Contribution of inelastic rescattering toB→ππ,KK¯decays

We discuss multichannel inelastic rescattering effects in B decays into a pair $\mathrm{PP}$ of pseudoscalar mesons $(PP=\pi \pi \hspace{0.5em}or\hspace{0.5em}K\overline{K}).\mathrm{}$ In agreement with short-distance models it is assumed that initially B meson decays dominantly into jet-like states composed of two flying-apart low-mass resonances $M_1{M}_2$ which rescatter into $\mathrm{PP}.\mathrm{}$ Since from all S-matrix elements $〈i|S|\mathrm{PP}〉$ involving $\mathrm{PP}$ only some ${(i=M}_1{M}_2)$ contribute to the final state rescattering, the latter is treated as a correction only. The rescattering of the resonance pair $M_1{M}_2$ into the final $\mathrm{PP}$ state is assumed to proceed through Regge exchange. Although effects due to a single intermediate state $M_1{M}_2$ are small, it is shown that the combined effect of all such states should be large. In particular, the amplitudes of B decays into $K\overline{K}$ become significantly larger than those estimated through short-distance penguin diagrams, to the point of being comparable to the $\overrightarrow{B}\pi \pi$ amplitudes.