Correlation Functions of Hadron Currents in the QCD Vacuum Calculated in Lattice QCD

TL;DR

This paper computes point-to-point vacuum correlation functions for hadron currents in quenched lattice QCD, analyzing their behavior across different distance scales and comparing results with experimental data and theoretical models.

Contribution

It provides a detailed lattice QCD calculation of hadron current correlation functions, bridging short-distance perturbative regimes and long-distance resonance dominance, with comparisons to sum rules and instanton models.

Findings

Semi-quantitative agreement with experimental data in certain channels

Lattice data complement experimental results in nucleon and delta channels

Comparison with sum rules and instanton models enhances understanding of QCD vacuum

Abstract

Point-to-point vacuum correlation functions for spatially separated hadron currents are calculated in quenched lattice QCD on a $16^3\times 24$ lattice with $6/g^2=5.7$. The lattice data are analyzed in terms of dispersion relations, which enable us to extract physical information from small distances where asymptotic freedom is apparent to large distances where the hadronic resonances dominate. In the pseudoscalar, vector, and axial vector channels where experimental data or phenomenological information are available, semi-quantitative agreement is obtained. In the nucleon and delta channels, where no experimental data exist, our lattice data complement experiments. Comparison with approximations based on sum rules and interacting instantons are made, and technical details of the lattice calculation are described.