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

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 Lüscher-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 $Q^2\le 0.7{\mathrm{GeV}}^2$. We outline our analysis of the stability of the fits varying the ansätze and different estimations of the covariance matrix and report on our strategy for a comprehensive determination of the physical form factor.

10 pages, 5 figures. Proceedings of the 41st International Symposium on Lattice Field Theory (Lattice 2024), University of Liverpool, UK, 2024