Inelastic Rescattering in $B\to \pi \pi ,K\bar{K}$

Abstract

Inelastic rescattering effects in B decays into a pair $PP$ of pseudoscalar mesons ($PP=\pi \pi$ or $K\bar{K}$) are discussed. It is assumed that $B$ meson decays through a short-distance tree-diagram process into two jet-like states composed of low-mass resonances $M_1{M}_2$ which rescatter into $PP$. The rescattering of resonance pair $M_1{M}_2$ into the final $PP$ state is assumed to proceed through a Regge flavour exchange. Since such processes constitute a fraction,diminishing with increasing energy, of total inelastic $PP$ scattering, the inelastic rescattering contribution should die out for $m_B\to \infty$. At $m_B=5.2GeV$, however, explicit estimates show that rescattering corrections could be substantial, leading to long-distance corrections to $B^0\to K\bar{K}$, comparable to short-distance penguin contributions.

11 LaTeX pages, 3 .ps figure files, presented at the Cracow Epiphany Conference on b Physics and CP Violation, Cracow, Poland, January 5-7, 2001