Experimental Tests of Asymptotic Freedom

TL;DR

This article reviews experimental tests of asymptotic freedom in QCD, tracing the theoretical foundation from renormalization and running coupling to high-energy jet and DIS measurements. It synthesizes results from e+e− annihilations, DIS, and lattice calculations, culminating in a precise world average αs(MZ)=0.1189±0.0010 that confirms the QCD running coupling and SU(3) gauge structure. The work demonstrates how higher-order perturbative calculations and nonperturbative approaches cohere to explain data across a wide energy range, establishing asymptotic freedom as a cornerstone of the Standard Model. Looking ahead, NNLO predictions and expanded observables promise further refinements in αs and tighter tests of QCD.

Abstract

Quantum Chromodynamics (QCD), the gauge field theory of the Strong Interaction, has specific features, asymptotic freedom and confinement, which determine the behaviour of quarks and gluons in particle reactions at high and at low energy scales. QCD predicts that the strong coupling strength $\as$ decreases with increasing energy or momentum transfer, and vanishes at asymptotically high energies. In this review, the history and the status of experimental tests of asymptotic freedom are summarised. The world summary of measurements of $\as$ is updated, leading to an unambiguous verification of the running of $\as$ and of asymptotic freedom, in excellent agreement with the predictions of QCD. Averaging a set of measurements balanced between different particle processes and the available energy range, results in a new and improved world average of $\amz = 0.1189 \pm 0.0010 .$

Figures (18)

• Figure 1: The structure function of the proton, describing the electron- proton scattering in units of the Mott cross section, i.e. the generalised Rutherford cross section at high energies, as measured at SLAC slac-data. $\omega = 4$ corresponds to $x = 0.25$ in figure \ref{['fig:f2']}.
• Figure 2: The first 3-jet event, observed by the TASSO experiment at the PETRA $\rm e^+\rm e^-$ storage ring gluon.
• Figure 3: Summary of measurements of $\alpha_{\rm s}$ in 1989 altarelli-89. Shown are results from various experiments in deep inelastic lepton-nucleon scattering as well as combined results from $\rm e^+\rm e^-$ collisions, together with the QCD expectation of a running $\alpha_{\rm s}$ for different values of $\Lambda_{\overline{MS}}$ (see section 3).
• Figure 4: (a) The running of $\alpha_{\rm s} (Q)$, according to equation \ref{['eq-as4loop']}, in 4-loop approximation, for different values of $\Lambda_{\overline{MS}}$; (b) same as full line in (a), but as function of 1/log(Q/GeV) to demonstrate asymptotic freedom, i.e. $\alpha_{\rm s} (Q^2 ) \rightarrow 0$ for $Q \rightarrow \infty$.
• Figure 5: (a) The running of $\alpha_{\rm s} (Q)$, according to equation \ref{['eq-as4loop']}, in 1-, 2- and 3-loop approximation, for $N_f = 5$ and the same value of $\Lambda_{\overline{MS}} = 0.22$ GeV. The 4-loop prediction is indistinguishable from the 3-loop curve. (b) Fractional difference between the 4-loop and the 1-, 2- and 3-loop presentations of $\alpha_{\rm s} (Q)$, for $N_f = 5$ and $\Lambda_{\overline{MS}}$ chosen such that, in each order, $\alpha_{\rm s}(M_{\rm Z^0}) = 0.119$.