Long-Distance Contributions to the $\Lambda_b\rightarrow\Lambda_ce^-\overline{\nu}_e$ Isgur-Wise Function

Abstract

The six independent formfactors describing the weak decay \semi\ are determined in terms of one universal function when both the $b$ and $c$ quarks are treated as heavy. The relations between these formfactors are modified by terms suppressed by inverse powers of the charm quark mass. We compute the formally leading long-distance corrections to these relations in chiral perturbation theory both at and away from zero recoil. They arise from the spin-symmetry breaking $\Sigma_c^* - \Sigma_c$ mass splitting and are nonanalytic in the pion mass. The correction at the zero-recoil point is found to be $ - (3.4 \pm 2.0) \times 10^{-4} g_3^2$ for a quark model estimate of $m_{\Sigma_c^*}-m_{\Sigma_c}$ and where $g_3\sim 1$ is an axial coupling constant. Further, the formfactors that vanish in the heavy quark limit do not receive such corrections.