The Pion-Nucleon Coupling Constant in QCD Sum Rules

The pion-nucleon coupling constant $g_{\pi N}$ is studied on the basis of the QCD sum rules. Both the Borel sum rules and the finite energy sum rules for $g_{\pi N}$ are used to examine the effects of higher dimensional operators (up to dim. 7) and $\alpha_s$ corrections in the operator product expansion. Agreement with the experimental number is reached only when $S_{\pi}/S_N$ is greater than one, where $S_{\pi}$ ($S_N$) is the continuum threshold for the $g_{\pi N}$ (nucleon) sum rule.