Determination of the QCD Λ Parameter and the Accuracy of Perturbation Theory at High Energies

We discuss the determination of the strong coupling alpha(MS)-(m(Z)) or, equivalently, the QCD Lambda parameter. Its determination requires the use of perturbation theory in alpha(s)(mu) in some scheme s and at some energy scale mu. The higher the scale mu, the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the Lambda parameter in three-flavor QCD, we perform lattice computations in a scheme that allows us to nonperturbatively reach very high energies, corresponding to alpha(s) = 0.1 and below. We find that (continuum) perturbation theory is very accurate there, yielding a 3% error in the Lambda parameter, while data around alpha(s) approximate to 0.2 are clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.