Extraction of the nucleon axial form factor from Lattice QCD using NNLO chiral perturbation theory

Abstract

We calculate the nucleon axial form factor in relativistic chiral perturbation theory with $\Delta (1232)$ up to next-to-next-to-leading order (NNLO). Relevant low-energy constants are determined by fitting to recent lattice-QCD results at several pion masses, while accounting for the uncertainty associated with the truncation of the chiral expansion. We obtain a good description of the lattice data for momentum transfers up to $\sqrt{Q^2}\simeq 0.6$ GeV and pion masses up to $M_{\pi }\simeq 400$ MeV. We find that the explicit inclusion of the $\Delta$ resonance is required to reproduce the lattice-QCD pion-mass dependence of the axial charge and axial radius, as well as the momentum dependence of the form factor. At the physical point we obtain $g_A=1.257\pm 0.011$ and $⟨r_A^2⟩=0.312\pm 0.037{\mathrm{fm}}^2$. Our analysis provides a model-independent and systematically improvable parametrization of the pion-mass and momentum dependence of the axial form factor, offering a framework for extrapolating lattice-QCD results to the physical point and for improving predictions of low-energy weak interactions involving nucleons.

Comments: 6 ancillary files, 17 pages, 10 figures, 4 tables