Asymptotic behavior in a model with Yukawa interaction from Schwinger-Dyson equations

Abstract

A system of Schwinger-Dyson equations for pseudoscalar four-dimensional Yukawa model in the two-particle approximation is investigated. The simplest iterative solution of the system corresponds to the mean-field approximation (or, equivalently, to the leading order of 1/N-expansion) and includes a non-physical Landau pole in deep-Euclidean region for the pseudoscalar propagator $\Delta$. It is argued, however, that a full solution may be free from non-physical singularities and has the self-consistent asymptotic behavior $p_e^2\Delta \simeq C{\log }^{-4/5}\frac{p_e^2}{M^2}$. An approximate solution confirms the positivity of $C$ and the absence of Landau pole.

15 pages; journal version

References in corpus (1)

• Renormalization Group Functions of ϕ^4 Theory from High-Temperature Expansions

Cited by in corpus (4)

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