A Bayesian analysis of the nucleon QCD sum rules

TL;DR

This paper applies the maximum entropy method to QCD sum rules for the nucleon, enabling a flexible analysis of the spectral function and revealing the dominant coupling to a scalar diquark operator.

Contribution

It introduces a Bayesian-based MEM approach to analyze nucleon QCD sum rules without restricting the spectral function to traditional forms.

Findings

The nucleon ground state mainly couples to a scalar diquark operator.

Gaussian sum rule is more effective than Borel sum rule for MEM analysis.

MEM can extract the nucleon pole more reliably in the Gaussian sum rule framework.

Abstract

QCD sum rules of the nucleon channel are reanalyzed, using the maximum entropy method (MEM). This new approach, based on the Bayesian probability theory, does not restrict the spectral function to the usual "pole + continuum"-form, allowing a more flexible investigation of the nucleon spectral function. Making use of this flexibility, we are able to investigate the spectral functions of various interpolating fields, finding that the nucleon ground state mainly couples to an operator containing a scalar diquark. Moreover, we formulate the Gaussian sum rule for the nucleon channel and find that it is more suitable for the MEM analysis to extract the nucleon pole in the region of its experimental value, while the Borel sum rule does not contain enough information to clearly separate the nucleon pole from the continuum.