Calculation and Interpretation of Hadron Correlation Functions in Lattice QCD

TL;DR

This paper introduces new methods for calculating and interpreting hadron correlation functions in lattice QCD, including corrections for finite lattice effects and techniques to extract physical properties like radii and polarizabilities.

Contribution

It develops a novel approach to analyze correlation functions, correct for finite lattice artifacts, and extract hadron physical properties from lattice QCD data.

Findings

Corrected correlation functions yield pion and nucleon sizes.

Method to extract hadron polarizability from unequal time correlators.

Asymptotic behavior determined from a tree diagram path integral.

Abstract

Several new developments in the calculation and interpretation of hadron density-density correlation functions are presented. The asymptotic behavior of correlation functions is determined from a tree diagram path integral. A method is developed to use this behavior to correct for leading image contributions on a finite periodic spatial lattice and to correct for the finite temporal extent of the lattice. Equal time correlation functions are shown to determine a sum of the ground state rms radius plus a polarization correction, and it is shown how to extract the hadron polarizability from unequal time correlation functions. Image-corrected correlation functions calculated in quenched lattice QCD are presented and used to determine the size of the pion and nucleon.