Rescattering effects in charmless B_{u,d,s} to P P decays

Abstract

We study the final-state interaction (FSI) effects in charmless B_{u,d,s} to PP decays. We consider a FSI approach with both short- and long-distance contributions, where the former are from in-elastic channels and are contained in factorization amplitudes, while the latter are from the residual rescattering among PP states. Flavor SU(3) symmetry is used to constrain the residual rescattering S-matrix. We fit to all available data on the CP-averaged decay rates and CP asymmetries, and make predictions on unmeasured ones. Our main results are as follows: (i) Results are in agreement with data in the presence of FSI. (ii) For B decays, the pi^+pi^- and pi^0pi^0 rates are suppressed and enhanced respectively by FSI. (iii) The FSI has a large impact on direct CP asymmetries of many modes. (iv) The deviation (Delta A) between A(B{bar}^0 to K^-pi^+) and A(B^-to K^-\pi^0) can be understood in the FSI approach. (v) Sizable and complex color-suppressed tree amplitudes, which are crucial for the large \pi^0\pi^0 rate and Delta A, are generated through exchange rescattering. The correlation of the ratio B(pi^0pi^0)/B(pi^+pi^-) and Delta A is studied. (vi) The B^- to pi^-pi^0 direct CP violation is very small and is not affected by FSI. (vii) Several B_s decay rates are enhanced. In particular, the eta'eta' branching ratio is enhanced to the level of 1.0X10^{-4}, which can be checked experimentally. (viii) Time-dependent CP asymmetries S in B_{d,s} decays are studied. CP asymmetries in these modes will be useful to test the SM.