Charmless Final State Interaction in B-> pi pi decays
Abstract
We estimate effects of the final state interactions in B -> pi pi decays coming from rescattering of pi pi via exchange of rho, sigma, f0 mesons. Then we include the rho rho rescattering via exchange of pi, omega, a1 mesons and finally we consider contributions of the a1 pi rescattering via exchange of rho. The absorptive parts of amplitudes for these processes are determined. In the case of pi+ pi- decay mode, due to model uncertainties, the calculated contribution is |MA| =< 1.7 x 10-8 GeV. This produces a small relative strong phase for the tree and color-suppressed B -> pi pi amplitudes consistent with the result of a recent phenomenological analysis based on the BaBar and Belle results for the B -> pi pi branching ratios and CP asymmetries.
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