Improved Perturbation Theory for Improved Lattice Actions

Abstract

We study a systematic improvement of perturbation theory for gauge fields on the lattice; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik coefficients, clover coefficient) by ``dressed'' values; the latter are solutions to certain coupled integral equations, which are easy to solve numerically. Some positive features of this method are: a) It is gauge invariant, b) it can be systematically applied to improve (to all orders) results obtained at any given order in perturbation theory, c) it does indeed absorb in the dressed parameters the bulk of tadpole contributions. Two different applications are presented: The additive renormalization of fermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector (axial) current. In many cases where non-perturbative estimates of renormalization functions are also available for comparison, the agreement with improved perturbative results is significantly better as compared to results from bare perturbation theory.

17 pages, 3 tables, 6 figures

References in corpus (19)

• On the Viability of Lattice Perturbation Theory
• Non-perturbative O(a) improvement of lattice QCD
• Light Hadron Spectroscopy with Two Flavors of Dynamical Quarks on the Lattice
• Lattice QCD on Small Computers
• O(a) improvement of lattice QCD with two flavors of Wilson quarks
• Effects of non-perturbatively improved dynamical fermions in QCD at fixed lattice spacing
• Quenched QCD with O(a) improvement: I. The spectrum of light hadrons
• Lattice QCD with the Overlap-Dirac Operator: Its $\Lambda$ Parameter, and One-Loop Renormalization of Fermionic Currents
• One-loop renormalization of fermionic currents with the overlap-Dirac operator
• Perturbative Renormalization of Weak-Hamiltonian Four-Fermion Operators with Overlap Fermions
• The Critical Mass of Wilson Fermions: A Comparison of Perturbative and Monte Carlo Results
• One-loop renormalisation of quark bilinears for overlap fermions with improved gauge actions
• The Critical Hopping Parameter in O(a) improved Lattice QCD
• Quenched Results for Light Quark Physics with Overlap Fermions
• Resummation of Cactus Diagrams in the Clover Improved Lattice Formulation of QCD
• Resummation of Cactus Diagrams in Lattice QCD
• Renormalization of lattice gauge theories with massless Ginsparg Wilson fermions
• Two-loop additive mass renormalization with clover fermions and Symanzik improved gluons
• Perturbative renormalization in parton distribution functions using Overlap fermions and Symanzik improved gluons

Cited by in corpus (8)

• Glue spin and helicity in proton from lattice QCD
• Higher representations on the lattice: perturbative studies
• Renormalization constants of local operators for Wilson type improved fermions
• Non-perturbative renormalization in coordinate space for $N_f=2$ maximally twisted mass fermions with tree-level Symanzik improved gauge action
• Multi-Representation Dynamics of SU(4) Composite Higgs Models: Chiral Limit and Spectral Reconstructions
• High-loop perturbative renormalization constants for Lattice QCD (I): finite constants for Wilson quark currents
• Two-loop additive mass renormalization with clover fermions and Symanzik improved gluons
• High loop renormalization constants by NSPT: a status report