Study of Multichannel Dynamics in the New Strip Approximation

Abstract

A systematic study of the dynamics of scattering with several coupled two-particle channels is made using the new strip approximation. The existence of a unique solution to the $N{D}^{-1\mathrm{}}$ equations is established from maximal analyticity of the second degree. The method used is an extension of Jones's proof in the single-channel case, making use of an explicit expression for the determinant of $D$ constructed by Gross. The general method is then applied to the particular case of a $\pi \pi -K\overline{K}$ two-channel calculation of the $\rho$ meson, first with fixed-spin particle and then with Reggeized particle exchange as the generalized potential. A detailed discussion of the numerical result is presented, with the conclusion that the effect of the inelastic channel ($K\overline{K}$) is not important in the present approximation scheme.