Final state interactions in hadronicBdecays

There exist many experimental indications that final-state interactions (FSIs) may play a prominent role not only in charmful $B$ decays but also in charmless $B$ ones. We examine the final-state rescattering effects on the hadronic $B$ decay rates and their impact on direct CP violation. The color-suppressed neutral modes such as $B^0\to D^0{\pi }^0,{\pi }^0{\pi }^0,{\rho }^0{\pi }^0,K^0{\pi }^0$ can be substantially enhanced by long-distance rescattering effects. The direct CP-violating partial rate asymmetries in charmless $B$ decays to $\pi \pi /\pi K$ and $\rho \pi$ are significantly affected by final-state rescattering, and their signs are generally different from that predicted by the short-distance (SD) approach. For example, direct CP asymmetry in $B^0\to {\rho }^0{\pi }^0$ is increased to around 60% due to final-state rescattering effects whereas the short-distance picture gives about 1%. Evidence of direct CP violation in the decay ${\overline{B}}^0\to K^{-}{\pi }^{+}$ is now established, while the combined BABAR and Belle measurements of ${\overline{B}}^0\to {\rho }^{\pm }{\pi }^{\mp }$ imply a $3.6\sigma$ direct CP asymmetry in the ${\rho }^{+}{\pi }^{-}$ mode. Our predictions for CP violation agree with experiment in both magnitude and sign, whereas the QCD factorization predictions (especially for ${\rho }^{+}{\pi }^{-}$) seem to have some difficulty with the data. Direct CP violation in the decay $B^{-}\to {\pi }^{-}{\pi }^0$ is very small ($\lesssim 1\%$) in the standard model even after the inclusion of FSIs. Its measurement will provide a nice way to search for new physics as in the standard model QCD penguins cannot contribute (except by isospin violation). Current data on $\pi K$ modes seem to violate the isospin sum-rule relation, suggesting the presence of electroweak penguin contributions. We have also investigated whether a large transverse polarization in $B\to \varphi K^{*}$ can arise from the final-state rescattering of $D^{(*)}{\overline{D}}_s^{(*)}$ into $\varphi K^{*}$. While the longitudinal polarization fraction can be reduced significantly from short-distance predictions due to such FSI effects, no sizable perpendicular polarization is found owing mainly to the large cancellations occurring in the processes $\overline{B}\to D_s^{*}\overline{D}\to \varphi {\overline{K}}^{*}$ and $\overline{B}\to D_s{\overline{D}}^{*}\to \varphi {\overline{K}}^{*}$, and this can be understood as a consequence of CP and SU(3) [CPS] symmetry. To fully account for the polarization anomaly (especially the perpendicular polarization) observed in $B\to \varphi K^{*}$, FSI from other states or other mechanism, e.g., the penguin-induced annihilation, may have to be invoked. Our conclusion is that the small value of the longitudinal polarization in $VV$ modes cannot be regarded as a clean signal for new physics.