The ππ Final State Interaction in K → ππ , pp → ppππ and Related Processes

Final state interactions in the S–wave ππ system (I=0,2) are reexamined on the basis of the Omnès-Muskhelishvili equation and the coupled channel formalism. The contributions to the pion scalar form factor from ρ 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 Omnès function in a coupled channel situation is elucidated. Applications are made to K → ππ and pp → ppππ. It is found that the contribution from the f 0 resonance to the form-factor is strongly reduced by a nearby zero.