Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2012-01-19
Physics
High Energy Physics
High Energy Physics - Theory
14 pages
Scientific paper
A system of Schwinger-Dyson equations (SDEs) for pseudoscalar four-dimensional Yukawa model in the two-particle approximation is investigated. A 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 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 $p^2_e\Delta\simeq C \log^{-4/5}\frac{p^2_e}{M^2}$. An approximate solution confirms the positivity of $C$ and an absence of Landau pole.
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