Coupled channel effects in pion pion S-wave interaction

Abstract

We study coupled channel effects upon isospin I=2 and I=0 $\pi \pi$ S-wave interaction. With introduction of the $\pi \pi \to \rho \rho \to \pi \pi$ coupled channel box diagram contribution into $\pi \pi$ amplitude in addition to $\rho$ and $f_2(1270)$ exchange, we reproduce the $\pi \pi$ I=2 S-wave and D-wave scattering phase shifts and inelasticities up to 2 GeV quite well in a K-matrix formalism. For I=0 case, the same $\pi \pi \to \rho \rho \to \pi \pi$ box diagram is found to give the largest contribution for the inelasticity among all possible coupled channels including $\pi \pi \to \omega \omega \to \pi \pi$, $\pi \pi \to K\bar{K}\to \pi \pi$. We also show why the broad $\sigma$ appears narrower in production processes than in $\pi \pi$ scattering process.

Comments: 5 pages, 7 figures