Pion couplings with low-lying nucleon resonances

TL;DR

This paper calculates the coupling constants of neutral pions with the lowest two nucleon resonances using QCD sum rules, extending previous methods to include both diagonal and non-diagonal couplings.

Contribution

It introduces an extended QCD sum rule approach to determine pion-nucleon resonance couplings, including non-diagonal interactions, with stability checks against input variations.

Findings

Calculated coupling constants for pion and nucleon resonances.

Validated stability of results across parameter variations.

Extended the sum rule method to include multiple states.

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.