Hadronic B decays containing an even-parity charmed meson in the final state are studied. Specifically we focus on the Cabibbo-allowed decays $\overline{B}\to D^{**}\pi \left(\rho \right),D^{**}{D}_s^{\left(*\right)},$ $D_s^{**}{D}^{\left(*\right)}$ and $B_s\to D_s^{**}\pi \left(\rho \right),$ where $D^{**}$ denotes generically a p-wave charmed meson. The $\overrightarrow{B}{D}^{**}$ transition form factors are studied in the improved version of the Isgur-Scora-Grinstein-Wise quark model. We apply heavy quark effective theory and chiral symmetry to study the strong decays of p-wave charmed mesons and determine the magnitude of the $D_1^{1/2}-D_1^{3/2}$ mixing angle (the superscript standing for the total angular momentum of the light quark). Except for the decay to $D_1{\mathrm{}\left(2427\right)\mathrm{}}^0{\pi }^{-}$ the predictions of $\mathcal{B}{(B}^{-}\to D^{**0}{\pi }^{-})$ agree with experiment. The sign of the $D_1^{1/2}-D_1^{3/2}$ mixing angle is found to be positive in order to avoid a severe suppression of the production of $D_1{\mathrm{}\left(2427\right)\mathrm{}}^0{\pi }^{-}.$ The interference between color-allowed and color-suppressed tree amplitudes is expected to be destructive in the decay $B^{-}\to D_1{\mathrm{}\left(2427\right)\mathrm{}}^0{\pi }^{-}.$ Hence, an observation of the ratio $D_1{\mathrm{}\left(2427\right)\mathrm{}}^0{\pi }^{-}{/D}_1{\mathrm{}\left(2427\right)\mathrm{}}^{+}{\pi }^{-}$ can be used to test the relative signs of various form factors as implied by heavy quark symmetry. Although the predicted $B^{-}\to D_1{\mathrm{}\left(2420\right)\mathrm{}}^0{\rho }^{-}$ at the level of $3\times {10}^{-3}$ exceeds the present upper limit, it leads to the ratio $D_1\mathrm{}\left(2420\right)\mathrm{}{\rho }^{-}{/D}_1\mathrm{}\left(2420\right)\mathrm{}{\pi }^{-}\approx 2.6,$ as expected from the factorization approach and from the ratio $f_{\rho }{/f}_{\pi }\approx \mathrm{1.6.}$ Therefore, it is crucial to have a measurement of this mode to test the factorization hypothesis. For $\overline{B}\to D_s^{**}D$ decays, it is expected that $D_{s0\mathrm{}}^{*}D\gtrsim D_{s1\mathrm{}}D$ as the decay constants of the multiplet ${(D}_{s0\mathrm{}}^{*}{,D}_{s1\mathrm{}})$ become the same in the heavy quark limit. The preliminary Belle observation of fairly less abundant production of $D_{s0\mathrm{}}^{*}D$ than $D_{s1\mathrm{}}D$ is thus a surprise. What is the cause for the discrepancy between theory and experiment remains unclear. Meanwhile, it is also important to measure the B decay into $D_{s1\mathrm{}}{\mathrm{}\left(2536\right)D}^{\left(*\right)}$ to see if it is suppressed relative to $D_{s1\mathrm{}}{\mathrm{}\left(2463\right)D}^{\left(*\right)}$ to test the heavy quark symmetry relation $f_{D_{s1\mathrm{}}\mathrm{}\left(2536\right)\mathrm{}}\ll f_{D_{s1\mathrm{}}\mathrm{}\left(2463\right)\mathrm{}}.$ Under the factorization hypothesis, the production of $D_{s2\mathrm{}}^{*}D$ is prohibited as the tensor meson cannot be produced from the $V-A$ current. Nevertheless, it can be induced via final-state interactions or nonfactorizable contributions and hence an observation of $\overline{B}\to D_{s2\mathrm{}}^{*}{D}^{\left(*\right)}$ could imply the importance of final-state rescattering effects.

• Received 15 July 2003

DOI:https://doi.org/10.1103/PhysRevD.68.094005