2005/05/04 by F. Palombi, Filippo Palombi, C. Pena +3
Mathematics · Physics and Astronomy · #High-Energy Particle Collisions Research #Lattice (music) #Lattice QCD #Mathematical physics #Mathematics #Non-perturbative #Particle physics #Particle physics theoretical and experimental studies #Perturbation theory (quantum mechanics) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quark #Renormalization #Scaling #hep-lat
paper · pdf · doi:10.1088/1126-6708/2006/03/089
published as JHEP 0603 (2006) 089 · 22 pages, 4 figures
arxiv created 2005/05/04 · openalex publication_date 2006/03/28 · arxiv updated 2015/06/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Starting from the QCD Schroedinger functional (SF), we define a family of renormalization schemes for two four-quark operators, which are, in the chiral limit, protected against mixing with other operators. With the appropriate flavour assignments these operators can be interpreted as part of either the ΔF=1 or ΔF=2 effective weak Hamiltonians. In view of lattice QCD with Wilson-type quarks, we focus on the parity odd components of the operators, since these are multiplicatively renormalized both on the lattice and in continuum schemes. We consider 9 different SF schemes and relate them to commonly used continuum schemes at one-loop order of perturbation theory. In this way the two-loop anomalous dimensions in the SF schemes can be inferred. As a by-product of our calculation we also obtain the one-loop cutoff effects in the step-scaling functions of the respective renormalization constants, for both O(a) improved and unimproved Wilson quarks. Our results will be needed in a separate study of the non-perturbative scale evolution of these operators.