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.
Categories: hep-lat hep-ph nucl-th
