Cargando…

A perturbative study of two four-quark operators in finite volume renormalization schemes

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...

Descripción completa

Detalles Bibliográficos
Autores principales: Palombi, Filippo, Pena, Carlos, Sint, Stefan
Lenguaje:eng
Publicado: 2005
Materias:
Acceso en línea:https://dx.doi.org/10.1088/1126-6708/2006/03/089
http://cds.cern.ch/record/834789
_version_ 1780905950284087296
author Palombi, Filippo
Pena, Carlos
Sint, Stefan
author_facet Palombi, Filippo
Pena, Carlos
Sint, Stefan
author_sort Palombi, Filippo
collection CERN
description 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 $\Delta F=1$ or $\Delta F=2$ 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.
id cern-834789
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2005
record_format invenio
spelling cern-8347892023-10-04T07:45:42Zdoi:10.1088/1126-6708/2006/03/089http://cds.cern.ch/record/834789engPalombi, FilippoPena, CarlosSint, StefanA perturbative study of two four-quark operators in finite volume renormalization schemesParticle Physics - LatticeStarting 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 $\Delta F=1$ or $\Delta F=2$ 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.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 $\Delta F=1$ or $\Delta F=2$ 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.hep-lat/0505003DESY-05-070CERN-PH-TH-2005-45FTUAM-05-2IFT-UAM-CSIC-05-16CERN-PH-TH-2005-045FTUAM-05-02CERN-PH-TH-2005-045DESY-05-070DESY-2005-070FTUAM-2005-02IFT-UAM-CSIC-2005-16oai:cds.cern.ch:8347892005-05-04
spellingShingle Particle Physics - Lattice
Palombi, Filippo
Pena, Carlos
Sint, Stefan
A perturbative study of two four-quark operators in finite volume renormalization schemes
title A perturbative study of two four-quark operators in finite volume renormalization schemes
title_full A perturbative study of two four-quark operators in finite volume renormalization schemes
title_fullStr A perturbative study of two four-quark operators in finite volume renormalization schemes
title_full_unstemmed A perturbative study of two four-quark operators in finite volume renormalization schemes
title_short A perturbative study of two four-quark operators in finite volume renormalization schemes
title_sort perturbative study of two four-quark operators in finite volume renormalization schemes
topic Particle Physics - Lattice
url https://dx.doi.org/10.1088/1126-6708/2006/03/089
http://cds.cern.ch/record/834789
work_keys_str_mv AT palombifilippo aperturbativestudyoftwofourquarkoperatorsinfinitevolumerenormalizationschemes
AT penacarlos aperturbativestudyoftwofourquarkoperatorsinfinitevolumerenormalizationschemes
AT sintstefan aperturbativestudyoftwofourquarkoperatorsinfinitevolumerenormalizationschemes
AT palombifilippo perturbativestudyoftwofourquarkoperatorsinfinitevolumerenormalizationschemes
AT penacarlos perturbativestudyoftwofourquarkoperatorsinfinitevolumerenormalizationschemes
AT sintstefan perturbativestudyoftwofourquarkoperatorsinfinitevolumerenormalizationschemes