Renormalons in the effective potential of the vectorial (Φ2)2 model

We study the properties of ultraviolet renormalons in the vectorial (Φ2)2 model. This is achieved by studying the effective potential of the theory at next to leading order of the 1N expansion, the appearence of the renormalons in the perturbative series and their relation to the imaginary part of the potential. We also consider the mechanism of renormalon cancellation by “irrelevant” higher dimensional operators. Adding to the lagrangian these operators we can remove the imeginary parts of the effective potential. We argue that the (Φ2)2 theory can be treated only as an effective theory and as a low energy limit of a more “complete” theory without UV renormalon problems.