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

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 $G_{\pi NN}$. 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 behaviour 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, $g_{\pi NN}/m_N=14.02(33)/\mathrm{GeV}$ is consistent with recent precision determinations.

27 pages, 13 figures, 1 table

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Cited by in corpus (9)

• Form Factors of the Nucleon Axial Current
• Nucleon axial form factor at large momentum transfers
• Contact interaction analysis of octet baryon axialvector and pseudoscalar form factors
• Polarised parton distribution functions and proton spin
• Composition of low-lying $\mathbf{J}={\frac{3}{2}}^{\pm }\mathbf{\Delta }$-baryons
• Space-like Electromagnetic Form Factors of Lambda- and Sigma-Baryons from Quark-Diquark Faddeev Equations
• Weak interaction axial form factors of the octet baryons in nuclear medium
• Constituent quark axial current couplings to light vector mesons in the vacuum and with a weak magnetic field
• Symplectic Effective Field Theory for Nuclear Structure Studies