Analysis of $N^{\star}$ spectra using matrices of correlation functions based on irreducible baryon operators

TL;DR

This paper employs matrix correlation functions and group theoretical operators in lattice QCD to accurately extract ground and excited nucleon masses, including high-spin states, using advanced statistical methods.

Contribution

It introduces a novel approach combining correlation matrices, group theory, and Bayesian inference to improve excited state mass extraction in lattice QCD.

Findings

Clear separation of excited and ground state masses achieved

High-spin states (spin >= 5/2) successfully isolated

Effective use of Bayesian inference enhances mass determination

Abstract

We present results for ground and excited-state nucleon masses in quenched lattice QCD using anisotropic lattices. Group theoretical constructions of local and nonlocal straight-link irreducible operators are used to obtain suitable sources and sinks. Matrices of correlation functions are diagonalized to determine the eigenvectors. Both chi-square fitting and Bayesian inference with an entropic prior are used to extract masses from the correlation functions in a given channel. We observe clear separation of the excited state masses from the ground state mass. States of spin >= 5/2 have been isolated by use of G_2 operators.