A Bayesian approach to QCD sum rules

TL;DR

This paper introduces a Bayesian-based Maximum Entropy Method to extract spectral functions from QCD sum rules without assuming specific functional forms, demonstrated through rho-meson analysis.

Contribution

It develops a novel Bayesian inference technique for QCD sum rules that avoids traditional assumptions about spectral function shapes.

Findings

Successfully identified the rho-meson peak structure

Validated the method against known QCD sum rule results

Demonstrated the efficiency of the Maximum Entropy Method

Abstract

QCD sum rules are analyzed with the help of the Maximum Entropy Method. We develop a new technique based on the Bayesion inference theory, which allows us to directly obtain the spectral function of a given correlator from the results of the operator product expansion given in the deep euclidean 4-momentum region. The most important advantage of this approach is that one does not have to make any a priori assumptions about the functional form of the spectral function, such as the "pole + continuum" ansatz that has been widely used in QCD sum rule studies, but only needs to specify the asymptotic values of the spectral function at high and low energies as an input. As a first test of the applicability of this method, we have analyzed the sum rules of the rho-meson, a case where the sum rules are known to work well. Our results show a clear peak structure in the region of the experimental mass of the rho-meson. We thus demonstrate that the Maximum Entropy Method is successfully applied and that it is an efficient tool in the analysis of QCD sum rules.