Coupled channel effects in ππ S-wave interaction

We study coupled channel effects upon isospin I = 2 and I = 0 pi pi S-wave interaction. With introduction of the pi pi -> rho rho -> 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 -> rho rho -> pi pi box diagram is found to give the largest contribution for the inelasticity among all possible coupled channels including pi pi -> omega omega -> pi pi, pi pi -> KK -> pi pi. We also show why the broad a appears narrower in production processes than in pi pi scattering process.