If one takes the physical values of the pion decay constant, the mass of the charged pion and the kaon masses as input, one should be able to calculate the masses of the light quarks u,d,s using lattice QCD and numerical simulations. One of the principal difficulties in this calculation is that the quark masses are initially obtained in a lattice scheme. The renormalization factor needed to match with the standard perturbative definitions of the masses is currently only known to one-loop order of perturbation theory and one may, moreover, be hesitant to apply this formula at the values of the bare coupling where the numerical data are obtained.
The finite-size scaling technique previously applied in the case of the running coupling may also be used to determine the scale evolution of the quark masses. The uncertainty in the renormalization factor can be eliminated in this way and the collaboration has now initiated such a calculation in quenched QCD.
Our computational strategy is described in outline in"Non-perturbative renormalization of lattice QCD at all scales",
Results can be found in"Running quark mass in two flavor QCD",