Nucleon Loop as a Force in theππChannel

Abstract

The $\ensuremath{\rho}$ meson is described as a $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{-}N\overline{N}$ composite system, with $N$ exchange as a nondiagonal force between the two channels. The resulting nucleon loop, as a force in the $\ensuremath{\pi}\ensuremath{\pi}$ channel, gives far too strong attraction, if calculated with unmodified nucleon propagators. The necessary cutoff parameter in the nucleon propagators is compared with the same quantity obtained in the $\ensuremath{\Delta}(1236)$ channel. Pion self-energy effects are introduced to improve the resulting $\ensuremath{\rho}$ width, and crossing properties of the $\ensuremath{\pi}\ensuremath{\pi} p$ waves are discussed.