Subleading Isgur-Wise form factors and ${O(1/m}_Q)$ corrections to the semileptonic decays $\overrightarrow{B}{D}_{1}l\overline{\nu }$ and $\overrightarrow{B}{D}_2^{*}l\overline{\nu }$

The exclusive semileptonic decays $\overrightarrow{B}{D}_1\mathrm{}\left(2420\right)l\overline{\nu }$ and $\overrightarrow{B}{D}_2^{*}\mathrm{}\left(2460\right)l\overline{\nu }$ are studied at the subleading order of heavy quark expansion. The subleading Isgur-Wise functions resulting from the kinetic energy and chromomagnetic corrections to the HQET Lagrangian are calculated by QCD sum rules in the framework of heavy quark effective theory. The decay rates and branching ratios are computed with the inclusion of the order of ${1/m}_Q$ corrections. It is found that the ${1/m}_Q$ correction to the decay rate is not large for $\overrightarrow{B}{D}_2^{*}$ but is very large for $\overrightarrow{B}{D}_1.$