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.

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

References in corpus (6)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• Excited Baryon Spectroscopy from Lattice QCD: Finite Size Effect and Hyperfine Mass Splitting
• Masses of excited baryons from chirally improved quenched lattice QCD
• Analysis of $N^{\star }$ spectra using matrices of correlation functions based on irreducible baryon operators
• Group-theoretical construction of extended baryon operators
• Baryonic sources using irreducible representations of the double-covered octahedral group

Cited by in corpus (60)

• Excited state baryon spectroscopy from lattice QCD
• A novel quark-field creation operator construction for hadronic physics in lattice QCD
• Toward the excited meson spectrum of dynamical QCD
• First results from 2+1 dynamical quark flavors on an anisotropic lattice: light-hadron spectroscopy and setting the strange-quark mass
• Light Nuclei and Hypernuclei from Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry
• Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD
• Tuning for Three-flavors of Anisotropic Clover Fermions with Stout-link Smearing
• Light Hadron Masses from Lattice QCD
• $N\Omega$ dibaryon from lattice QCD near the physical point
• Multichannel one-to-two transition amplitudes in a finite volume
• Two-Nucleon Higher Partial-Wave Scattering from Lattice QCD
• Quantum Numbers of Recently Discovered ${\Omega }_c^0$ Baryons from Lattice QCD
• Nucleon-Nucleon Scattering Parameters in the Limit of SU(3) Flavor Symmetry
• Excited hadrons on the lattice: Baryons
• Extracting Scattering Phase-Shifts in Higher Partial-Waves from Lattice QCD Calculations
• Group-theoretical construction of extended baryon operators in lattice QCD
• Lattice QCD determination of patterns of excited baryon states
• Nuclear correlation functions in lattice QCD
• Excited State Nucleon Spectrum with Two Flavors of Dynamical Fermions
• Excited hadrons on the lattice: Mesons
• Generalized Lüscher Formula in Multi-channel Baryon-Meson Scattering
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• On the Feynman-Hellmann Theorem in Quantum Field Theory and the Calculation of Matrix Elements
• Restoration of Rotational Symmetry in the Continuum Limit of Lattice Field Theories
• Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD
• Angular Momentum on the Lattice: The Case of Non-Zero Linear Momentum
• A variational study of two-nucleon systems with lattice QCD
• First lattice QCD study of the gluonic structure of light nuclei
• S-wave scattering of strangeness -3 baryons
• Derivative sources in lattice spectroscopy of excited light-quark mesons
• An accurate calculation of the nucleon axial charge with lattice QCD
• Strongly Bound Dibaryon with Maximal Beauty Flavor from Lattice QCD
• Sparsening Algorithm for Multi-Hadron Lattice QCD Correlation Functions
• Lattice operators for scattering of particles with spin
• Nuclear Reactions from Lattice QCD
• Möbius domain-wall fermions on gradient-flowed dynamical HISQ ensembles
• Excited-State Effective Masses in Lattice QCD
• Even parity excitations of the nucleon in lattice QCD
• Scale setting the Möbius Domain Wall Fermion on gradient-flowed HISQ action using the omega baryon mass and the gradient-flow scales $t_0$ and $w_0$
• Study of decuplet baryon resonances from lattice QCD
• Flavor structure of $\Lambda$ baryons from lattice QCD: From strange to charm quarks
• The Shape of Covariantly Smeared Sources in Lattice QCD
• Exploring the meson spectrum with twisted mass lattice QCD
• The negative-parity spin-1/2 $\Lambda$ baryon spectrum from lattice QCD and effective theory
• Bi-local baryon interpolating fields with two flavours
• Detailed analysis of excited state systematics in a lattice QCD calculation of $g_A$
• Spin-3/2 baryons from an anisotropic lattice QCD action
• Prospects for a lattice calculation of the rare decay ${\Sigma }^{+}\to p{\ell }^{+}{\ell }^{-}$
• Evolutionary Fitting Methods for the Extraction of Mass Spectra in Lattice Field Theory
• New extended interpolating fields built from three-dimensional fermions
• Exploring the Spectrum of QCD using the Lattice
• Baryon Operators and Baryon Spectroscopy
• Bi-Local Baryon Interpolating Fields with Three Flavours
• Excited-state effects in nucleon structure on the lattice using hybrid interpolators
• Precise study of triply charmed baryons ${\Omega }_{ccc}$
• Construction of general $N$-body lattice operators with arbitrary momenta
• Lattice QCD Study of Positive Parity Dibaryons with Maximal Charm and Strangeness
• Quantum Operator Design for Lattice Baryon Spectroscopy
• $N^{\ast }$ Resonances in Lattice QCD from (mostly) Low to (sometimes) High Virtualities
• Formal Developments for Lattice QCD with Applications to Hadronic Systems