Pion couplings with low-lying nucleon resonances

Abstract

We have calculated coupling constants of a neutral pion with the lowest two nucleon resonances. This includes both the diagonal as well as non-diagonal coupling constants involving a nucleon resonance and a nucleon. For this, we first calculate vacuum-to-pion correlation function of the interpolating fields of two nucleons and then take its matrix elements with respect to a nucleon spinor and/or a nucleon resonance spinor(s). Using different QCD sum rules obtained from different matrix elements we eliminate unwanted coupling constants and solve for the desired ones. This is a simple extension of the projected correlation function approach used in the literature where we use multiple of states involving those of a nucleon and its resonances. We have also checked the stability of our results with respect to variation of different QCD and phenomenological input parameters.