# Lorentz Structure of Vector Part of Matrix Elements of Transitions n <-> p, Caused by Strong Low-Energy Interactions and Hypothesis of Conservation of Charged Vector Current

## TL;DR

This paper investigates the Lorentz structure of neutron-proton transition matrix elements induced by the charged hadronic vector current, revealing the dynamical origin of current conservation and the absence of G-odd contributions due to G-parity invariance.

## Contribution

It demonstrates that the conservation of the charged hadronic vector current arises from G-even contributions and shows G-odd terms with $q_{\mu}$ do not appear due to G-parity invariance.

## Key findings

- Current conservation linked to G-even contributions.
- G-odd Lorentz structures are absent in the matrix elements.
- Dynamical origin of current conservation explained.

## Abstract

We analyse the Lorentz structure of the matrix elements of the transitions "neutron <-->proton", induced by the charged hadronic vector current. We show that the term maintaining conservation of the charged hadronic vector current even for different masses of the neutron and proton (see T. Leitner et al., Phys. Rev. C 73, 065502 (2006) and A. M. Ankowski, arXiv:1601.06169 [hep-ph]) has a dynamical origin, related to the G-even first class current contribution. We show that because of invariance of strong low-energy interactions under the G-parity transformations, the G-odd contribution with the Lorentz structure $q_{\mu}$, where $q_{\mu}$ is a momentum transferred, does not appear in the matrix elements of the ``neutron <-> proton' transitions.