Spectral sum of current correlators from lattice QCD

TL;DR

This paper introduces a lattice QCD method to compute the Borel transform of vacuum polarization functions, enabling direct comparison between nonperturbative lattice results and QCD sum rule predictions.

Contribution

It presents a novel lattice-based approach to calculate the Borel transform of current correlators, bridging lattice QCD and QCD sum rule analyses.

Findings

Results are consistent with the operator product expansion at large Borel mass.

Method successfully computes spectral sums from lattice two-point functions.

Continuum limit taken with three lattice spacings.

Abstract

We propose a method to use lattice QCD to compute the Borel transform of the vacuum polarization function appearing in the Shifman-Vainshtein-Zakharov QCD sum rule. We construct the spectral sum corresponding to the Borel transform from two-point functions computed on the Euclidean lattice. As a proof of principle, we compute the $s \bar{s}$ correlators at three lattice spacings and take the continuum limit. We confirm that the method yields results that are consistent with the operator product expansion in the large Borel mass region. The method provides a ground on which the OPE analyses can be directly compared with nonperturbative lattice computations.