Axial, induced pseudoscalar, and pion-nucleon form factors in manifestly Lorentz-invariant chiral perturbation theory

We calculate the nucleon form factors G_A and G_P of the isovector axial-vector current and the pion-nucleon form factor G_πN in manifestly Lorentz-invariant baryon chiral perturbation theory up to and including order O(p⁴). In addition to the standard treatment including the nucleon and pions, we also consider the axial-vector meson a₁ as an explicit degree of freedom. This is achieved by using the reformulated infrared renormalization scheme. We find that the inclusion of the axial-vector meson effectively results in one additional low-energy coupling constant that we determine by a fit to the data for G_A. The inclusion of the axial-vector meson results in an improved description of the experimental data for G_A, while the contribution to G_P is small.