Nucleon relativistic weak-neutral axial-vector four-current distributions

TL;DR

This paper systematically studies relativistic weak-neutral axial-vector four-current distributions inside spin-1/2 hadrons, revealing their frame dependence, the role of second-class currents, and providing insights into light-front distortions, with applications to proton structure.

Contribution

First comprehensive analysis of relativistic axial-vector four-current distributions including second-class currents and their frame dependence.

Findings

The 3D axial charge distribution relates to the induced pseudotensor FF, not the axial FF.

Frame dependence of distributions is characterized and compared with light-front results.

Second-class current contribution does not affect mean-square axial and spin radii.

Abstract

Relativistic full weak-neutral axial-vector four-current distributions inside a general spin-$\frac{1}{2}$ hadron are systematically studied for the first time, where the second-class current contribution associated with the induced pseudotensor form factor (FF) is included. We clearly demonstrate that the 3D axial charge distribution, being parity-odd in the Breit frame, is in fact related to the induced pseudotensor FF $G_T^Z(Q^2)$ rather than the axial FF $G_A^Z(Q^2)$. We study the frame-dependence of full axial-vector four-current distributions for a moving hadron, and compare them with their light-front counterparts. We revisit the role played by the Melosh rotation, and understand more easily and intuitively the origins of distortions appearing in light-front distributions (relative to the Breit frame ones) using the conjecture that we propose in this work. In particular, we show that the second-class current contribution, although explicitly included, does not contribute in fact to the mean-square axial and spin radii. We finally illustrate our results in the case of a proton using the weak-neutral axial-vector FFs extracted from experimental data.