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

Abstract

We discuss the determination of the strong coupling α MS ð m Z Þ or, equivalently, the QCD Λ parameter. Its determination requires the use of perturbation theory in α s ð μ Þ in some scheme s and at some energy scale μ . The higher the scale μ , the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the Λ parameter in three-flavor QCD, we perform lattice computations in a scheme that allows us to nonperturbatively reach very high energies, corresponding to α s ¼ 0 . 1 and below. We find that (continuum) perturbation theory is very accurate there, yielding a 3% error in the Λ parameter, while data around α s ≈ 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.