RENORMALONS FROM EIGHT LOOP EXPANSION OF THE GLUON CONDENSATE IN LATTICE GAUGE THEORY,

Abstract

We use a numerical method to obtain the weak coupling perturbative coefficients of local operators with lattice regularization. Such a method allows us to extend the perturbative expansions obtained so far by analytical Feynman diagrams calculations. In SU(3) lattice gauge theory in four dimensions we compute the first eight coefficients of the expectation value of the Wilson loop on the elementary plaquette which is related to the gluon condensate. The computed eight coefficients grow with the order much faster than predicted by the presence of the infrared renormalon associated to the dimension of the gluon condensate. However the renormalon behaviour for large order is quite well reproduced if one considers the expansion coefficients in a new coupling related to the lattice coupling by large perturbative corrections. This is expected since the lattice and continuum Lambda scales differ by almost two orders of magnitude.