Renormalons from eight-loop expansion of the gluon condensate in lattice gauge theory Original Research Article

In SU(3) lattice gauge theory in four dimensions we compute the first eight perturbative coefficients of the expectation value of the Wilson loop on the elementary plaquette which is related to the gluon condensate. This result is obtained by using a numerical method recently proposed. Only the first three coefficients have been computed analytically. The coefficients grow with the order. We show that this growth is related to the non-convergence of the perturbative expansion due to the infrared renormalon associated to the gluon condensate. This conclusion is based on assuming that the renormalon expansion is expressed in a continuum coupling (e.g. in the MS scheme), taking into account the large perturbative corrections between the continuum and the lattice coupling (up to three loops in MS). To corroborate this conclusion we have computed, with less statistics, the first eight perturbative coefficients for the double plaquette. The coefficients for the elementary and double plaquette grow in a similar way and this is in agreement with the universality of the renormalon singularity.