Nucleon axial form factors in generalized nonlocal chiral effective theory

In this work, we first investigate the chiral transformation properties of the nonlocal pion field operator and construct a generalized nonlocal chiral Lagrangian that is invariant under $\mathrm{SU}(2)$ chiral symmetry transformations. As a simple application, we then calculate the leading and next-leading order pion one loop corrections to the nucleon axial form factors within nonlocal chiral perturbation theory. Then, we fit the next leading order and next-next leading order low energy coupling constants (LECs) to lattice QCD data. The fitted results show that the nonlocal LECs are comparatively smaller than their local counterparts. Finally, using these LECs, we compute the $Q^{2}$ dependence of the nucleon axial form factors. The numerical results indicate that the nonlocal nucleon axial form factors are consistent with lattice QCD data in a wide $\rm Q^{2}$ range, up to $\rm Q^{2} = 1~\mathrm{GeV}^{2}$