Conformal Symmetry as a Template:Commensurate Scale Relations and Physical Renormalization Schemes Page: 1 of 27
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SLAC-PUB-8176
June 1999
CONFORMAL SYMMETRY AS A TEMPLATE:
COMMENSURATE SCALE RELATIONS AND
PHYSICAL RENORMALIZATION SCHEMES*
Stanley J. Brodsky and Johan Rathsman
Stanford Linear Accelerator Center
Stanford, California 94309
Abstract
Commensurate scale relations are perturbative QCD predictions which
relate observable to observable at fixed relative scale, such as the "generalized
Crewther relation", which connects the Bjorken and Gross-Llewellyn Smith deep in-
elastic scattering sum rules to measurements of the e+e- annihilation cross section.
We show how conformal symmetry provides a template for such QCD predictions,
providing relations between observables which are present even in theories which are
not scale invariant. All non-conformal effects are absorbed by fixing the ratio of the
respective momentum transfer and energy scales. In the case of fixed-point theo-
ries, commensurate scale relations relate both the ratio of couplings and the ratio of
scales as the fixed point is approached. In the case of the av scheme defined from
heavy quark interactions, virtual corrections due to fermion pairs are analytically
incorporated into the Gell-Mann Low function, thus avoiding the problem of explic-
itly computing and resumming quark mass corrections related to the running of the
coupling. Applications to the decay width of the Z boson, the BFKL pomeron, and
virtual photon scattering are discussed.
Invited talk presented at Les Rencontres de Physique de la Vallie d'Aoste
La Thuile, Aosta Valley, Italy, February 28-March 6, 1999*Work partially supported by the Department of Energy, contract DE-AC03-76SF00515.
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Brodsky, Stanley J. Conformal Symmetry as a Template:Commensurate Scale Relations and Physical Renormalization Schemes, report, June 9, 1999; Menlo Park, California. (https://digital.library.unt.edu/ark:/67531/metadc624225/m1/1/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.