Group-theoretical construction of extended baryon operators in lattice QCD

TL;DR

This paper presents a group-theoretical method for constructing spatially-extended, gauge-invariant baryon operators in lattice QCD, improving the identification of low-lying states and optimizing computational efficiency.

Contribution

It introduces a systematic group-theoretical approach to design baryon operators with better overlap and minimal sources, enhancing lattice QCD spectrum analysis.

Findings

Operators constructed for all isospin channels.

Maximized overlaps with low-lying states.

Reduced computational sources needed.

Abstract

The design and implementation of large sets of spatially-extended, gauge-invariant operators for use in determining the spectrum of baryons in lattice QCD computations are described. Group-theoretical projections onto the irreducible representations of the symmetry group of a cubic spatial lattice are used in all isospin channels. The operators are constructed to maximize overlaps with the low-lying states of interest, while minimizing the number of sources needed in computing the required quark propagators. Issues related to the identification of the spin quantum numbers of the states in the continuum limit are addressed.