The QCD running coupling

Abstract

We review the present theoretical and empirical knowledge for α s , the fundamental coupling underlying the interactions of quarks and gluons in Quantum Chromodynamics (QCD). The dependence of α 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 review constraints on α s (Q 2 ) at high Q 2 , as predicted by perturbative QCD, and its analytic behavior at small Q 2 , based on models of nonperturbative dynamics. In the 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 the behavior of α s (Q 2 ) in the high momentum transfer domain of QCD. We review how α 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 significant 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 theoretical conventions such as the renormalization scheme. In the last part of the review, we discuss the challenge of understanding the analytic behavior α s (Q 2 ) in the low momentum transfer domain. We survey various theoretical models for the nonperturbative strongly coupled regime, such as the light-front holographic approach to QCD. This new framework predicts the form of the quark-confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale Λ 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, the Schwinger-Dyson equations and the GribovZwanziger analysis. 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 α s (Q 2 ) in order to bring better unity to the subject.2

Spin effects in the pion holographic light-front wavefunction

“…QCD , in excellent agreement with the world average value [18]. Furthermore, light-front holographic wavefunctions have also been used to predict diffractive vector meson production [19,20].…”

“…In the most recent application of LFH to predict nucleon EM form factors [21], it is pointed out that this universality holds up to 10% accuracy. In this paper, we shall use the value of κ = 523 MeV which fits the meson/baryon Regge slopes and accurately predicts Λ M S QCD [9,18]. In earlier applications of LFH with massless quarks, much lower values of κ were required to fit the pion data: κ = 375 MeV in Ref.…”

Dynamical spin effects in the pion

“…Previous work [7,14,16] has shown that κ ≈ 0.5 GeV for light mesons. Specifically, we shall take the most recent universal value κ = 523 MeV which fits the meson/baryon Regge slopes [17] and accurately predicts Λ MS QCD [18]. We shall predict the pion EM form factor, the pion radius and decay constant and the photon-to-pion transition form factor.…”

Self-interacting scalar fields at high-temperature

“…The QCD coupling at long distance is large [23]. There, effects from the higher order cubic and quartic terms of Eq.…”

“…In QCD, the non-linear regime arises for distances greater than 2 × 10 −16 m when α s becomes large: α s 0.5 in the M S scheme [23]. Likewise, such a regime should arise in GR when g = √ 16π G M is large, with M the system mass, and the system size is comparable to the field correlation length L. For a galaxy, typically √ 16π G M/L 10 −2 , with L = 10 kpc taken to be a third of a typical galaxy size, and M = 3 × 10 11 M , a typical galaxy mass.…”