A. Deur, S. J. Brodsky, G. F. de Teramond
We review the present knowledge for αs, the fundamental coupling underlying the interactions of quarks and gluons in QCD. The dependence of αs(Q2) on momentum transfer Q encodes the underlying dynamics of hadron physics -from color confinement in the infrared domain to asymptotic freedom at short distances. We review constraints on αs(Q2) at high Q2, as predicted by perturbative QCD, and its analytic behavior at small Q2, based on models of nonperturbative dynamics. In the introductory part of this review, we explain the phenomenological meaning of αs, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain. In the second, more technical, part of the review, we discuss the behavior of αs(Q2) in the high Q2 domain of QCD. We review how αs is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as well as Commensurate Scale Relations which connect the various definitions of αs without renormalization-scale ambiguity. We also report recent measurements and theoretical analyses which have led to precise QCD predictions at high energy. In the last part of the review, we discuss the challenge of understanding the analytic behavior αs(Q2) in the infrared domain. We also review important methods for computing αs, including lattice QCD, the Schwinger-Dyson equations, the Gribov-Zwanziger analysis and light-front holographic QCD. After describing these approaches and enumerating their conflicting predictions, we discuss the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances in this difficult area, but also to suggest what could be an optimal definition of αs in order to bring better unity to the subject.
Comments: Invited review article for Progress in Particle and Nuclear Physics. 195 pages, 18 figures. V3: Minor corrections and addenda compared to V1 and V2. V4: typo fixed in Eq. (3.21)
Subjects: High Energy Physics - Phenomenology (hep-ph)
Journal reference: Prog. Part. Nuc. Phys. 90 1 (2016)