RENORMALONS ON THE LATTICE AND THE OPE FOR THE PLAQUETTE: A STATUS REPORT

The first ten coefficients in the perturbative expansion of the plaquette in Lattice SU(3) are computed both on a 8⁴ and on a 24⁴ lattice. They are shown to be fully consistent with the growth dictated by the first IR Renormalon and with the expected finite size effects on top of that. As already pointed out a few years ago, this leads to a puzzling result on the smaller lattice: when the contribution associated with the Renormalon is subtracted from Monte Carlo measurements of the plaquette, what is left over does not scale (as expected) as a⁴, but as a². While the analysis is not yet complete on the larger lattice, the implications of such a finding is discussed.