Renormalon disappearance in Borel sum of the 1/N expansion of the Gross-Neveu model mass gap

@article{Kneur2001RenormalonDI,
  title={Renormalon disappearance in Borel sum of the 1/N expansion of the Gross-Neveu model mass gap},
  author={Jean-Lo{\"i}c Kneur and D. Reynaud},
  journal={arXiv: High Energy Physics - Theory},
  year={2001}
}
The exact mass gap of the O(N) Gross-Neveu model is known, for arbitrary $N$, from non-perturbative methods. However, a "naive" perturbative expansion of the pole mass exhibits an infinite set of infrared renormalons at order 1/N, formally similar to the QCD heavy quark pole mass renormalons, potentially leading to large ${\cal O}(\Lambda)$ perturbative ambiguities. We examine the precise vanishing mechanism of such infrared renormalons, which avoids this (only apparent)contradiction, and… 
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Renormalons beyond the Borel plane

The renormalon singularities are a known source of the divergent behavior of asymptotic perturbative series from field theoretical models. These singularities live in the Borel plane and are

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Note that, even if DR regularizes the momenta integrals, we define the integral over the IR region

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