Determination of the QCD Λ Parameter and the Accuracy of Perturbation Theory at High Energies.
We discuss the determination of the strong coupling α_{MS[over ¯]}(m_{Z}) or, equivalently, the QCD Λ parameter. Its determination requires the use of perturbation theory in α_{s}(μ) 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}=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.
John von Neumann Institute for Computing (NIC), DESY, Platanenallee 6, 15738 Zeuthen, Germany.
Mattia
M
Dalla Brida
Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid, C/ Nicolás Cabrera 13-15, Cantoblanco, Madrid 28049, Spain.
Patrick
P
Fritzsch
Department of Physics, Bergische Universität Wuppertal, Gaußstrasse 20, 42119 Wuppertal, Germany.
Tomasz
T
Korzec
Theoretical Physics Department, CERN, CH 1211 Geneva 23, Switzerland.
Alberto
A
Ramos
School of Mathematics, Trinity College Dublin, Dublin 2, Ireland.
Stefan
S
Sint
John von Neumann Institute for Computing (NIC), DESY, Platanenallee 6, 15738 Zeuthen, Germany.|Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany.
Rainer
R
Sommer