Possible resolution of the B -> pi pi, pi K puzzles

We show that there exist uncanceled soft divergences in the k_T factorization for nonfactorizable amplitudes of two-body nonleptonic B meson decays, similar to those identified in hadron hadroproduction. These divergences can be grouped into a soft factor using the eikonal approximation, which is then treated as an additional nonperturbative input in the perturbative QCD formalism. Viewing the special role of the pion as a q-qbar bound state and as a pseudo Nambu-Goldstone boson, we postulate that the soft effect associated with it is significant. This soft factor enhances the nonfactorizable color-suppressed tree amplitudes, such that the branching ratios B(pi^0 pi^0) and B(pi^0 rho^0) are increased under the constraint of the B(rho^0 rho^0) data, the difference between the direct CP asymmetries A_{CP}(pi^\mp K^\pm) and A_{CP}(pi^0 K^\pm) is enlarged, and the mixing-induced CP asymmetry S_{pi^0 K_S} is reduced. Namely, the known pi pi and pi K puzzles can be resolved simultaneously.