Coupling constants in the quantum field theories of the Standard Model (SM) are not constant. The couplings, which set the strength for the interactions, change their value if one probes smaller distances with higher energies. This is due to contributions of virtual particles that cause a 'running' of the coupling with the energy scale. This energy scale is also referred to as the 'sliding scale'. If one evaluates the necessary Feynman diagrams to compute this effect, it turns out that the couplings run logarithmically with the sliding scale, and their slope depends on the particle content.
The left side of the above plot shows the inverse of the three SM couplings αi as a function of the sliding scale Q (in GeV) [see comment]. The thickness of the lines depicts the experimental error (LEP data '91). The scale on the x-axis is logarithmic, such that the curves become straight lines. This running of the coupling constants has been experimentally confirmed in the accessible energy range, but the more interesting thing here is that one can extrapolate the curves far beyond where we can test them experimentally. One sees then that these couplings form a triangle somewhere around 1016 GeV.
The plot to the right shows the running of the gauge couplings within the Minimal Supersymmetric extension of the Standard Model (MSSM). Since the particle content with Supersymmetry (SUSY) is different, the slope of the curves changes. Interestingly, the result is that the gauge couplings meet almost exactly (within the errorbars) in one point, somewhere around 1016 GeV, usually referred to as the GUT scale (which isn't too far off the Planck scale).
The above depicted fit of the curves depends on the scale where SUSY is (un)broken. Below this energy, the running is according to the SM, and only changes above the SUSY breaking scale. This is why in the plot to the right the curves have a kink and change slope around a TeV, which was assumed to be the SUSY breaking scale.
This calculation has first been done by Amaldi, de Boer and Fürstenau in 1991 (Phys. Lett. B 260 447-455, 1991), and this result is to be considered one of the most compelling arguments for SUSY.
This post is part of our 2007 advent calendar A Plottl A Day.