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

Abstract

We study the heavy quark effective theory prediction for semileptonic $B$ decays into an orbital excited $F$-wave charmed doublet, the ($2^{+}$, $3^{+}$) states ($D_2^{{\ast }^{\prime }}$, $D_3$), 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 ${\Gamma }_{B\to D_2^{{\ast }^{\prime }}\ell \overline{\nu }}=1.85\times 10^{-19}GeV$ and ${\Gamma }_{B\to D_3\ell \overline{\nu }}=1.78\times 10^{-19}GeV$. The branching ratios are $\mathcal{B}(B\to D_2^{{\ast }^{\prime }}\ell \overline{\nu })=4.6\times 10^{-7}$ and $\mathcal{B}(B\to D_3\ell \overline{\nu })=4.4\times 10^{-7}$, respectively.

Comments: 6 pages,2 figures