Perturbative renormalization factors and O(a^2) corrections for lattice 4-fermion operators with improved fermion/gluon actions

Abstract

In this work we calculate the corrections to the amputated Green's functions of 4-fermion operators, in 1-loop Lattice Perturbation theory. One of the novel aspects of our calculations is that they are carried out to O(a^2) (a: lattice spacing). We employ the Wilson/clover action for massless fermions (also applicable for the twisted mass action in the chiral limit) and a family of Symanzik improved actions for gluons. Our calculations have been carried out in a general covariant gauge. Results have been obtained for several popular choices of values for the Symanzik coefficients. While our Green's function calculations regard any pointlike 4-fermion operators which do not mix with lower dimension ones, we pay particular attention to DF=2 operators, both Parity Conserving and Parity Violating (F: flavour). We compute the perturbative renormalization constants for a complete basis of 4-fermion operators and we study their mixing pattern. For some of the actions considered here, even O(a^0) results did not exist in the literature to date. The correction terms which we calculate are essential ingredients for minimizing the lattice artifacts which are present in non-perturbative evaluations of renormalization constants with the RI'-MOM method. Our perturbative results, for the matrix elements of DF=2 operators and for the corresponding renormalization matrices, depend on a large number of parameters: coupling constant, number of colors, lattice spacing, external momentum, clover parameter, Symanzik coefficients, gauge parameter. To make these results most easily accessible, we have included them in the distribution package of this paper, as an ASCII file named: 4-fermi.m; the file is best perused as Mathematica input. The main results of this work have been applied to improve non-perturbative estimates of the B_K-parameter in N_F=2 twisted mass lattice QCD.

30 pages, 1 figure, 8 tables

References in corpus (10)

• A General Method for Non-Perturbative Renormalization of Lattice Operators
• Delta M_K and epsilon_K in SUSY at the Next-to-Leading order
• Two-Loop QCD Anomalous Dimensions of Flavour-Changing Four-Quark Operators Within and Beyond the Standard Model
• Chirally improving Wilson fermions II. Four-quark operators
• Next-to-Leading Order QCD Corrections to the Lifetime Difference of $B_s$ Mesons
• Non-perturbative renormalization of quark bilinear operators with Nf=2 (tmQCD) Wilson fermions and the tree-level improved gauge action
• Perturbative Renormalization Factors of Bilinear Quark Operators for Improved Gluon and Quark Actions in Lattice QCD
• O(a^2) corrections to the one-loop propagator and bilinears of clover fermions with Symanzik improved gluons
• BK-parameter from Nf = 2 twisted mass lattice QCD
• Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action

Cited by in corpus (5)

• QED Corrections to Hadronic Processes in Lattice QCD
• ΔS=2 and ΔC=2 bag parameters in the SM and beyond from Nf=2+1+1 twisted-mass LQCD
• BK-parameter from Nf = 2 twisted mass lattice QCD
• Non-leptonic kaon decays at large $N_c$
• On the perturbative renormalisation of four-quark operators for new physics