Production of P-wave Charmed Mesons in Hadronic B Decays

Production of even-parity charmed mesons in hadronic B decays is studied. Specifically, we focus on the Cabibbo-allowed decays $\bar{B}\to D^{\ast \ast }\pi$ and ${\bar{D}}_s^{\ast \ast }{D}^{(\ast )}$, where $D^{\ast \ast }$ denotes generically a p-wave charmed meson. While the measured color-allowed decays ${\bar{B}}^0\to D^{\ast \ast +}{\pi }^{-}$ are consistent with the theoretical expectation, the experimental observation of $B^{-}\to D^{\ast \ast 0}{\pi }^{-}$ for the broad $D^{\ast \ast }$ states is astonishing as it requires that the color-suppressed contribution dominates over the color-allowed one, even though the former is $1\mathrm{/}{m}_b$ suppressed in the heavy quark limit. In order to accommodate the data of $\bar{B}\to D^{\ast \ast }{\pi }^{-}$, it is found that $a_2\mathrm{/}{a}_1\approx -0.5$ with a sign opposite to that in $\bar B\to D\pi$decays,where$a_1$and$a_2$ are the effective Wilson coefficients for color-allowed and color-suppressed decay amplitudes, respectively. The decay constants and form factors for $D^{\ast \ast }$ and the Isgur-Wise functions ${\tau }_{1\mathrm{/}2}(\omega )$ and ${\tau }_{3\mathrm{/}2}(\omega )$ are extracted from the data of $B\to D^{\ast \ast }\pi$ decays. The Isgur-Wise functions calculated in the covariant light-front quark model are in good agreement with experiment. The neutral modes ${\bar{B}}^0\to D^{\ast \ast 0}{\pi }^0$ for $D^{\ast \ast }=D_0^{\ast }(2400),D_1^{\mathrm{\prime }}(2430)$ and $\bar B^0\to D’^0_1(2430)\omega$arepredictedtohavebranchingratiosoforder$10^{-4}$whicharealsosupportedbyisospinargument\mathrm{.}Thedecayconstantsof$D_{s0}^*(2317)$and$D’_{s1}(2460)$areinferredfromthemeasurementsof$\bar B\to D_s^{**-}D$tobe$58\sim 86$MeVand$130\sim 200$ MeV, respectively. Contrary to the decay constants $f_{D_0^{\ast }}$ and $f_{D_1^{\mathrm{\prime }}}$ which are similar in size, the large disparity between $f_{D_{s0}^{\ast }}$ and $f_{D_{s1}^{\mathrm{\prime }}}$ is surprising and unexpected.