The $\Delta(1232)$ axial charge and form factors from lattice QCD

TL;DR

This paper reports the first lattice QCD calculation of the $(1232)$ axial-vector and pseudoscalar form factors, deriving and testing Goldberger-Treiman relations, and performing a combined chiral fit for related axial quantities.

Contribution

It introduces the first lattice QCD computation of $(1232)$ axial form factors and examines associated Goldberger-Treiman relations with a combined chiral analysis.

Findings

First lattice QCD results for $(1232)$ axial form factors.

Validation of Goldberger-Treiman relations for $(1232)$.

Chiral fit connecting nucleon and $(1232)$ axial properties.

Abstract

We present the first calculation on the $\Delta$ axial-vector and pseudoscalar form factors using lattice QCD. Two Goldberger-Treiman relations are derived and examined. A combined chiral fit is performed to the nucleon axial charge, N to $\Delta$ axial transition coupling constant and $\Delta$ axial charge.