A long-term goal of the ALPHA collaboration is to determine the running coupling alpha(q) at large momenta q given in units of the low-energy scales of the theory (such as the pion decay constant). The calculation involves a non-perturbative finite-size scaling technique, which allows one to step up the energy scale in a recursive manner with controlled errors. In the case of the pure SU(2) and SU(3) gauge theories the problem has been completely solved in the years 1992-1994. Much work has since then been spent for the next step, the calculation of alpha(q) in full QCD with a doublet of massless quarks.
For the SU(2) and SU(3) results seeUniversality and the approach to the continuum limit in lattice gauge theory,