The textbook description of quantum chromodynamics (the quantum theory that explains the interaction of quarks and gluons through the strong force), notes that unlike the electromagnetic force, which grows stronger at higher energies (a phenomena known as the running of the coupling constant for electromagnetism), the coupling constant of the strong force grows weaker at higher energies. These observations, together with the running of the coupling constant of the weak force, produces the charts favored by Grand Unified Theory proponents that show the three coupling constants converging on a common strength at very high energies around 15 TeV (the GUT scale).

The mere fact that coupling constants aren't actually constants, but instead run with the energy level of the interaction via Beta functions is itself a major surprise for most people unfamiliar with quantum physics.

But, even the textbook description has a flaw. It turns out, as QCD theorist Marco Frasca noted in his Gauage Connection blog in a recent post on research in the field, that the running coupling constant of the strong force weakens on both the low energy and high energy sides of the strong force scale (of about 216 MeV) where its coupling constant peaks, something that was not previously noted by researchers using perturbative methods to approximate QCD equation solutions numerically, rather than the numerical approximations used in Lattice QCD, which do not contain a linearizing approximation method used in peturbative QCD calculuations.

This would be a pretty trival matter unimportant except to QCD theorists were it not for some key point that it illustrates that pertinent to all GUT theories.

First, perturbative approximations are not an accurate way of inferring beta functions at extreme values, because they are insufficiently non-linear. If a widely assumed curve for the highly non-linear beta function of the QCD coupling constant is quite wrong, why shouldn't the beta function of some other force be a little bit wrong? Why come up with a major new tweak to theoretical physics that proposes all sorts of new particles and interactions to make the running coupling constants converge when all you really have to do tweak an obscure phenomenological beta function for a coupling constant or two at energy scales where the perturbative approximations used to estimate them probably aren't valid anyway? Tweaking beta functions may be a way to save the Standard Model from problems that seem to be present at high energy and require other fixes. Maybe that isn't the right answer, but there are far too few papers being written that probe whether it could be the right answer.

Second, the chart that GUT theorists favor as an empirical and emotional motivation for GUT theories looks a lot less compelling when you have a running coupling constant for the strong force that goes up before it goes down, rather than converging inexorably upon a unified GUT scale convergence point.

The issue also comes to a head when you look at top quark physics. At the sufficiently high energy scales found in top quarks, QCD breaks down. Top quarks decay before the strong force can produce the hadronization and confinement seen in the physics of the other five quarks. At the energy scale of the top quark (each top quark has a rest mass of between 173 GeV and 174 GeV v. a bottom quark with a rest mass of between 4 GeV and 5 GeV), the strong force seemingly ceases to become a meaningful concept at all. How can you talk about the running of the strong force coupling constant at energy levels where the strong force empirically seems to vanish? What if rather than converging to a fixed point, the strong force coupling constant effectively dips all of the way to zero and drops below the weak force and electromagnetic force coupling constant before any of the three have converged? Yet, doesn't the fact that the weak force produces top quark decays before the strong force can hadronize top quarks just what you would predict in that scenario? Maybe the apparent convergence in coupling constants that we observe is really just a product of true convergence of a unified electroweak force and wild overextrapolation of the running of the strong force coupling constant that doesn't actually converge toward the other two coupling constants at all if better modeled?

It may also not be coincidental that the top quark mass is a great departure from the patterns shown by the mass matrix of the other five quarks that do hadronize (it is much larger in mass than expected). One possible source for this discrepency could be that the conventional masses of the hadronizing quarks are deflated relative to binding energy from gluons in the formula used to parse them out of the confined structures in which they appear. If more of the mass of hadronized quarks than conventionally assumed is in the quarks themselves, and less of the mass of hadronized quarks is in the glue (which is absent from estimates of top quark mass), then the top quark mass isn't anomalous after all.

On the other hand, the apparent experimental confirmation of experimental predictions for a ground state glueball mass would suggest that the conventional quark masses can't be too far off, since the theory seems to estimate glueball mass accurately even when quark contributions are absent.

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