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Title: The QCD running coupling

Here, we review present knowledge on $$\alpha_{s}$$, the Quantum Chromodynamics (QCD) running coupling. The dependence of $$\alpha_s(Q^2)$$ 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 will survey our present theoretical and empirical knowledge of $$\alpha_s(Q^2)$$, including constraints at high $Q^2$ predicted by perturbative QCD, and constraints at small $Q^2$ based on models of nonperturbative dynamics. In the first, introductory, part of this review, we explain the phenomenological meaning of the coupling, 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 $$\alpha_s(Q^2)$$ in the high momentum transfer domain of QCD. We review how $$\alpha_s$$ 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 the QCD coupling without renormalization scale ambiguity. We also report recent important experimental measurements and advanced theoretical analyses which have led to precise QCD predictions at high energy. As an example of an important optimization procedure, we discuss the ``Principle of Maximum Conformality" which enhances QCD's predictive power by removing the dependence of the predictions for physical observables on the choice of the gauge and renormalization scheme. In last part of the review, we discuss $$\alpha_s(Q^2)$$ in the low momentum transfer domain, where there has been no consensus on how to define $$\alpha_s(Q^2)$$ or its analytic behavior. We will discuss the various approaches used for low energy calculations. Among them, we will discuss the light-front holographic approach to QCD in the strongly coupled regime and its prediction for the analytic form of $$\alpha_s(Q^2)$$. The AdS/QCD light-front holographic analysis predicts the color confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale $$\Lambda$$ and hadron masses. One can also identify a specific scale $$Q_0$$ which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including Lattice QCD, Schwinger-Dyson equations and the Gribov-Zwanziger analysis. After describing these approaches and enumerating conflicting results, we provide a partial discussion on the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances on this difficult subject, but also to suggest what could be the best definition of $$\alpha_s(Q^2)$$ in order to bring better unity to the subject.
 [1] ;  [2] ;  [3]
  1. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  3. Univ. of Costa Rica, San Jose (Costa Rica)
Publication Date:
Report Number(s):
JLAB-PHY-16-2199; DOE/OR/-23177-3645
Journal ID: ISSN 0146-6410; PII: S0146641016300035
Grant/Contract Number:
AC05–06OR23177; AC02–76SF00515. SLAC-PUB-16448; DE–AC05–06OR23177; DE–AC02–76SF00515. SLAC-PUB-16448
Accepted Manuscript
Journal Name:
Progress in Particle and Nuclear Physics
Additional Journal Information:
Journal Volume: 90; Journal Issue: C; Journal ID: ISSN 0146-6410
Research Org:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
Country of Publication:
United States
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; QCD; coupling constant; non-perturbative; renormalization; infrared properties; hadron physics
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1359800