Nucleon axial-vector and pseudoscalar form factors and PCAC relations
Chen Chen, Christian S. Fischer, Craig D. Roberts, Jorge Segovia
Abstract
We use a continuum $\mathrm{quark}+\mathrm{diquark}$ 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 ${G}_{\ensuremath{\pi}NN}$. 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, ${g}_{\ensuremath{\pi}NN}/{m}_{N}=14.02(33)/\mathrm{GeV}$ is consistent with recent precision determinations.