Clebsch-Gordan Construction of Lattice Interpolating Fields for Excited Baryons

TL;DR

This paper develops a comprehensive set of baryon interpolating operators for lattice QCD, classified by symmetry groups, to improve the study of excited baryon states with various angular momenta.

Contribution

It introduces a systematic construction of local and nonlocal baryon operators using Clebsch-Gordan coefficients to enhance lattice QCD analyses of excited baryons.

Findings

Operators classified by octahedral group symmetries

Construction of nonlocal operators with orbital angular momentum coupling

Maximal overlap with continuum SU(2) symmetry

Abstract

Large sets of baryon interpolating field operators are developed for use in lattice QCD studies of baryons with zero momentum. Operators are classified according to the double-valued irreducible representations of the octahedral group. At first, three-quark smeared, local operators are constructed for each isospin and strangeness and they are classified according to their symmetry with respect to exchange of Dirac indices. Nonlocal baryon operators are formulated in a second step as direct products of the spinor structures of smeared, local operators together with gauge-covariant lattice displacements of one or more of the smeared quark fields. Linear combinations of direct products of spinorial and spatial irreducible representations are then formed with appropriate Clebsch-Gordan coefficients of the octahedral group. The construction attempts to maintain maximal overlap with the continuum SU(2) group in order to provide a physically interpretable basis. Nonlocal operators provide direct couplings to states that have nonzero orbital angular momentum.