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

Details (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 the O(N) Gross-Neveu model mass gap

2002-05-14

arxiv.org/abs/hep-th/0205133v2

Phys.Rev. D66 (2002) 085020

Physics

High Energy Physics

High Energy Physics - Theory

33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording corrections, 2 references added. To appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.66.085020

We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass dependence) are transmuted into expansions in 1/F, where $F \sim 1/g(m)$ for $m \gg \Lambda$ while $F \sim (m/\Lambda)^\alpha$ for $m \lsim \Lambda$, $\Lambda$ being the basic scale and $\alpha$ given by renormalization group coefficients. (Borel) convergence holds in a range of $F$ which corresponds to reach unambiguously the strong coupling infrared regime near $m\to 0$, which can define certain "non-perturbative" quantities, such as the mass gap, from a resummation of this alternative expansion. Convergence properties can be further improved, when combined with $\delta$ expansion (variationally improved perturbation) methods. We illustrate these results by re-evaluating, from purely perturbative informations, the O(N) Gross-Neveu model mass gap, known for arbitrary $N$ from exact S matrix results. Comparing different levels of approximations that can be defined within our framework, we find reasonable agreement with the exact result.

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