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

TL;DR

This paper demonstrates that the perturbative 1/N expansion of the Gross-Neveu model's mass gap is free of infrared renormalon ambiguities due to a specific vanishing mechanism, ensuring its Borel summability and suggesting similar features might exist in QCD.

Contribution

It reveals the precise mechanism by which infrared renormalons vanish in the 1/N expansion of the Gross-Neveu model's mass gap, ensuring Borel summability without contour prescriptions.

Findings

Infrared renormalons cancel in the 1/N expansion of the mass gap.

The perturbative series is directly Borel summable.

Potential implications for non-perturbative QCD quantities.

Abstract

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 operates without need of (Borel) summation contour prescription, usually preventing unambiguous separation of perturbative contributions. As a consequence we stress the direct Borel summability of the (1/N) perturbative expansion of the mass gap. We briefly speculate on a possible similar behaviour of analogous non-perturbative QCD quantities.