The $\pi \pi$ Final State Interaction in $K\to \pi \pi$, $pp\to pp\pi \pi$ and Related Processes

Abstract

Final state interactions in the $S$--wave $\pi \pi$ system (I=0,2) are re-examined on the basis of the Omnès-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 Omnès 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.

arXiv commentPACS numbers: 13.75.Lb, 13.25.Es, 13.25.+m, 15 pages in plain latex with epsf.sty, 10 figures

References in corpus (1)

• UNDERSTANDING THE SCALAR MESON $q\bar{q}$ NONET

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