Renormalons in the effective potential of the vectorial $(\vec{\varphi}^{2})^{2}$ model

TL;DR

This paper investigates ultraviolet renormalons in the vectorial $(oldsymbol{}^{2})^{2}$ model by analyzing the effective potential at next-to-leading order, exploring their perturbative series appearance, and examining cancellation mechanisms.

Contribution

It provides a detailed analysis of ultraviolet renormalons in the $(oldsymbol{}^{2})^{2}$ model using the $1/N$ expansion and discusses their cancellation via higher-dimensional operators.

Findings

Renormalons appear in the perturbative series of the effective potential.

The imaginary part of the potential is related to renormalon singularities.

Higher-dimensional operators can cancel renormalon effects.

Abstract

We study the properties of ultraviolet renormalons in the vectorial $(\vec{\phi}^{2})^{2}$ model. This is achieved by studying the effective potential of the theory at next to leading order of the $1/N$ expansion, the appearence ofthe 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.