The baryon differential spectrum of the baryon decay ${\Lambda }_b\to {\Lambda }_c\ell {\overline{\nu }}_{\ell }$ will hopefully be measured in detail at LHCb. We obtain some new results on the form factors in the heavy quark expansion of Heavy Quark Effective Theory that can be useful in the interpretation of the data. We formulate a sum rule for the elastic subleading form factor $A(w)$ at order $1/m_Q$, that originates from the Lagrangian perturbation ${\mathcal{L}}_{\mathrm{kin}}$. In the sum rule appear only the intermediate states $(j^P,J^P)=(0^{+},{\frac{1}{2}}^{+})$, entering also in the $1/m_Q^2$ correction to the axial form factor $G_1(w)$, that contributes to the differential rate at zero recoil $w=1$. This result, together with another sum rule in the forward direction for $|G_1(1){|}^2$, allows to obtain a lower bound for the correction at zero recoil $-{\delta }_{1/m_Q^2}^{(G_1)}$ in terms of the derivative $A_1^{\prime }(1)$ and the slope ${\rho }_{\Lambda }^2$ and curvature ${\sigma }_{\Lambda }^2$ of the elastic Isgur-Wise function ${\xi }_{\Lambda }(w)$. Another theoretical implication is that $A^{\prime }(1)$ must vanish for some relation between ${\rho }_{\Lambda }^2$ and ${\sigma }_{\Lambda }^2$, as well as for ${\rho }_{\Lambda }^2\to 0$, establishing a nontrivial correlation between the leading IW function ${\xi }_{\Lambda }(w)$ and the subleading one $A(w)$. A phenomenological estimation of these two functions allows to obtain a lower bound on $-{\delta }_{1/m_Q^2}^{(G_1)}$.

• Received 18 February 2012

DOI:https://doi.org/10.1103/PhysRevD.86.014002