# Analysis of Hadron Propagators with One Thousand Configurations on a $24^3\times 64$ Lattice at $\beta=6.0$

## TL;DR

This paper investigates the statistical behavior of hadron propagators on a large lattice, revealing that effective mass measurements inherently fluctuate beyond error margins at large times, impacting mass extraction methods.

## Contribution

It provides a theoretical explanation for the difficulty in observing long plateaux in effective mass plots and discusses implications for fitting procedures in lattice QCD.

## Key findings

- Effective mass fluctuates beyond error bars at large times.
- Long plateaux are statistically unlikely regardless of data volume.
- Implications for global fit strategies in hadron mass calculations.

## Abstract

Statistical properties of effective mass are analyzed. We show from a general ground that effective mass as a function of time should not exhibit long plateaux whatever high statistics simulations are made: the mass should fluctuate beyond the one standard deviation of error bars after a few time slices for large times where the ground state dominates. This explains the difficulty of obtaining long plateaux experienced in previous simulations. Implications of the observation for global $\chi^2$ fits are discussed, and results for hadron masses are presented.