N/D Formalism for Scattering Amplitudes with Unstable Particles

概要

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The consistent N/D formalism is developed for a two-channel problem including unstable particles (in practice, for π, N and ρ, N channels). In order to obtain a consistent formalism with analytic properties for both variables s and ω (ω is the squared ρ-meson mass), independent ω-variables with adequate small imaginary parts are introduced for each ρ-meson. Analytic continuation in ω-variables is carried out without any ambiguity and resultant partial wave amplitudes T_<ij> have required analytic properties in s and ω variables. Some remarks are made for ω-channel discontinuity of T_<12> (s, ω) and T_<22> (s, ω, ω´), discontinuities of T_<22> (s, ω, ω´) across the anomalous cuts, etc. Our procedure and results are also different in some other respects from ones given previously by Ball, Frazer and Nauenberg.
理論物理学刊行会の論文
1964-04-25