Exclusive semileptonic $B$ decays into excited charmed mesons are investigated at order ${\Lambda }_{\mathrm{QCD}}{/m}_Q$ in the heavy quark effective theory. Differential decay rates for each helicity state of the four lightest excited $D$ mesons ($D_1,$ $D_2^{*},$ $D_0^{*},$ and $D_1^{*}$) are examined. At zero recoil, ${\Lambda }_{\mathrm{QCD}}{/m}_Q$ corrections to the matrix elements of the weak currents can be written in terms of the leading Isgur-Wise functions for the corresponding transition and meson mass splittings. A model independent prediction is found for the slope parameter of the decay rate into helicity zero $D_1$ at zero recoil. The differential decay rates are predicted, including ${\Lambda }_{\mathrm{QCD}}{/m}_Q$ corrections with some model dependence away from zero recoil and including order ${\alpha }_s$ corrections. Ratios of various exclusive branching ratios are computed. Matrix elements of the weak currents between $B$ mesons and other excited charmed mesons are discussed at zero recoil to order ${\Lambda }_{\mathrm{QCD}}{/m}_Q.$ These amplitudes vanish at leading order, and can be written at order ${\Lambda }_{\mathrm{QCD}}{/m}_Q$ in terms of local matrix elements. Applications to $B$ decay sum rules and factorization are presented.

• Received 30 May 1997

DOI:https://doi.org/10.1103/PhysRevD.57.308