Lattice calculation of 1/p2 corrections to αs and of ΛQCD in the (MOM)over-tilde scheme.

We report on very strong evidence of the occurrence of power terms in alpha(<(MOM)over tilde>) (p), the QCD running coupling constant in the <(MOM)over tilde> 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(<(MS)over bar>)((nf=0)) = 237 +/- 3(-10)(+0) MeV in perfect agreement with the result obtained by the ALPHA group with a totally different method. The power correction to alpha(<(MOM)over tilde>) (p) is fitted to (0.63 +/- 0.03(-0.13)(+0.0)) GeV2/p(2).