Non-perturbative renormalization

Hadronic and semi-leptonic weak decay amplitudes are proportional to matrix elements of an effective Hamilton operator, which is obtained from the electro-weak theory using Wilson's operator product expansion. The normalization of the local operators appearing in the expansion is initially defined in perturbation theory, using dimensional regularization and minimal subtraction, for example.

On the lattice the matrix elements of the corresponding lattice operators can be evaluated through numerical simulations and one then needs to match the lattice with the perturbative normalizations. It is not obvious that this can be done reliably in perturbation theory, because the renormalization scale at which the lattice operators can be studied is rather low in physical units. The finite-size scaling technique applied previously to compute the running coupling should be useful here too, and first steps are being made to calculate the scale-dependence of hadronic matrix elements of local operators in this way.

Further details can be found in

"Non-perturbative renormalization of lattice QCD at all scales",

Phys. Lett. B372 (1996) 275, hep-lat/9512009 and

"Nonperturbative renormalization of HQET and QCD",

Nucl.Phys.Proc.Suppl. 119 (2003) 185, hep-lat/0209162