ar X iv : 0 70 7 . 28 38 v 2 [ he p - ph ] 2 6 Ju l 2 00 7 A solution to B → ππ puzzle and B → KK

The large ratio of color-suppressed tree amplitude to color-allowed one in B → ππ decays is difficult to understand within the Standard Model, which is known as the “B → ππ puzzle”. The two tree diagrams contain the upand charm-quark component of penguin amplitude, Puc, which cannot be separated by measuring B → ππ decays alone. We show that the measurements of the branching ratio and direct CP asymmetry of B+ → K+K0 decay enable one to disentangle the Puc with two-fold ambiguity. One of the two degenerate solutions of the Puc can solve the B → ππ 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 B0 → K0K0. We point out that if the B → ππ puzzle is solved in this way, the corresponding puzzle in B → πK decays should have a different origin.