Axial-vector Current and General Unpolarized Electroweak Single-nucleon Responses

TL;DR

This paper extends previous work on nucleon response functions by detailing the axial-vector current and analyzing unpolarized electroweak responses, aiding understanding of weak interactions in nucleons.

Contribution

It develops the axial-vector single-nucleon current in detail and provides response functions for unpolarized electroweak interactions, including approximation schemes and numerical insights.

Findings

Derived full set of vector and axial-vector response functions.

Provided approximation schemes with validity indications.

Enhanced understanding of nucleon form factors in weak reactions.

Abstract

The present study provides an extension to our recent work on the vector (V) electromagnetic single-nucleon current and associated response functions, both for unpolarized situations and in situations where the target nucleon is polarized. Here the axial-vector (A) single-nucleon current matrix element is developed in detail and the full set of vector and axial-vector currents used to obtain the electroweak VV, AA and VA response functions. Only the unpolarized case is studied in the present work. The general forms for all of these elements are developed together with various approximation schemes in which numerical studies are provided to indicate where these approximations may be expected to be valid. The results of this work provide the basis for a deeper understanding of the roles played by the various single-nucleon form factors in weak interaction reactions on free nucleons and when using the standard ``prescription for nuclear physics'' in reactions involving nucleons in nuclei.