Reggeized Deck model forπ−p→ρ0π−pobeying the Steinmann relation

Abstract

We construct a Reggeized Deck model for the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}p$ that satisfies the Steinmann relation in the physical region. The $\ensuremath{\rho}\ensuremath{-}\ensuremath{\pi}$ mass spectrum is reproduced with a slightly improved width, and the $\ensuremath{\rho}\ensuremath{-}\ensuremath{\pi}$ partial waves agree with the results of previous calculations. An explanation for the success of the Reggeization in this low-$\ensuremath{\rho}\ensuremath{\pi}$-mass region is given. Resonancelike behavior is isolated in the $\ensuremath{\rho}\ensuremath{-}\ensuremath{\pi}$-cut term, and a resonance-type loop is shown to be present in the ${1}^{+}s$-wave Argand diagram. The difficulty associated with observing a hypothetical ${A}_{1}$ meson in this reaction is discussed.