Parity projection of QCD sum rules for the nucleon

TL;DR

This paper develops a parity projection method for QCD sum rules of the nucleon, incorporating higher order corrections and a phase-rotated kernel to improve the extraction of positive and negative parity states using maximum entropy analysis.

Contribution

The authors derive a generalized parity projected sum rule for baryons that includes higher order OPE terms and large alpha_s corrections, enhancing the analysis of nucleon states.

Findings

Successfully extracted positive and negative parity nucleon states.

Improved convergence of the OPE with phase-rotated Gaussian kernel.

Sum rule dominated by the chiral condensate term.

Abstract

The nucleon and its negative-parity excited states are examined in a maximum entropy method analysis of QCD sum rules. First, we rederive the parity projected sum rules for baryons using forward correlation functions. Doing this, the method is generalized so that higher order operator product expansion (OPE) terms can be calculated unambiguously. We then apply this approach to the nucleon channel taking into account all known first order alpha_s corrections to the Wilson coefficients of the OPE. As these corrections have turned out to be large, we suppress them by using a phase-rotated Gaussian kernel. Simultaneously, this phase rotation strongly suppresses the continuum contribution and improves the convergence of the OPE. The resulting sum rule has the interesting feature that it is dominated by the term containing the chiral condensate of dimension 3. Analyzing this sum rule by the maximum entropy method, we are able to extract information of both the positive and negative parity states.