Nucleon axial-vector and pseudoscalar form factors and PCAC relations

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 pionnucleon form factor G(pi NN). 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 behavior 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(pi NN)/m(N) = 14.02(33)/GeV is consistent with recent precision determinations.

Automated summary

This study presents a continuum quark + diquark approach to solve the nucleon bound-state problem in relativistic quantum field theory and provides parameter-free predictions for the nucleon axial and induced pseudoscalar form factors. By constructing the necessary couplings between the external current and the building blocks of the nucleon consistently, the partial conservation of the axial-vector current and the associated Goldberger-Treiman relation are satisfied. The results show accurate descriptions of the pointwise behavior of the axial form factor and reliable estimates of the pseudoscalar form factor and pion-nucleon coupling constant.