Isovector Axial Vector Form Factors of the Nucleon from Lattice QCD with $N_{f}=2+1$ $\mathcal O(a)$-improved Wilson Fermions

TL;DR

This paper analyzes isovector axial vector nucleon form factors using lattice QCD with $N_f=2+1$ Wilson fermions, covering a range of pion masses and lattice spacings, and employs advanced methods to extract physical form factors.

Contribution

It provides a comprehensive lattice QCD study of nucleon axial form factors at near-physical pion masses with improved analysis techniques and chiral extrapolations.

Findings

Axial charge and radius are extracted with controlled excited-state effects.

Results include physical point extrapolations consistent with experimental data.

The study demonstrates the effectiveness of combined summation and two-state fit methods.

Abstract

We present the analysis of isovector axial vector nucleon form factors on a set of $N_f=2+1$ CLS ensembles with $\mathcal O(a)$-improved Wilson fermions and L\"uscher-Weisz gauge action. The set of ensembles covers a pion mass range of $130-353\,$MeV with lattice spacings between $0.05\,$fm and $0.09\,$fm. In particular, the set includes a $L/a=96$ ensemble at the physical pion mass. For the purpose of the form factor extraction, we employ both the summed operator insertion method (summation method) and explicit two-state fits in order to account for excited-state contributions to the nucleon correlation functions. To describe the $Q^{2}$-behavior of the form factors, we perform $z$-expansion fits. Finally, we present HBChPT-inspired chiral and continuum extrapolations of the axial charge and radius.