Two-loop renormalization of vector, axial-vector, and tensor fermion bilinears on the lattice

2008/11/30 by A. Skouroupathis, H. Panagopoulos · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Effective action #Fermion #Feynman diagram #Gauge theory #Lattice (music) #Lattice QCD #Mathematical physics #Meson #Particle physics #Particle physics theoretical and experimental studies #Physics #Pseudovector #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quark #Quenched approximation #Renormalization #hep-lat

paper · pdf · doi:10.1103/physrevd.79.094508

published as Phys.Rev.D79:094508,2009 · 42 pages, 10 figures. Version accepted in PRD. Added comments and references, provided per diagram numerical values; final results and conclusions left unchanged. This paper is a sequel to arXiv:0707.2906 (Phys. Rev. D76 (2007) 094514), which regards the scalar and pseudoscalar cases.

arxiv created 2009/04/24 · openalex publication_date 2009/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We compute the two-loop renormalization functions, in the RI^\ensuremath' scheme, of local bilinear quark operators \ensuremathψ\ensuremathΓ\ensuremathψ, where \ensuremathΓ corresponds to the vector, axial-vector, and tensor Dirac operators, in the lattice formulation of QCD. We consider both the flavor nonsinglet and singlet operators. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in c_SW, in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. Finally, we present our results in the MS scheme, for easier comparison with calculations in the continuum. The corresponding results, for fermions in an arbitrary representation, together with some special features of superficially divergent integrals, are included in the appendices.

Citations

• Gluino zero-modes for non-trivial holonomy calorons
• Adjoint modes as probes of gauge field structure
• Integration by parts: The algorithm to calculate β-functions in 4 loops
• High-loop perturbative renormalization constants for lattice QCD (I): finite constants for Wilson quark currents
• Three loop anomalous dimension of non-singlet quark currents in the RI′ scheme
• Free energy and plaquette expectation value for gluons on the lattice, in three dimensions
• Conformal windows of SU(N) gauge theories, higher dimensional representations, and the size of the unparticle world
• Quark mass renormalization in the and RI schemes up to the NNLO order
• Volume independence in largeNcQCD-like gauge theories
• Regularization and renormalization of gauge fields

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