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 up- and 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 the corresponding puzzle in B→πK decays is not solved in this way.