The isoscalar non-singlet axial form factor of the nucleon from lattice QCD

TL;DR

This paper reports progress in calculating the nucleon's isoscalar non-singlet axial form factor using lattice QCD with multiple ensembles, employing advanced techniques to control systematic uncertainties and fit the form factor's momentum dependence.

Contribution

The study introduces a comprehensive lattice QCD analysis of the nucleon axial form factor with improved methods for excited state suppression and form factor parametrization.

Findings

Progress in lattice QCD computation of the axial form factor.

Use of the summation method to reduce excited state contamination.

Application of the $z$-expansion for form factor parametrization.

Abstract

We present our progress on the computation of the axial form factor of the nucleon with flavour structure $u+d-2s$ from lattice QCD. We employ a set of $N_f=2+1$ CLS ensembles with $O(a)$-improved Wilson fermions and the L\"uscher-Weisz gauge action, with lattice spacings ranging from $0.05\,\text{fm}$ to $0.086\,\text{fm}$ and pion masses spanning between $130\,\text{MeV}$ and $350\,\text{MeV}$. We employ multiple source-sink separations and use the summation method to suppress the contamination from excited states. We use a $z$-expansion on each ensemble to parametrize the $Q^2$-dependence of the form factor and simultaneously fit the available source-sink separations for all $Q^2\leq 0.7 \,{\rm GeV}^2$. We outline our analysis of the stability of the fits varying the ans\"atze and different estimations of the covariance matrix and report on our strategy for a comprehensive determination of the physical form factor.