A solution to B -> pi pi puzzle and B -> KK

Abstract

The large ratio of color-suppressed tree amplitude to color-allowed one in B -> pi pi decays is difficult to understand within the Standard Model, which is known as the "B -> pi pi puzzle". The two tree diagrams contain the up- and charm-quark component of penguin amplitude, P-uc, which cannot be separated by measuring B -> pi pi decays alone. We show that the measurements of the branching ratio and direct CP asymmetry of B+ -> K + (K-0) over bar decay enable one to disentangle the P-uc with two-fold ambiguity. One of the two degenerate solutions of the P,, can solve the B -> pi pi puzzle by giving C/T|0.3 which is consistent with the expectation in the Standard Model. We also show that the two solutions can be discriminated by the measurement of the indirect CP asymmetry of B-0 -> K-0(K-0) over bar. We point out that the corresponding puzzle in B -> pi K decays is not solved in this way. (C) 2007 Elsevier B.V. All rights reserved.