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 pion-nucleon 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 $g_p^ast = 8.80(23)$, 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, $g_{pi NN}/m_N =14.02(33)/{rm GeV}$ is consistent with a Roy--Steiner-equation analysis of pion-nucleon scattering. We also observe a marked suppression of the size of the $d$-quark component relative to that of the $u$-quark in the ratio $g_A^d/g_A^u=-0.16(2)$, which highlights the presence of strong diquark correlations inside the nucleon -- both scalar and axial-vector, with the scalar diquark being dominant.