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

A bstract Relativistic full weak-neutral axial-vector four-current distributions inside a general spin- $$ \frac{1}{2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> 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 $$ {G}_T^Z\left({Q}^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>G</mml:mi> <mml:mi>T</mml:mi> <mml:mi>Z</mml:mi> </mml:msubsup> <mml:mfenced> <mml:msup> <mml:mi>Q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mfenced> </mml:math> rather than the axial FF $$ {G}_A^Z\left({Q}^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>G</mml:mi> <mml:mi>A</mml:mi> <mml:mi>Z</mml:mi> </mml:msubsup> <mml:mfenced> <mml:msup> <mml:mi>Q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mfenced> </mml:math> . 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.