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

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 Δ. It is argued, however, that a full solution may be free from non-physical singularities and has the self-consistent asymptotic behavior pe2Δ≅C log-4/5 pe2/M2. An approximate solution confirms the positivity of C and the absence of Landau pole. (paper)