High-loop perturbative renormalization constants for Lattice QCD (II): three-loop quark currents for tree-level Symanzik improved gauge action and n_f=2 Wilson fermions

Abstract

Numerical Stochastic Perturbation Theory was able to get three- (and even four-) loop results for finite Lattice QCD renormalization constants. More recently, a conceptual and technical framework has been devised to tame finite size effects, which had been reported to be significant for (logarithmically) divergent renormalization constants. In this work we present three-loop results for fermion bilinears in the Lattice QCD regularization defined by tree-level Symanzik improved gauge action and n_f=2 Wilson fermions. We discuss both finite and divergent renormalization constants in the RI'-MOM scheme. Since renormalization conditions are defined in the chiral limit, our results also apply to Twisted Mass QCD, for which non-perturbative computations of the same quantities are available. We emphasize the importance of carefully accounting for both finite lattice space and finite volume effects. In our opinion the latter have in general not attracted the attention they would deserve.

23 pages, 7 figures, pdflatex

References in corpus (4)

• On the reduction of hypercubic lattice artifacts
• High-loop perturbative renormalization constants for Lattice QCD (I): finite constants for Wilson quark currents
• Two-point functions of quenched lattice QCD in Numerical Stochastic Perturbation Theory. (II) The gluon propagator in Landau gauge
• Two-loop additive mass renormalization with clover fermions and Symanzik improved gluons

Cited by in corpus (3)

• Gauge-invariant Renormalization Scheme in QCD: Application to fermion bilinears and the energy-momentum tensor
• High-loop perturbative renormalization constants for Lattice QCD (III): three-loop quark currents for Iwasaki gauge action and n_f=4 Wilson fermions
• NSPT estimate of the improvement coefficient $c_A$ to two loops