Conformal Symmetry as a Template:Commensurate Scale Relations and Physical Renormalization Schemes
- SLAC
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
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Related Subjects
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANNIHILATION
CROSS SECTIONS
DEEP INELASTIC SCATTERING
ELECTRON-POSITRON COLLISIONS
FERMIONS
INTERMEDIATE VECTOR BOSONS
MOMENTUM TRANSFER
PHOTONS
POMERANCHUK PARTICLES
QUANTUM CHROMODYNAMICS
QUARKS
RENORMALIZATION
SCATTERING
SUM RULES
SYMMETRY