Determination of the pion-nucleon coupling constant from QCD sum rules

Abstract

We evaluate the $\pi N$ coupling constant using a QCD sum rule based on the pion-to-vacuum matrix element of the correlator of two interpolating nucleon fields. The part of the correlator with Dirac structure $k\llap/\gamma_5$ is used, keeping all terms up to dimension 5 in the OPE and including continuum contributions on the phenomenological side. The ratio of this sum rule to the nucleon sum rule involving condensates of odd dimension yields stable results with values of $g_{\pi N}$ in the range $12\pm 5$. The sources of uncertainty are discussed.