Determination of the $\Delta(1232)$ axial and pseudoscalar form factors from lattice QCD

TL;DR

This paper uses lattice QCD to calculate the axial and pseudoscalar form factors of the $
232$ resonance, testing theoretical relations and analyzing their pion mass dependence.

Contribution

It develops and tests new techniques for calculating $
232$ form factors using lattice QCD with different fermion schemes and examines related theoretical relations.

Findings

Support for Goldberger-Treiman type relations

Validation of pion-pole dominance hypothesis

Chiral extrapolation of axial form factors

Abstract

We present a lattice QCD calculation of the $\Delta(1232)$ matrix elements of the axial-vector and pseudoscalar currents. The decomposition of these matrix elements into the appropriate Lorentz invariant form factors is carried out and the techniques to calculate the form factors are developed and tested using quenched configurations. Results are obtained for 2+1 domain wall fermions and within a hybrid scheme with domain wall valence and staggered sea quarks. Two Goldberger-Treiman type relations connecting the axial to the pseudoscalar effective couplings are derived. These and further relations based on the pion-pole dominance hypothesis are examined using the lattice QCD results, finding support for their validity. Utilizing lattice QCD results on the axial charges of the nucleon and the $\Delta$, as well as the nucleon-to-$\Delta$ transition coupling constant, we perform a combined chiral fit to all three quantities and study their pion mass dependence as the chiral limit is approached.