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

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.