Charming penguins in B decays Original Research Article

Full expressions of the Bd0 → π+π− and Bd0 → π0π0 amplitudes, given in terms of matrix elements of operators of the effective weak Hamiltonian, are used to study the dependence of the relevant branching ratios on the different contributions. The uncertainty in the extraction of the weak phase α from the measurement of the time-dependent asymmetry in Bd0 → π+π− decays is also analyzed. We find that, among several effects which may enhance the Bd0 → π0π0 branching ratio, the most important is due to “charming penguin” diagrams. These diagrams easily increase BR(Bd0 → π0π0) up to a value of 1−3 × 106. The same effect produces, however, a large error in the extraction of a from the measurement of the Bd0 → π+π− time-dependent asymmetry. We show that it is possible to determine charming-penguin amplitudes from the experimental measurement of many decay rates. Their effect is impressive in B+ → π+K0 and Bd0 → K+π− decays, where charming-penguin contributions easily give values of BR(B+ → π+K0) and BR(Bd0 → K+π−) of about 1 × 105. Among other possibilities, we also suggest to use Bd0 → K0K0, the BR of which can be as large as 2−3 x 106, to determine the size of charming-penguin amplitudes.