paper

Nucleon axial-vector and pseudoscalar form factors, and PCAC relations

arXiv:2103.02054 · doi:10.1103/PhysRevD.105.094022

Abstract

We use a continuum quark+diquark approach to the nucleon bound-state problem in relativistic quantum field theory to deliver parameter-free predictions for the nucleon axial and induced pseudoscalar form factors, $G_{A}$ and $G_{P}$ , and unify them with the pseudoscalar form factor $G_{5}$ or, equivalently, the pion-nucleon form factor $G_{I ¨ N N}$ . We explain how partial conservation of the axial-vector current and the associated Goldberger-Treiman relation are satisfied once all necessary couplings of the external current to the building blocks of the nucleon are constructed consistently; in particular, we fully resolve the seagull couplings to the diquark-quark vertices associated with the axial-vector and pseudoscalar currents. Among the results we describe, the following are worth highlighting. A dipole form factor defined by an axial charge $g_{A} = G_{A} (0) = 1.25 (3)$ and a mass-scale $M_{A} = 1.23 (3) m_{N}$ , where $m_{N}$ is the nucleon mass, can accurately describe the pointwise behaviour of $G_{A}$ . Concerning $G_{P}$ , we obtain the pseudoscalar charge $g_{p}^{*} = 8.80 (23)$ , and find that the pion pole dominance approach delivers a reliable estimate of the directly computed result. Our computed value of the pion-nucleon coupling constant, $g_{I ¨ N N} / m_{N} = 14.02 (33) / GeV$ is consistent with recent precision determinations.

27 pages, 13 figures, 1 table