Contribution of Inelastic Rescatterring to $B \to ππ, K \bar{K}$ Decays

Abstract

We discuss multichannel inelastic rescatterring effects in B decays into a pair $PP$ of pseudoscalar mesons ($PP = ππ$ or $K\bar{K}$). 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 $PP$. Since from all S-matrix elements $ $ involving $PP$ only some ($i = M_1 M_2$) contribute to the final state rescatterring, the latter is treated as a correction only. The rescatterring of resonance pair $M_1 M_2$ into the final $PP$ 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, amplitudes of B decays into $K\bar{K}$ become significantly larger than those estimated through short-distance penguin diagrams, to the point of being comparable to the $B\to ππ$ amplitudes.