Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Conformal Symmetry as a Template:Commensurate Scale Relations and Physical Renormalization Schemes

Technical Report ·
DOI:https://doi.org/10.2172/10102· OSTI ID:10102

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 inelastic scattering sum rules to measurements of the e{sup +}e{sup {minus}} 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 theories, 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 {alpha}{sub V} 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 explicitly computing and resuming 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.

Research Organization:
Stanford Linear Accelerator Center, Menlo Park, CA (US)
Sponsoring Organization:
USDOE Office of Energy Research (ER) (US)
DOE Contract Number:
AC03-76SF00515
OSTI ID:
10102
Report Number(s):
SLAC-PUB-8176
Country of Publication:
United States
Language:
English