Perturbative Corrections for Staggered Four-Fermion Operators

Abstract

We present results for one-loop matching coefficients between continuum four-fermion operators, defined in the Naive Dimensional Regularization scheme, and staggered fermion operators of various types. We calculate diagrams involving gluon exchange between quark lines, and ``penguin'' diagrams containing quark loops. For the former we use Landau gauge operators, with and without $O(a)$ improvement, and including the tadpole improvement suggested by Lepage and Mackenzie.For the latter we use gauge-invariant operators. Combined with existing results for two-loop anomalous dimension matrices and one-loop matching coefficients, our results allow a lattice calculation of the amplitudes for $K\bar{K}$ mixing and $K\to \pi \pi$ decays with all corrections of $O(g^2)$ included. We also discuss the mixing of $\Delta S=1$ operators with lower dimension operators, and show that, with staggered fermions, only a single lower dimension operator need be removed by non-perturbative subtraction.

44 pages latex (uses psfig), 3 ps figures, all bundled using uufiles (correctly this time!), UW/PT-93-1

References in corpus (2)

• The Two-Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays I: $\mathcal{O}({\alpha }_s^2)$
• Perturbative Corrections for Staggered Fermion Bilinears

Cited by in corpus (43)

• Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks
• Partial Flavor Symmetry Restoration for Chiral Staggered Fermions
• Kaon Matrix Elements and CP-violation from Quenched Lattice QCD: (I) the 3-flavor case
• An Upgraded Analysis of $\epsilon \prime /\epsilon$ at the Next-to-Leading Order
• Matrix Elements of 4-fermion Operators with Quenched Wilson Fermions
• Kaon B parameter from quenched Lattice QCD
• New lattice approaches to the $\Delta I=1/2$ rule
• Staggered Chiral Perturbation Theory at Next-to-Leading Order
• One-loop matching coefficients for improved staggered bilinears
• Unquenched determination of the kaon parameter B_K from improved staggered fermions
• Perturbative matching of staggered four-fermion operators with hypercubic fat links
• Perturbative Renormalization of Weak-Hamiltonian Four-Fermion Operators with Overlap Fermions
• On the Nf and a Dependence of BK
• Staggered fermion matrix elements using smeared operators
• B_K in Staggered Chiral Perturbation Theory
• Hadronic Weak Interactions of Light Quarks
• Combined analysis of the unitarity triangle and CP violation in the Standard Model
• Perfect Lattice Actions for Staggered Fermions
• Analysis of the DeltaI=1/2 Rule and e'/e with Overlap Fermions
• Renormalising vector currents in lattice QCD using momentum-subtraction schemes
• Theoretical status of epsilon'/epsilon
• Nonperturbative comparison of clover and HISQ quarks in lattice QCD and the properties of the phi meson
• On the foundations of partially quenched chiral perturbation theory
• Matrix elements relevant for Delta I=1/2 rule and epsilon-prime from Lattice QCD with staggered fermions
• On-shell improved lattice QCD with staggered fermions
• Taste symmetry breaking with HYP-smeared staggered fermions
• 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
• Weak matrix elements for CP violation
• The Schwinger Model with Perfect Staggered Fermions
• Perturbative Matching of the staggered four-fermion operators for e'/e
• One Spin Trace Formalism for $B_K$
• Weak matrix elements: on the way to delta I = 1/2 rule and epsilon-prime with staggered fermions
• One-loop matching of Delta S=2 four-quark operators with improved staggered fermions
• Results for Quenched $B_K$ from JLQCD
• Penguin diagrams for the HYP staggered fermions
• Toolkit for staggered $\Delta S=2$ matrix elements
• Recent progress in calculating weak matrix elements using staggered fermions
• Toward Precision Measurement of $B_K$ with Quenched Kogut-Susskind Quarks
• K^0--\bar{K}^0 mixing in full lattice QCD
• Progress report on the staggered epsilon'/epsilon project
• Penguin diagrams for improved staggered fermions