Production of P-wave Charmed Mesons in Hadronic B Decays

Abstract

Production of even-parity charmed mesons in hadronic B decays is studied. Specifically, we focus on the Cabibbo-allowed decays $\bar B\to D^{**}\pi$ and $\bar D^{**}_sD^{(*)}$, where $D^{**}$ denotes generically a p-wave charmed meson. While the measured color-allowed decays $\bar B^0\to D^{**+}\pi^-$ are consistent with the theoretical expectation, the experimental observation of $B^-\to D^{**0}\pi^-$ for the broad $D^{**}$ states is astonishing as it requires that the color-suppressed contribution dominates over the color-allowed one, even though the former is $1/m_b$ suppressed in the heavy quark limit. In order to accommodate the data of $\bar B\to D^{**}\pi^-$, it is found that $a_2/a_1\approx -0.5$ 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 $D^{**}$ and the Isgur-Wise functions $\tau_{1/2}(\omega)$ and $\tau_{3/2}(\omega)$ are extracted from the data of $B\to D^{**}\pi$ decays. The Isgur-Wise functions calculated in the covariant light-front quark model are in good agreement with experiment. The neutral modes $\bar B^0\to D^{**0}\pi^0$ for $D^{**}=D^*_0(2400),D'_1(2430)$ and $\bar B^0\to D'^0_1(2430)\omega$ are predicted to have branching ratios of order $10^{-4}$ which are also supported by isospin argument. The decay constants of $D_{s0}^*(2317)$ and $D'_{s1}(2460)$ are inferred from the measurements of $\bar B\to D_s^{**-}D$ to be $58\sim 86$ MeV and $130\sim 200$ MeV, respectively. Contrary to the decay constants $f_{D_0^*}$ and $f_{D'_1}$ which are similar in size, the large disparity between $f_{D_{s0}^*}$ and $f_{D'_{s1}}$ is surprising and unexpected.