From Wikipedia Coupling Constants, using QED as an example. I realise that the one-loop beta function in quantum chromodynamics is negative.
If a beta function is positive, the corresponding coupling increases with increasing energy. An example is quantum electrodynamics (QED), where one finds by using perturbation theory that the beta function is positive. In particular, at low energies, α ≈ 1/137, whereas at the scale of the Z boson, about 90 GeV, one measures α ≈ 1/127. Moreover, the perturbative beta function tells us that the coupling continues to increase, and QED becomes strongly coupled at high energy. In fact the coupling apparently becomes infinite at some finite energy.
My questions are based on pure curiosity (and a total lack of experimental experience, so my apologies if this combination displays naivety on my part).
Have we tested coupling constants at the lowest temperature/energy to confirm a reduction at the far end of the energy scale from the LHC?
It may be that low temperature experiments have to take any changes in values as a matter of routine, to correspond to theoretical predictions, so "yes, of course!!!" is an perfectly acceptable answer.
If a reduction has been observed in the value of any arbitrary constant, at these extremely low temperatures, can we compare this to conditions if the "heat death of the universe" scenario is true and predict what effects will occur as the temperature drops?