Hadronic B Decays Involving Even Parity Charmed Mesons

Abstract

Hadronic B decays containing an parity-even charmed meson in the final state are studied. Specifically we focus on the Cabibbo-allowed decays $\bar B\to D^{**} π(ρ), D^{**}\bar D_s^{(*)}, \bar D^{**}_sD^{(*)}$ and $\bar B_s\to D_s^{**}π(ρ)$, where $D^{**}$ denotes generically a p-wave charmed meson. The $B\to D^{**}$ 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. Except the decay to $D_1(2427)^0π^-$ the predictions for $B^-\to D^{**0}π^-$ agree with experiment. The sign of $D_1^{1/2}-D_1^{3/2}$ mixing angle is found to be positive in order to avoid a severe suppression on the production of $D_1(2427)^0π^-$. The interference between color-allowed and color-suppressed tree amplitudes is expected to be destructive in the decay $B^-\to D_1(2427)^0π^-$. Hence, an observation of the ratio $D_1(2427)^0π^-/D_1(2427)^+π^-$ can be used to test the relative signs of various form factors as implied by heavy quark symmetry. Although the predicted $B^-\to D_1(2420)^0ρ^-$ at the level of $3\times 10^{-3}$ exceeds the present upper limit, it leads to the ratio $D_1(2420)ρ^-/D_1(2420)π^-\approx 2.6$ as expected from the factorization approach and from the ratio $f_ρ/f_π\approx 1.6$ . Therefore, it is crucial to have a measurement of this mode to test the factorization hypothesis. For $\bar B\to \bar D_s^{**}D$ decays, it is expected that $\bar D_{s0}^*D\gsim \bar D_{s1}D$ as the decay constants of the multiplet $(D_{s0}^*,D_{s1})$ become the same in the heavy quark limit.