Rescattering contributions to rare<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>-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 $\overline{b}d\ensuremath{\rightarrow}\overline{u}u$, $\overline{b}s\ensuremath{\rightarrow}\overline{u}u$, and $\overline{b}u\ensuremath{\rightarrow}{W}^{*}\ensuremath{\rightarrow}\overline{c}s$, 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 ${B}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$, ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, and ${B}^{+}\ensuremath{\rightarrow}{D}_{s}^{+}\ensuremath{\phi}$, 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 ${10}^{\ensuremath{-}9}$ to ${10}^{\ensuremath{-}4}$.

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