Speaker
Description
We present the first systematic study of the relativistic intrinsic spin structure of a general spin-$1/2$ hadron in position space. We show in particular that the slope of the nucleon axial form factor $G_A^Z(Q^2)$ in the forward limit, conventionally denoted as $R^2_A \equiv -\frac{6}{G_A^Z(0) } \frac{ \text{d} G_A^Z(Q^2) }{\text{d} Q^2} \Big|_{Q^2=0} $ in the literature, does not faithfully characterize the size of the weak axial charge content of the nucleon in the Breit frame, but corresponds instead to a contribution to the nucleon 3D spin radius $r_\text{spin} \equiv \sqrt{\langle r_\text{spin}^2 \rangle}$, with $\langle r_\text{spin}^2 \rangle = R_A^2 + \frac{1}{4M^2}\left( 1 + \frac{G_P^Z(0)}{G_A^Z(0) } \right)$. We derive explicit expressions for the spin radius in different frames, and find in general additional contributions that depend on both the nucleon mass and the forward values of the axial-vector form factors $G_A^Z(0)$ and $G_P^Z(0)$. We also show that the second-class current contribution associated with the induced pseudo-tensor form factor $G_T^Z(Q^2)$ does not contribute in fact to both the nucleon axial and spin radii. Our work paves a new and direct way for investigating the nucleon 3D intrinsic spin structures using the weak-neutral axial-vector form factors $G_{A,P,T}^Z(Q^2)$ extracted from elastic (anti)neutrino-nucleon scattering data, or calculated in lattice QCD and various models and approaches.
