Perturbative Corrections for Staggered Fermion Bilinears

Abstract

We calculate the perturbative corrections to fermion bilinears that are used in numerical simulations when extracting weak matrix elements using staggered fermions. This extends previous calculations of Golterman and Smit, and Daniel and Sheard. In particular, we calculate the corrections for non-local bilinears defined in Landau gauge with gauge links excluded. We do this for the simplest operators, i.e. those defined on a $2^4$ hypercube, and for tree level improved operators which live on $4^4$ hypercubes. We also consider gauge invariant operators in which the ``tadpole'' contributions are suppressed by projecting the sums of products of gauge links back in to the gauge group. In all cases, we find that the variation in the size of the perturbative corrections is smaller than those with the gauge invariant unimproved operators. This is most strikingly true for the smeared operators. We investigate the efficacy of the mean-field method of Lepage and Mackenzie at summing up tadpole contributions. In a companion paper we apply these results to four-fermion operators.

29 pages latex, 4 postscript figures included, UW/PT-92-13 and CEBAF-TH-92-20

Cited by in corpus (47)

• Partial Flavor Symmetry Restoration for Chiral Staggered Fermions
• A complete non-perturbative renormalization prescription for quasi-PDFs
• Perturbative Renormalization of quasi-PDFs
• Matrix Elements of 4-fermion Operators with Quenched Wilson Fermions
• Magnetic susceptibility of QCD at zero and at finite temperature from the lattice
• Non-perturbative determination of quark masses in quenched lattice QCD with the Kogut-Susskind fermion action
• Staggered Chiral Perturbation Theory at Next-to-Leading Order
• Perturbative Corrections for Staggered Four-Fermion Operators
• $B_K$ Using Staggered Fermions: An Update
• One-loop matching coefficients for improved staggered bilinears
• Perturbative Renormalization of Neutron-Antineutron Operators
• One-loop renormalization of staple-shaped operators in continuum and lattice regularizations
• Renormalization of Wilson-line operators in the presence of nonzero quark masses
• Perturbative matching of staggered four-fermion operators with hypercubic fat links
• One loop matching coefficients for a variant overlap action--and some of its simpler relatives
• Staggered fermion matrix elements using smeared operators
• Singlet vs Nonsinglet Perturbative Renormalization of Fermion Bilinears
• B_K in Staggered Chiral Perturbation Theory
• Perturbative renormalization factors for bilinear and four-quark operators for Kogut-Susskind fermions on the lattice
• Perturbative improvement of staggered fermions using fat links
• Perfect Lattice Actions for Staggered Fermions
• Improvement of the Staggered Fermion Operators
• Supersymmetric QCD on the Lattice: An Exploratory Study
• Lattice QCD at the end of 2003
• Pion decay constant for the Kogut-Susskind quark action in quenched lattice QCD
• On-shell improved lattice QCD with staggered fermions
• Gauge-invariant Renormalization Scheme in QCD: Application to fermion bilinears and the energy-momentum tensor
• Non-perturbative Renormalization for Improved Staggered Bilinears
• Power-counting theorem for staggered fermions
• One-loop matching of improved four-fermion staggered operators with an improved gluon action
• Heavy-light and light-light weak matrix elements on the lattice
• Perturbative Matching of the staggered four-fermion operators for e'/e
• The Schwinger Model with Perfect Staggered Fermions
• Perturbative renormalization functions of local operators for staggered fermions with stout improvement
• One Spin Trace Formalism for $B_K$
• On tadpole improvement for staggered fermions
• The chiral phase transition for lattice QCD with 2 colour-sextet quarks
• One-loop matching factors for staggered bilinear operators with improved gauge actions
• Dynamical Generation of Elementary Fermion Mass: First Lattice Evidence
• Toolkit for staggered $\Delta S=2$ matrix elements
• Testing a non-perturbative mechanism for elementary fermion mass generation: lattice setup
• Recent progress in calculating weak matrix elements using staggered fermions
• Toward a systematic analysis of the fourth-root trick
• Progress report on the staggered epsilon'/epsilon project
• Pion decay constant in quenched QCD with Kogut-Susskind quarks
• Penguin diagrams for improved staggered fermions
• Singlet vs Nonsinglet Perturbative Renormalization factors of Staggered Fermion Bilinears