Running coupling in QCD

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 see

Universality and the approach to the continuum limit
in lattice gauge theory, 

Nucl. Phys. B437 (1995) 447, hep-lat/9411017

A precise determination of the running coupling in the SU(3)
Yang-Mills Theory,

Nucl. Phys. B413 (1994) 481, hep-lat/9309005

and references quoted therein. For the unquenched case, see

Lattice investigations of the running coupling,

Nucl. Phys. B (Proc. Suppl.) 47 (1996) 71, hep-lat/9511017

Recent results on the running coupling in QCD with two massless flavors,
DESY-02-124, hep-lat/0209023

Computation of the strong coupling in QCD with two dynamical flavours,
DESY-04-217, HU-EP-04-64, MS-TP-04-31, BICOCCA-FT-04-16, SFB-CPP-04-59, hep-lat/0411025