Rescattering effects in charmless Bu,d,s → PP decays

Final-state interaction effects in charmless Bu,d,s → PP decays are studied. We investigate the B 0 → π+π−, π0π0 rates and the Kπ direct CP violations, which lead to the so-called Kπ puzzle in CP violation. Our main results are as follows: (i) Results are in agreement with data in the presence of FSI. (ii) For B decays, the π+π− and π0π0 rates are suppressed and enhanced respectively by FSI. (iii) The FSI has a large impact on direct CP asymmetries (A) of many modes. (iv) The deviation(∆A) between A(B0 → K−π+) and A(B → K−π0) can be understood in the FSI approach. (v) Sizable and complex color-suppressed tree amplitudes, which are crucial for the large π0π0 rate and ∆A, are generated through exchange rescattering. The correlation of the ratio B(π0π0)/B(π+π−) and ∆A is studied. (vi) The B → π−π0 direct CP violation is very small and is not affected by FSI. (vii) Several Bs decay rates are enhanced. In particular, the ηη branching ratio is enhanced to the level of 1.0 × 10−4. (viii) Time-dependent CP asymmetries S in Bd,s decays are studied. The ∆S(B 0 → KSη ) is very small (≤ 1%). We found that the asymmetries |S| for Bs → ηη, ηη ′ and ηη decays are all below 0.06. CP asymmetries in these modes will be useful to test the SM.