Clebsch-Gordan Construction of Lattice Interpolating Fields for Excited Baryons
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.
Keywords
Cite
@article{arxiv.hep-lat/0508018,
title = {Clebsch-Gordan Construction of Lattice Interpolating Fields for Excited Baryons},
author = {Subhasish Basak and Robert Edwards and George T. Fleming and Urs M. Heller and Colin Morningstar and David Richards and Ikuro Sato and Stephen J. Wallace},
journal= {arXiv preprint arXiv:hep-lat/0508018},
year = {2014}
}
Comments
This manuscript provides an anlytical construction of operators and is related to hep-lat/0506029, which provides a computational construction. This e-print version contains a full set of Clebsch-Gordan coefficients for the octahedral group