# Empirical investigation of nuclear correlation function distributions in lattice QCD

## TL;DR

This paper empirically analyzes the distributions of two-point correlation functions in lattice QCD for various baryon numbers, finding that simpler O(N) model distributions accurately describe the empirical data across different separations.

## Contribution

It demonstrates that O(N) model distributions can effectively model the empirical correlation function distributions in lattice QCD, revealing a relationship between baryon number and the model parameter N.

## Key findings

- O(N) model distributions fit QCD data well at zero momentum
- Distribution behavior at large temporal separation matches O(N) predictions
- Correlation function distributions are accurately described across different baryon numbers

## Abstract

Two-point correlation functions of systems with baryon number $B \in \{1,2,3,4\}$ are investigated using lattice Quantum Chromodynamics (QCD). In particular, the empirical distributions of importance-sampling Monte-Carlo samples of these correlation functions are examined as a function of the spacetime separation between the two points and the baryon number. While the exact forms of these distributions are not known for QCD, recent work has determined asymptotic expressions for analogous correlation function distributions in simpler theories such as scalar field theory and the disordered phase of the $O(N)$ model. The theoretical O(N) model distributions are found to provide an accurate description of the empirical QCD distributions at zero momentum over a wide range of temporal separations for each baryon number when assessed with a range of different statistical tests. In particular, the behaviour of the baryon number $B$ QCD correlation function at large temporal separation is well-reproduced by the $O(N \sim 2/B)$ model distribution.