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

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 Lüscher-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.