Irreducible Multiplets of Three-Quark Operators on the Lattice: Controlling Mixing under Renormalization

Abstract

High luminosity accelerators have greatly increased the interest in semi-exclusive and exclusive reactions involving nucleons. The relevant theoretical information is contained in the nucleon wavefunction and can be parametrized by moments of the nucleon distribution amplitudes, which in turn are linked to matrix elements of three-quark operators. These can be calculated from first principles in lattice QCD. However, on the lattice the problems of operator mixing under renormalization are rather involved. In a systematic approach we investigate this issue in depth. Using the spinorial symmetry group of the hypercubic lattice we derive irreducibly transforming three-quark operators, which allow us to control the mixing pattern.

arXiv comment13 pages

References in corpus (3)

• Nucleon Form Factors in QCD
• Lattice Operators for Moments of the Structure Functions and their Transformation under the Hypercubic Group
• Structure and Representation Theory for Double Group of Four-Dimensional Cubic Group

Cited by in corpus (10)

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• The Nucleon Distribution Amplitudes and their application to nucleon form factors and the $N\to \Delta$ transition at intermediate values of $Q^2$
• Nonperturbative Renormalization in Lattice QCD with three Flavors of Clover Fermions: Using Periodic and Open Boundary Conditions
• Non-perturbative renormalization of three-quark operators
• Updated determination of light-cone distribution amplitudes of octet baryons in lattice QCD