B \to D'_0 (D'_1)\ell \bar \nu decays in HQEFT

Semileptonic B decays into excited charmed mesons $D'_0$ and $D'_1$ are studied in the framework of heavy quark effective field theory (HQEFT) up to order $1/m_Q$. They are characterized by a single leading Isgur-Wise function $\tau$ and several wave functions arising at $1/m_Q$ order. $\tau$ and the $1/m_Q$ order functions $\chi^b_0$, $\chi^c_0$ related to the kinetic energy operators are evaluated through QCD sum rule approach; zero recoil values of the $1/m_Q$ order functions $\kappa_1$, $\kappa_2$, $\kappa'_1$ and $\kappa'_2$ are extracted from the meson masses; and the branching ratios are found to be suppressed by the $1/m_Q$ corrections. It is concluded that the next leading order wave functions can be significant. However it does not change the previous prediction that the production rate of $j_l^P=3/2^+$ charmed mesons dominates over that of $1/2^+$ doublets.