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

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 $\mathcal{O}(\Lambda )$ 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.

16 pp., 1 figure. v2: a few paragraphs and one appendix added, title and abstract slightly changed, essential results unchanged

References in corpus (2)

• (Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap
• Borel convergence of the variationally improved mass expansion and dynamical symmetry breaking

Cited by in corpus (6)

• Critical and Tricritical Points for the Massless 2d Gross-Neveu Model Beyond Large N
• Renormalization Group Improved Optimized Perturbation Theory: Revisiting the Mass Gap of the O(2N) Gross-Neveu Model
• Interplay Between Approximation Theory and Renormalization Group
• Thermodynamics of the O(N) Nonlinear Sigma Model in 1+1 Dimensions
• Treating Divergent Perturbation Theory: Lessons from Exactly Solvable 2D Models at Large $N$
• Renormalons beyond the Borel plane