Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation

TL;DR

This paper calculates the nucleon axial and pseudoscalar form factors using a covariant Faddeev approach within the Dyson-Schwinger framework, respecting key symmetries and comparing results with experimental and lattice data.

Contribution

It introduces a covariant three-body Faddeev equation solution for nucleon form factors, incorporating a phenomenological quark-gluon interaction and respecting the axial Ward-Takahashi identity.

Findings

Reproduces Goldberger-Treiman relation across quark masses.

Axial charge underestimates experimental value by 20-25%.

Form factors agree with phenomenological and lattice data above 1-2 GeV^2.

Abstract

We compute the axial and pseudoscalar form factors of the nucleon in the Dyson-Schwinger approach. To this end, we solve a covariant three-body Faddeev equation for the nucleon wave function and determine the matrix elements of the axialvector and pseudoscalar isotriplet currents. Our only input is a well-established and phenomenologically successful ansatz for the nonperturbative quark-gluon interaction. As a consequence of the axial Ward-Takahashi identity that is respected at the quark level, the Goldberger-Treiman relation is reproduced for all current-quark masses. We discuss the timelike pole structure of the quark-antiquark vertices that enters the nucleon matrix elements and determines the momentum dependence of the form factors. Our result for the axial charge underestimates the experimental value by 20-25% which might be a signal of missing pion-cloud contributions. The axial and pseudoscalar form factors agree with phenomenological and lattice data in the momentum range above Q^2 ~ 1...2 GeV^2.