Color suppressed contribution to Bd0→π0π0

The decay modes of the type B→ππ are dynamically different. For the case Bd0→π+π- there is a substantial factorized contribution which dominates. In contrast, the decay mode Bd0→π0π0 has a small factorized contribution, being proportional to a small Wilson coefficient combination. However, for the decay mode Bd0→π0π0 there is a sizeable nonfactorizable (color suppressed) contribution due to soft (long distance) interactions, which dominate the amplitude. We estimate the branching ratio for the mode Bd0→π0π0 in the heavy quark limit for the b quark. In order to estimate color suppressed contributions we treat the energetic light (u, d, s) quark within a variant of Large Energy Effective Theory combined with a recent extension of chiral quark models in terms of model- dependent gluon condensates. We find that our calculated color suppressed amplitude is suppressed by a factor of order ΛQCD/mb with respect to the factorizable amplitude, as it should according to QCD-factorization. Further, for reasonable values of the constituent quark mass and the gluon condensate, the calculated nonfactorizable amplitude for Bd0→π0π0 can easily accommodate the experimental value. Unfortunately, the color suppressed amplitude is very sensitive to the values of these model-dependent parameters. Therefore fine-tuning is necessary in order to obtain an amplitude compatible with the experimental result for Bd0→π0π0. A possible link to the triangle anomaly is discussed.