analyzed. Specifically we discuss relativistic effects, quantify the size of the direct-exchange interferences, and the relative importance of the axial versus vector current.