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

Abstract

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 $m \lsim Λ$, $\Lambda$ 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.

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

References in corpus (4)

• Asymptotic Improvement of Resummation and Perturbative Predictions in Quantum Field Theory
• Borel convergence of the variationally improved mass expansion and dynamical symmetry breaking
• Dynamical mass generation by source inversion: Calculating the mass gap of the Gross-Neveu model
• Dynamical mass generation by source inversion: calculating the mass gap of the chiral Gross-Neveu model

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