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

Abstract

We calculate the nucleon form factors ${G}_{A}$ and ${G}_{P}$ of the isovector axial-vector current and the pion-nucleon form factor ${G}_{\ensuremath{\pi}N}$ in manifestly Lorentz-invariant baryon chiral perturbation theory up to and including order $\mathcal{O}({p}^{4})$. In addition to the standard treatment including the nucleon and pions, we also consider the axial-vector meson ${a}_{1}$ 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.