Rescattering contributions to rare B-meson decays

Several B and B_s decays have been observed that have been cited as evidence for exchange (E), penguin annihilation (PA), and annihilation (A) processes, such as b¯d→u¯u, b¯s→u¯u, and b¯u→W^*→c¯s, respectively. These amplitudes are normally thought to be suppressed, as they involve the spectator quark in the weak interaction and thus should be proportional to the B-meson decay constant f_B. However, as pointed out a number of years ago, they can also be generated by rescattering from processes whose amplitudes do not involve f_B, such as color-favored tree amplitudes. In this paper we investigate a number of processes such as B⁰→K⁺K^-, B_s→π⁺π^-, and B⁺→D_s⁺ϕ, and identify promising states from which they can be generated by rescattering. We find that E-and PA-type processes are characterized, respectively, by amplitudes ranging from 5% to 10% and from 15% to 20% with respect to the largest amplitude from which they can rescatter. Based on this regularity, using approximate flavor SU(3) symmetry in some cases and time-reversal invariance in others, we predict the branching fractions for a large number of as-yet-unseen B and B_s decays in an extensive range from order 10^-9 to 10^-4.