pi pi final state interaction in K->pi pi, pp->pp pi pi, and related processes

Final state interactions in the S-wave pi pi system (I=0,2) are reexamined on the basis of the Omnes-Muskhelishvili equation and the coupled channel formalism. The contributions to the pion scalar form factor from rho and f(2)(1270) exchange in the t channel and from the f(0)(980) s-channel resonance are separately evaluated and the role of the nontrivial polynomial in the Omnes function in a coupled channel situation is elucidated. Applications are made to K --> pi pi and pp --> pp pi pi. It is found that the contribution from the f(0) resonance to the form factor is strongly reduced by a nearby zero.