$\pi NN$ and Pseudoscalar Form Factors from Lattice QCD

TL;DR

This paper uses lattice QCD to calculate the pion-nucleon form factor, confirming its monopole shape and consistency with phenomenological values, and explores pion dominance in the axial form factor.

Contribution

It provides the first quenched lattice QCD determination of the $ ext{ extpi NN}$ form factor and compares it with the axial form factor to test pion dominance.

Findings

The $ ext{ extpi NN}$ form factor fits well with a monopole form.

The monopole mass is determined to be approximately 0.75 GeV.

The extrapolated $ ext{ extpi N}$ coupling constant agrees with phenomenological values.

Abstract

The $\pi NN$ form factor $g_{\pi NN}(q^2)$ is obtained from a quenched lattice QCD calculation of the pseudoscalar form factor $g_P(q^2)$ of the proton with pion pole dominance. We find that $g_{\pi NN}(q^2)$ fitted with the monopole form agrees well with the Goldberger-Treiman relation and is much preferred over the dipole form. The monopole mass is determined to be $0.75 \pm 0.14 {\rm GeV}$ which shows that $g_{\pi NN}(q^2)$ is rather soft. The extrapolated $\pi N$ coupling constant $g_{\pi NN} = 12.7 \pm 2.4$ is quite consistent with the phenomenological values. We also compare $g_{\pi NN}(q^2)$ with the axial form factor $g_A(q^2)$ to check the pion dominance in the induced pseudoscalar form factor $h_A(q^2)$ vis \`{a} vis chiral Ward identity.