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

Abstract

We compute the two-loop renormalization functions, in the RI' scheme, of local bilinear quark operators $\bar{\psi }\Gamma \psi$, where $\Gamma$ 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 MSbar 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.

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.

References in corpus (30)

• A General Method for Non-Perturbative Renormalization of Lattice Operators
• The three-loop QCD $\beta$-function and anomalous dimensions
• Non-perturbative O(a) improvement of lattice QCD
• The renormalization of the axial anomaly in dimensional regularization
• Walking in the SU(N)
• Light Composite Higgs from Higher Representations versus Electroweak Precision Measurements -- Predictions for LHC
• Renormalization and Running of Quark Mass and Field in the Regularization Invariant and MS-bar Schemes at Three and Four Loops
• Chirally improving Wilson fermions II. Four-quark operators
• Volume independence in large Nc QCD-like gauge theories
• Phase diagram of SU(2) with 2 flavors of dynamical adjoint quarks
• Conformal Windows of SU(N) Gauge Theories, Higher Dimensional Representations and The Size of The Unparticle World
• Three loop anomalous dimension of non-singlet quark currents in the RI' scheme
• High-precision determination of the light-quark masses from realistic lattice QCD
• Proton decay matrix elements with domain-wall fermions
• Quark Mass Renormalization in the $\MSbar$ and RI schemes up to the NNLO order
• Computation of the relation between the bare lattice coupling and the MSbar coupling in SU(N) gauge theories to two loops
• Perturbative Renormalization Factors of Bilinear Quark Operators for Improved Gluon and Quark Actions in Lattice QCD
• Scaling and Goldstone effects in a QCD with two flavours of adjoint quarks
• Two-loop relation between the bare lattice coupling and the MSbar coupling in pure SU(N) gauge theories
• Three-loop Three-Linear Vertices and Four-Loop MOM beta functions in massless QCD
• Non-perturbative renormalization of the static axial current in two-flavour QCD
• The three-loop beta-fuction of QCD with the clover action
• Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice
• Exploring twisted mass Lattice QCD with the Clover term
• Free Energy and Plaquette expectation value for gluons on the lattice, in three dimensions
• Hadron spectrum, quark masses and decay constants from light overlap fermions on large lattices
• High-loop perturbative renormalization constants for Lattice QCD (I): finite constants for Wilson quark currents
• Nonperturbative renormalization of composite operators with overlap fermions
• Adjoint modes as probes of gauge field structure
• Gluino zero-modes for non-trivial holonomy calorons

Cited by in corpus (42)

• Exploration of new superconductors and functional materials and fabrication of superconducting tapes and wires of iron pnictides
• Effective noise reduction techniques for disconnected loops in Lattice QCD
• Charmonium properties in hot quenched lattice QCD
• A complete non-perturbative renormalization prescription for quasi-PDFs
• Perturbative Renormalization of quasi-PDFs
• Flavour blindness and patterns of flavour symmetry breaking in lattice simulations of up, down and strange quarks
• Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD
• Nucleon axial, tensor and scalar charges and $\sigma$-terms in lattice QCD
• Nucleon charges with dynamical overlap fermions
• Strangeness Contribution to the Proton Spin from Lattice QCD
• Up, down, and strange nucleon axial form factors from lattice QCD
• Strange quark contributions to nucleon mass and spin from lattice QCD
• Disconnected quark loop contributions to nucleon observables in lattice QCD
• Perturbative and Nonperturbative Renormalization in Lattice QCD
• O(a^2) corrections to the one-loop propagator and bilinears of clover fermions with Symanzik improved gluons
• Renormalization constants of local operators for Wilson type improved fermions
• Weak decay of magnetized pions
• One-loop renormalization of staple-shaped operators in continuum and lattice regularizations
• Renormalization of Wilson-line operators in the presence of nonzero quark masses
• Non-perturbative renormalization in coordinate space for $N_f=2$ maximally twisted mass fermions with tree-level Symanzik improved gauge action
• Singlet vs Nonsinglet Perturbative Renormalization of Fermion Bilinears
• Nonperturbative comparison of clover and HISQ quarks in lattice QCD and the properties of the phi meson
• Two loop renormalization of the n = 2 Wilson operator in the RI'/SMOM scheme
• A novel approach to nonperturbative renormalization of singlet and nonsinglet lattice operators
• Amplitudes for the n = 3 moment of the Wilson operator at two loops in the RI/'SMOM scheme
• Spectral and transport properties from lattice QCD
• Charm and beauty in the deconfined plasma from quenched lattice QCD
• Supersymmetric QCD: Renormalization and Mixing of Composite Operators
• Charge Symmetry Breaking in Spin Dependent Parton Distributions and the Bjorken Sum Rule
• Perturbative renormalization functions of local operators for staggered fermions with stout improvement
• A lattice study of the strangeness content of the nucleon
• RI'/SMOM scheme amplitudes for deep inelastic scattering operators at one loop in QCD
• Non-perturbative renormalization of tensor currents: strategy and results for $N_f=0$ and $N_f=2$ QCD
• Bilinear quark operator renormalization at generalized symmetric point
• Non-perturbative renormalization of the QCD flavour-singlet local vector current
• Symmetric point flavour singlet axial vector current renormalization at two loops
• Meson spectrum in the large $N$ limit
• Disconnected contributions to hadronic structure
• Two-loop renormalization of fermion bilinear operators on the lattice
• Three-loop QCD Mass Relation between the $\overline{\mathrm{MS}}$ and Symmetric-momentum Subtraction Scheme Away from the Chiral Limit
• Quark flavor decomposition of the nucleon axial form factors
• Non-perturbative renormalization of tensor bilinears in Schrödinger Functional schemes