Conformal Symmetry as a Template for QCD

Technical Report · Wed Aug 04 00:00:00 EDT 2004

DOI:https://doi.org/10.2172/829728· OSTI ID:829728

Brodsky, S ^[1]

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1. SLAC

Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero {beta} function as well as higher-twist effects. For example, commensurate scale relations which relate QCD observables to each other, such as the generalized Crewther relation, have no renormalization scale or scheme ambiguity and retain a convergent perturbative structure which reflects the underlying conformal symmetry of the classical theory. The ''conformal correspondence principle'' also dictates the form of the expansion basis for hadronic distribution amplitudes. The AdS/CFT correspondence connecting superstring theory to superconformal gauge theory has important implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for hard exclusive processes as well as determining essential aspects of hadronic light-front wavefunctions. Theoretical and phenomenological evidence is now accumulating that QCD couplings based on physical observables such as {tau} decay become constant at small virtuality; i.e., effective charges develop an infrared fixed point in contradiction to the usual assumption of singular growth in the infrared. The near-constant behavior of effective couplings also suggests that QCD can be approximated as a conformal theory even at relatively small momentum transfer. The importance of using an analytic effective charge such as the pinch scheme for unifying the electroweak and strong couplings and forces is also emphasized.

• Research Organization: Stanford Linear Accelerator Center, Menlo Park, CA (US)
• Sponsoring Organization: USDOE Office of Science (US)
• DOE Contract Number: AC03-76SF00515
• OSTI ID: 829728
• Report Number(s): SLAC-PUB-10576
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
DECAY
DISTRIBUTION
EFFECTIVE CHARGE
HADRONS
MOMENTUM TRANSFER
QUANTUM CHROMODYNAMICS
RENORMALIZATION
SYMMETRY