Non-leptonic decays in an extended chiral quark model

We consider the color suppressed (nonfactorizable) amplitude for the decay mode $\overline{B_d^0}\to {\pi }^0{\pi }^0$. We treat the $b$-quark in the heavy quark limit and the energetic light ($u,d,s$) quarks within a variant of Large Energy Effective Theory combined with an extension of chiral quark models. Our calculated amplitude for $\overline{B_d^0}\to {\pi }^0{\pi }^0$ is suppressed by a factor of order ${\mathrm{\Lambda }}_{QCD}\mathrm{/}{m}_b$ with respect to the factorized amplitude, as it should according to QCD-factorization. Further, for reasonable values of the (model dependent) gluon condensate and the constituent quark mass, the calculated nonfactorizable amplitude for $\bar{B_{d}^0} \rightarrow \pi^0 \pi^{0} $ can easily accomodate 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 $\overline{B_d^0}\to {\pi }^0{\pi }^0$.