On the Interface between Perturbative and Nonperturbative QCD

Abstract

The QCD running coupling ${\alpha }_s(Q^2)$ sets the strength of the interactions of quarks and gluons as a function of the momentum transfer $Q$. The $Q^2$ dependence of the coupling is required to describe hadronic interactions at both large and short distances. In this article we adopt the light-front holographic approach to strongly-coupled QCD, a formalism which incorporates confinement, predicts the spectroscopy of hadrons composed of light quarks, and describes the low-$Q^2$ analytic behavior of the strong coupling ${\alpha }_s(Q^2)$. The high-$Q^2$ dependence of the coupling ${\alpha }_s(Q^2)$ is specified by perturbative QCD and its renormalization group equation. The matching of the high and low $Q^2$ regimes of ${\alpha }_s(Q^2)$ then determines the scale $Q_0$ which sets the interface between perturbative and nonperturbative hadron dynamics. The value of $Q_0$ can be used to set the factorization scale for DGLAP evolution of hadronic structure functions and the ERBL evolution of distribution amplitudes. We discuss the scheme-dependence of the value of $Q_0$ and the infrared fixed-point of the QCD coupling. Our analysis is carried out for the $\overline{MS}$, $g_1$, $MOM$ and $V$ renormalization schemes. Our results show that the discrepancies on the value of ${\alpha }_s$ at large distance seen in the literature can be explained by different choices of renormalization schemes. We also provide the formulae to compute ${\alpha }_s(Q^2)$ over the entire range of space-like momentum transfer for the different renormalization schemes discussed in this article.

20 pages, 3 figures. V2: Version accepted for publication (Phys.Lett. B757 275 (2016)). V3: Corrected Fig.3 for wrong label (data were plotted vs Q, not Q^2)

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