Group Theoretical Construction of Nucleon Operators using All-to-All Quark Propagators

TL;DR

This paper presents a group theoretical method to construct irreducible baryon operators using all-to-all quark propagators, enabling better extraction of excited nucleon states in lattice QCD simulations.

Contribution

It introduces a novel approach combining group theory and all-to-all propagators to improve baryon operator construction for excited state analysis.

Findings

Successful construction of irreducible baryon operators.

Preliminary nucleon effective mass results obtained.

Method facilitates studying multi-particle contributions in light dynamical configurations.

Abstract

We describe a method to construct irreducible baryon operators using all-to-all quark propagators. It was demonstrated earlier that a large basis of extended baryon operators on anisotropic, quenched lattices can be used to reliably extract the masses of 5 or more excited states in the nucleon channel. All-to-all quark propagators are expected to be needed when studying these excited states on light, dynamical configurations because contributions from multi-particle states are expected to be significant. The dilution method is used to approximate the all-to-all quark propagators. Low-lying eigenmodes can also be used if necessary. For efficient computation of matrix elements of the interpolating operators, the algorithms should exploit the fact that many extended baryon operators can be obtained from the different linear combinations of three-quark colour-singlet operators. The sparseness of the diluted noise vectors also afford several computation simplifications. Some preliminary results are presented for nucleon effective masses.