High-Order Corrections to the Lipatov Asymptotics in the ϕ^4 Theory

D. A. Lobaskin; I. M. Suslov

doi:10.1134/1.1800180

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arXiv · hep-ph/0509274

High-Order Corrections to the Lipatov Asymptotics in the ϕ^4 Theory

D. A. Lobaskin·I. M. Suslov

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Abstract

High orders in perturbation theory can be calculated by the Lipatov method. For most field theories, the Lipatov asymptotics has the functional form c a^N Γ(N+b) (N is the order of perturbation theory); relative corrections to this asymptotics have the form of a power series in 1/N. The coefficients of high order terms of this series can be calculated using a procedure analogous to the Lipatov approach and are determined by the second instanton in the considered field theory. These coefficients are calculated quantitatively for the n-component ϕ^4 theory under the assumption that the second instanton is (i) a combination of two elementary instantons and (ii) a spherically asymmetric localized function. The technique of two-instanton calculations is developed, as well as the method for integrating over rotations of an asymmetric instanton in the coordinate state.

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D. A. Lobaskin, I. M. Suslov. 2005-09-25. High-Order Corrections to the Lipatov Asymptotics in the ϕ^4 Theory. https://doi.org/10.1134/1.1800180

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