$\pi NN$ coupling determined beyond the chiral limit

Abstract

Within the conventional QCD sum rules, we calculate the $\pi NN$ coupling constant, $g_{\pi N}$, beyond the chiral limit using two-point correlation function with a pion. We consider the Dirac structure, $i\gamma_5$, at $m_\pi^2$ order, which has clear dependence on the PS and PV coupling schemes for the pion-nucleon interactions. For a consistent treatment of the sum rule, we include the linear terms in quark mass as they constitute the same chiral order as $m_\pi^2$. Using the PS coupling scheme for the pion-nucleon interaction, we obtain $g_{\pi N}=13.3\pm 1.2$, which is very close to the empirical $\pi NN$ coupling. This demonstrates that going beyond the chiral limit is crucial in determining the coupling and the pseudoscalar coupling scheme is preferable from the QCD point of view.