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Johan Rathsman. Photo.

Johan Rathsman

Senior lecturer

Johan Rathsman. Photo.

Disentangling running coupling and conformal effects in QCD


  • S. J. Brodsky
  • E. Gardi
  • G. Grunberg
  • J. Rathsman

Summary, in English

We investigate the relation between a postulated skeleton expansion and the conformal limit of QCD. We begin by developing some consequences of an Abelian-like skeleton expansion, which allows one to disentangle running-coupling effects from the remaining skeleton coefficients. The latter are by construction renormalon free, and hence hopefully better behaved. We consider a simple ansatz for the expansion, where an observable is written as a sum of integrals over the running coupling. We show that in this framework one can set a unique Brodsky-Lepage-Mackenzie (BLM) scale-setting procedure as an approximation to the running-coupling integrals, where the BLM coefficients coincide with the skeleton ones. Alternatively, the running-coupling integrals can be approximated using the effective charge method. We discuss the limitations in disentangling running coupling effects in the absence of a diagrammatic construction of the skeleton expansion. Independently of the assumed skeleton structure we show that BLM coefficients coincide with conformal coefficients defined in the small (Formula presented) (Banks-Zaks) limit where a perturbative infrared fixed point is present. This interpretation of the BLM coefficients should explain their previously observed simplicity and smallness. Numerical examples are critically discussed.

Publishing year





Physical Review D - Particles, Fields, Gravitation and Cosmology





Document type

Journal article


American Physical Society


  • Subatomic Physics




  • ISSN: 1550-7998