The $ππ$ Final State Interaction in $K\toππ$, $pp\to ppππ$ and Related Processes

M. P. Locher, V. E. Markushin, H. Q. Zheng

Published 1996-04-12Version 1

Final state interactions in the $S$--wave $\pi\pi$ system (I=0,2) are re-examined on the basis of the Omn\`es-Mus\-khe\-li\-shvili 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 Omn\`es function in a coupled channel situation is elucidated. Applications are made to $K\to \pi\pi$ and $pp\to pp\pi\pi$. It is found that the contribution from the $f_0$ resonance to the form-factor is strongly reduced by a nearby zero.