Spectral Functions, Maximum Entropy Method and Unconventional Methods in Lattice Field Theory

TL;DR

This paper introduces two innovative methods for extracting spectral information from lattice field theory data, enhancing traditional exponential fitting techniques with QCD sum rules and the Maximum Entropy Method.

Contribution

It presents novel applications of QCD sum rules combined with lattice data and the Maximum Entropy Method to analyze hadronic correlators, expanding the toolkit for lattice field theory analysis.

Findings

QCD sum rule approach applied to lattice data.

Maximum Entropy Method used for spectral function estimation.

Both methods improve data analysis beyond traditional exponential fits.

Abstract

We present two unconventional methods of extracting information from hadronic 2-point functions produced by Monte Carlo simulations. The first is an extension of earlier work by Leinweber which combines a QCD Sum Rule approach with lattice data. The second uses the Maximum Entropy Method to invert the 2-point data to obtain estimates of the spectral function. The first approach is applied to QCD data, and the second method is applied to the Nambu--Jona-Lasinio model in (2+1)D. Both methods promise to augment the current approach where physical quantities are extracted by fitting to pure exponentials.