$πNN$ coupling determined beyond the chiral limit

Within the conventional QCD sum rules, we calculate the $πNN$ coupling constant, $g_{πN}$, beyond the chiral limit using two-point correlation function with a pion. We consider the Dirac structure, $iγ_5$, at $m_π^2$ 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 $m_π^2$. Using the PS coupling scheme for the pion-nucleon interaction, we obtain $g_{πN}=13.3\pm 1.2$, which is very close to the empirical $πNN$ 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.

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