We prove a factorization theorem in QCD for the color suppressed decays $B^0\to D^0{M}^0$ and $B^0\to D^{*0}{M}^0$ where M is a light meson. Both the color-suppressed and W-exchange or annihilation amplitudes contribute at lowest order in ${\Lambda }_{\mathrm{QCD}}/Q$ where $Q=\{m_b{,m}_c{,E}_{\pi }\},$ so no power suppression of annihilation contributions is found. A new mechanism is given for generating nonperturbative strong phases in the factorization framework. Model-independent predictions that follow from our results include the equality of the $B^0\to D^0{M}^0$ and $B^0\to D^{*0}{M}^0$ rates and the equality of nonperturbative strong phases between isospin amplitudes, ${\delta }^{\mathrm{}\left(\mathrm{DM}\right)\mathrm{}}={\delta }^{{(D}^{*}M)}.$ Relations between amplitudes and phases for $M=\pi ,\rho$ are also derived. These results do not follow from large $N_c$ factorization with heavy quark symmetry.

• Received 11 July 2003

DOI:https://doi.org/10.1103/PhysRevD.68.114009