Semileptonic ${\Lambda }_b$ decay to excited ${\Lambda }_c$ baryons at order ${\Lambda }_{\mathrm{QCD}}{/m}_Q$

Exclusive semileptonic ${\Lambda }_b$ decays to excited charmed ${\Lambda }_c$ baryons are investigated at order ${\Lambda }_{\mathrm{QCD}}{/m}_Q$ in the heavy quark effective theory. The differential decay rates are analyzed for the $J^{\pi }{=1/2\mathrm{}}^{-}$ ${\Lambda }_c\mathrm{}\left(2593\right)\mathrm{}$ and the $J^{\pi }{=3/2\mathrm{}}^{-}$ ${\Lambda }_c\mathrm{}\left(2625\right).$ They receive ${1/m}_{c,b}$ corrections at zero recoil that are determined by mass splittings and the leading order Isgur-Wise function. With some assumptions, we find that the branching fraction for ${\Lambda }_b$ decays to these states is 2.5–3.3%. The decay rate to the helicity $\pm 3/2$ states, which vanishes for $m_Q\to \infty ,$ remains small at order ${\Lambda }_{\mathrm{QCD}}{/m}_Q$ since ${1/m}_c$ corrections do not contribute. Matrix elements of weak currents between a ${\Lambda }_b$ and other excited ${\Lambda }_c$ states are analyzed at zero-recoil to order ${\Lambda }_{\mathrm{QCD}}{/m}_Q.$ Applications to baryonic heavy quark sum rules are explored.