Model independent results for $B\to D_1(2420)\ell\bar\nu$ and $B\to D_2^*(2460)\ell\bar\nu$ at order $\Lambda_{QCD}/m_{c,b}$

Abstract

Exclusive semileptonic B decays into $D_1$ and $D_2^*$ mesons are investigated including order $\Lambda_{QCD}/m_{c,b}$ corrections using the heavy quark effective theory. At zero recoil, the $\Lambda_{QCD}/m_{c,b}$ corrections can be written in terms of the leading Isgur-Wise function for these transitions, $\tau$, and known meson mass splittings. We obtain an almost model independent prediction for the shape of the spectrum near zero recoil, including order $\Lambda_{QCD}/m_{c,b}$ corrections. We determine $\tau(1)$ from the measured $B\to D_1\ell\bar\nu$ branching ratio. Implications for B decay sum rules are discussed.