Setting the renormalization scale in QCD: The principle of maximum conformality

S. J. Brodsky, L. Di Giustino

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when the renormalization scale is set properly, all nonconformal beta not equal 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with beta = 0. The resulting scale-fixed predictions using the principle of maximum conformality (PMC) are independent of the choice of renormalization scheme-a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale setting in the Abelian limit. The PMC is also the theoretical principle underlying the Brodsky-Lepage-Mackenzie procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors n(f) in the QCD beta function is also correctly determined. We discuss several methods for determining the PMC scale for QCD processes. We show that a single global PMC scale, valid at leading order, can be derived from basic properties of the perturbative QCD cross section. The elimination of the renormalization scale ambiguity and the scheme dependence using the PMC will not only increase the precision of QCD tests, but it will also increase the sensitivity of collider experiments to new physics beyond the Standard Model.
OriginalsprogEngelsk
TidsskriftPhysical Review D (Particles, Fields, Gravitation and Cosmology)
Vol/bind86
Udgave nummer8
ISSN0556-2821
DOI
StatusUdgivet - 2012

Citer dette

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abstract = "A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when the renormalization scale is set properly, all nonconformal beta not equal 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with beta = 0. The resulting scale-fixed predictions using the principle of maximum conformality (PMC) are independent of the choice of renormalization scheme-a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale setting in the Abelian limit. The PMC is also the theoretical principle underlying the Brodsky-Lepage-Mackenzie procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors n(f) in the QCD beta function is also correctly determined. We discuss several methods for determining the PMC scale for QCD processes. We show that a single global PMC scale, valid at leading order, can be derived from basic properties of the perturbative QCD cross section. The elimination of the renormalization scale ambiguity and the scheme dependence using the PMC will not only increase the precision of QCD tests, but it will also increase the sensitivity of collider experiments to new physics beyond the Standard Model.",
author = "Brodsky, {S. J.} and {Di Giustino}, L.",
year = "2012",
doi = "10.1103/PhysRevD.86.085026",
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journal = "Physical Review D. Particles and fields",
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Setting the renormalization scale in QCD: The principle of maximum conformality. / Brodsky, S. J.; Di Giustino, L.

I: Physical Review D (Particles, Fields, Gravitation and Cosmology), Bind 86, Nr. 8, 2012.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Setting the renormalization scale in QCD: The principle of maximum conformality

AU - Brodsky, S. J.

AU - Di Giustino, L.

PY - 2012

Y1 - 2012

N2 - A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when the renormalization scale is set properly, all nonconformal beta not equal 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with beta = 0. The resulting scale-fixed predictions using the principle of maximum conformality (PMC) are independent of the choice of renormalization scheme-a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale setting in the Abelian limit. The PMC is also the theoretical principle underlying the Brodsky-Lepage-Mackenzie procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors n(f) in the QCD beta function is also correctly determined. We discuss several methods for determining the PMC scale for QCD processes. We show that a single global PMC scale, valid at leading order, can be derived from basic properties of the perturbative QCD cross section. The elimination of the renormalization scale ambiguity and the scheme dependence using the PMC will not only increase the precision of QCD tests, but it will also increase the sensitivity of collider experiments to new physics beyond the Standard Model.

AB - A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when the renormalization scale is set properly, all nonconformal beta not equal 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with beta = 0. The resulting scale-fixed predictions using the principle of maximum conformality (PMC) are independent of the choice of renormalization scheme-a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale setting in the Abelian limit. The PMC is also the theoretical principle underlying the Brodsky-Lepage-Mackenzie procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors n(f) in the QCD beta function is also correctly determined. We discuss several methods for determining the PMC scale for QCD processes. We show that a single global PMC scale, valid at leading order, can be derived from basic properties of the perturbative QCD cross section. The elimination of the renormalization scale ambiguity and the scheme dependence using the PMC will not only increase the precision of QCD tests, but it will also increase the sensitivity of collider experiments to new physics beyond the Standard Model.

U2 - 10.1103/PhysRevD.86.085026

DO - 10.1103/PhysRevD.86.085026

M3 - Journal article

VL - 86

JO - Physical Review D. Particles and fields

JF - Physical Review D. Particles and fields

SN - 0556-2821

IS - 8

ER -