The QCD Running Coupling

TL;DR

This paper explains the nature, scale dependence, and calculation methods of the strong force coupling constant, $oldsymbol{oldsymbol{ ext{α}_s}}$, in quantum chromodynamics, including experimental measurements at various scales.

Contribution

It provides a comprehensive overview of the theoretical foundations, calculation techniques, and experimental determinations of the QCD coupling constant $ ext{α}_s$, highlighting its scale dependence.

Findings

Description of the quantum origin of $ ext{α}_s$ scale dependence

Comparison of perturbative and nonperturbative calculation methods

Summary of experimental measurements of $ ext{α}_s$ at different scales

Abstract

We describe the coupling of the strong force. Denoted as $\alpha_s$, it sets the strength of that force, just as $G$ or $\alpha$ specify the strength of the gravity and electromagnetism. Its value depends on the scale at which phenomena are observed. In this chapter, we will explain the nature of the coupling, the quantum origin of its scale dependence, and the crucial consequences this entails for quantum chromodynamics, the gauge theory for the strong force. We describe the theories for the calculation of $\alpha_s$, using the perturbative method at high-momentum scales (equivalently, short-distance scales) and nonperturbative approaches at low-momentum scales (equivalently, long-distance scales). We also present the experimental determinations of $\alpha_s$ at both short and long distance scales.