Lattice calculation of $1/p^2$ corrections to $α_s$ and of $Λ_{\rm {QCD}}$ in the $\widetilde{MOM}$ scheme

Ph. Boucaud, G. Burgio, F. Di Renzo, J. P. Leroy, J. Micheli, C. Parrinello, O. Pène, C. Pittori, J. Rodríguez-Quintero, C. Roiesnel, K. Sharkey

Published 2000-03-03, updated 2000-03-06Version 2

We report on very strong evidence of the occurrence of power terms in $\as(p)$, the QCD running coupling constant in the $\widetilde{MOM}$ scheme, by analyzing non-perturbative measurements from the lattice three-gluon vertex between 2.0 and 10.0 GeV at zero flavor. While putting forward the caveat that this definition of the coupling is a gauge dependent one, the general relevance of such an occurrence is discussed. We fit $\Lambda_{\bar{\rm MS}}^{(n_f=0)}= 237 \pm 3 ^{+ 0}_{-10}$ MeV in perfect agreement with the result obtained by the ALPHA group with a totally different method. The power correction to $\as(p)$ is fitted to $(0.63\pm 0.03 ^{+ 0.0}_{- 0.13}) {\rm GeV}^2/p^2$.