Semileptonic $B$ Meson Decays Into A Highly Excited Charmed Meson Doublet

We study the heavy quark effective theory prediction for semileptonic $B$ decays into an orbital excited $F$-wave charmed doublet, the ($2^{+}$, $3^{+}$) states ($D^{*'}_{2}$, $D_{3}$), at the leading order of heavy quark expansion. The corresponding universal form factor is estimated by using the QCD sum rule method. The decay rates we predict are $Γ_{B\to D^{*'}_{2}\ell\overlineν}=1.85\times10^{-19} {GeV}$ and $Γ_{B\to D_{3}\ell\overlineν}=1.78\times10^{-19} {GeV}$. The branching ratios are $\mathcal {B}(B\to D_{2}^{*'}\ell\overlineν)=4.6\times10^{-7}$ and $\mathcal {B}(B\to D_{3}\ell\overlineν)=4.4\times10^{-7}$, respectively.

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