Eur. Phys. J. A (2012) 48: 9
https://doi.org/10.1140/epja/i2012-12009-6

Regular Article - Theoretical Physics

Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation

Institut für Theoretische Physik, Justus-Liebig-Universität Giessen, D-35392, Giessen, Germany

^* e-mail: gernot.eichmann@theo.physik.uni-giessen.de

Received: 16 November 2011
Accepted: 14 January 2012
Published online: 30 January 2012

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 non-perturbative 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 GeV².