Non-factorisable Contributions of Strong-Penguin Operators in $\Lambda_b \to \Lambda \ell^+\ell^-$ Decays

We investigate for the first time a certain class of non-factorisable contributions of the four-quark operators ${\cal O}_{3-6}$ in the weak effective Hamiltonian to the $\Lambda_b \to \Lambda \ell^+\ell^-$ decay amplitude. We focus on the case where a virtual photon is radiated from one of the light constituents of the $\Lambda_b$ baryon, in the kinematic situation of large hadronic recoil with an energetic $\Lambda$ baryon in the final state. The effect on the suitably defined ``non-local form factors'' is calculated using the light-cone sum rule approach for a correlator with an interpolating current for the light $\Lambda$ baryon. We find that this approach requires the introduction of new soft functions that generalise the standard light-cone distribution amplitudes (LCDAs) for the heavy $\Lambda_b$ baryon. We give a heuristic discussion of their properties and a model that relates them to the standard LCDAs. Within this framework, we provide numerical results for the size of the non-local form factors considered.