An impurity immersed in a Bose-Einstein condensate is no longer accurately described by the Frohlich Hamiltonian as the coupling between the impurity and the boson bath gets stronger. We study the dominant effects of the two-phonon terms beyond the Frohlich model on the ground-state properties of the polaron using Feynmans variational path-integral approach. The previously reported discrepancy in the effective mass between the renormalization group approach and this theory is shown to be absent in the beyond-Frohlich model on the positive side of the Feshbach resonance. Self-trapping, characterized by a sharp and dramatic increase of the effective mass, is no longer observed for the repulsive polaron once the two-phonon interactions are included. For the attractive polaron we find a divergence of the ground-state energy and effective mass at weaker couplings than previously observed within the Frohlich model.
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