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A measurement of the shape of the differential decay rate and the associatedIsgur-Wise function for the decay$\Lambda_b^0\to\Lambda_c^+\mu^-\overline{\nu}$ is reported, using datacorresponding to $3 fb^{-1}$ collected with the LHCb detector in proton-protoncollisions. The $\Lambda_c^+\mu^-\overline{\nu}$(+ anything) final states arereconstructed through the detection of a muon and a $\Lambda_c^+$ baryondecaying into $pK^-\pi^+$, and the decays$\Lambda_b^0\to\Lambda_c^+\pi^+\pi^-\mu^-\overline{\nu}$ are used to determinecontributions from $\Lambda_b^0\to \Lambda_c^{\star+}\mu ^-\bar{\nu}$ decays.The measured dependence of the differential decay rate upon the squaredfour-momentum transfer between the heavy baryons, $q^2$, is compared withexpectations from heavy-quark effective theory and from unquenched lattice QCDpredictions.

Measurement of the shape of the $\Lambda_b^0\to\Lambda_c^+ \mu^- \overline{\nu}$ differential decay rate