QCD sum rules: Borel parameter vs. Euclidean time

TL;DR

This paper compares traditional Borel sum rules with a coordinate space Euclidean time approach for QCD sum rules, highlighting differences in uncertainties and applicability for nucleon mass estimates.

Contribution

It introduces Euclidean time sum rules as an alternative to Borel sum rules and analyzes their advantages and limitations in nucleon channel calculations.

Findings

Euclidean time sum rules can estimate nucleon mass and residue.

These sum rules are more sensitive to uncertainties in power corrections.

Fiducial interval is nearly absent in Euclidean time sum rules.

Abstract

We explore a modification of QCD sum rules where, instead of Borel transforms of current correlators, one considers the correlators in coordinate space as functions of Euclidean time. Taking the nucleon channel as an example, we derive such Euclidean time sum rules and compare them with the traditional Borel sum rules. We show that a rough estimate of nucleon mass and residue is also possible working in coordinate space, but such sum rules are much more affected by the uncertainties in power corrections and continuum contribution than the Borel ones: the fiducial interval is practically absent.