Fitting Correlated Hadron Mass Spectrum Data

TL;DR

This paper presents methods for fitting correlated hadron mass spectrum data in lattice QCD, addressing challenges with limited data samples by modeling correlations to achieve stable and reliable fits.

Contribution

It introduces novel correlation modeling techniques that improve the stability and reliability of fits in lattice QCD data analysis with small sample sizes.

Findings

Correlation models yield stable fits with limited data

Improved goodness-of-fit estimation

Enhanced extraction of hadron masses from lattice data

Abstract

We discuss fitting hadronic Green functions versus time $t$ to extract mass values in quenched lattice QCD. These data are themselves strongly correlated in $t$. With only a limited number of data samples, the method of minimising correlated $\chi^2$ is unreliable. We explore several methods of modelling the correlations among the data set by a few parameters which then give a stable and sensible fit even if the data sample is small. In particular these models give a reliable estimate of the goodness of fit.