A nice, comprehensive primer on the running of the QCD coupling constant is now available and runs to a mere 195 pages.
If you prefer to get right down to bottom line, the five loop beta function for the QCD coupling constant (a.k.a. the strong force coupling constant) in the MS bar renormalization scheme is also available. Notable, at the QCD scale in that renormalization scheme of about a third of one GeV, the precision of the theory is only about +/- 5%. This QCD scale, in turn, is fundamentally connected to the scale of the hadron masses.
Generically, the running of the QCD coupling constant described by this beta function differs from the Standard Model version linked above in most beyond the Standard Model theories and so comparing the data to this Standard Model prediction provides a useful experimental test of such theories.
QCD fans may also appreciate a 2013 summary of eighteen significant open problems in QCD. This article ultimately distills thirteen lessons from its eighteen puzzles (emphasis added):
We point out numerous areas wherein often-used procedures in QCD and hadron physics have been challenged. These include the following conventional assumptions.
1. The structure function of a hadron reflects only the physics of the wave function of the hadron and thus must be process independent. In fact, the observed structure functions are sensitive to rescattering processes at leading twist, which are process dependent.
2. Antishadowing is a property of the nuclear wave function and is thus process independent. In fact, as the NuTeV data show, each quark may have its own antishadowing distribution.
3. Initial-state and final-state interactions are always power-law suppressed and process independent. This hypothesis is contradicted by the Sivers effect in SIDIS and the breakdown of the Lam–Tung relation in Drell–Yan reactions.
4. High–transverse momentum hadrons always arise only from jet fragmentation. In fact, there is a significant probability that high-pT hadrons arise from hard color-transparent subprocesses. As we discuss above, direct higher-twist processes wherein the hadron wave function appears in the subprocess matrix element can explain anomalies in the fixed-xT cross section and the remarkable baryon anomaly, the large proton-to-pion ratio observed in heavy-ion collisions at RHIC.
5. The renormalization scale in QCD cannot be fixed and can only be guessed to minimize sensitivity. In fact, it can be fixed at each order in perturbation theory in a scheme-independent way that agrees with the conventional QED procedure.
6. QCD condensates must be properties of the vacuum. As we discuss above, contrary results are obtained in Bethe–Salpeter and LF analyses. The conflict with the cosmological constant highlights the need to distinguish different concepts of the vacuum obtained from the usual instant form versus the causal LF definition.
7. Infrared slavery: The QCD running coupling must diverge at long distances. This is not correct in LF holographic QCD, nor is it true if one defines the QCD coupling through an effective charge defined from experiment.
8. Nuclei can be regarded as composites of color-singlet nucleons. In fact, QCD predicts hidden-color configurations of the quarks, which can dominate short-distance nuclear reactions.
9. The real part of DVCS is an arbitrary subtraction term. In fact, local four-point photonquark scattering can lead to a novel amplitude that is constant in energy and independent of the photons’ virtuality at fixed t.
10. Heavy quark thresholds cause minimal effects. In fact, the charm and strangeness thresholds can lead to unexpectedly large competing amplitudes and striking polarization effects, such as the remarkable spin-spin correlations observed in elastic pp scattering and, at large angles, the breakdown of pQCD color transparency.
11. Gluon degrees of freedom should be manifest at all scales. In fact, the effects of soft gluons may well be sublimated in favor of the QCD confinement potential.
12. Orbital angular momentum effects are negligible. In fact, in the LF framework the hadron eigensolutions for the light quarks have orbital components that are comparable in strength to the L = 0 components.
To summarize further, in my words:13. The heavy quark sea arises only from gluon splitting and is thus confined to the low-x domain. In fact, QCD predicts contributions where the heavy quarks are multiconnected to the valence quarks and thus appear at high x.
* Many observables which one would naively assume are process independent are in fact dependent upon the process involved in QCD. (1), (2) and (3).
* Holographic light front relativistic approaches make significantly different predictions than non-relativistic or non-causal approaches in many circumstances. (6), (7) and (12).
* Detailed technical analysis of every possibility including those that might seem unnatural or irrelevant often has a measurable impact on observables in QCD. (4), (8), (9), (10), (12) and (13).
* But, sometimes technical details that seem like they should be important are not. (5) and (11).