Possible complex annihilation and B -> K pi direct CP asymmetry

Abstract

We point out that a strong phase from the penguin annihilation channel in B meson decays is sensitive to the treatment of subleading terms with physical b quark mass m(b). In the limit of infinite heavy-quark mass, both the soft-collinear effective theory and the perturbative QCD approach based on the k(T) factorization theorem agree that the strong phase is suppressed. For finite heavy-quark mass, the two approaches predict different results, which are related to the treatment of subleading terms. This is illustrated by taking a toy model for soft-collinear effective theory, in which a small quantity, suppressed by O(Lambda/m(b)), with Lambda being a hadronic scale, is kept in the denominators of internal particle propagators. This model can generate a sizable strong phase to accommodate the data of the B-0 -> K--/+pi(+/-) direct CP asymmetry.