Spectra of heavy polarons and molecules coupled to a Fermi sea

We study the spectrum of an impurity coupled to a Fermi sea (e.g., minority atom in an ultracold gas, exciton in a solid) by attraction strong enough to form a molecule/trion. We introduce a diagrammatic scheme which allows treating a finite mass impurity while reproducing the Fermi edge singularity in the immobile limit. For large binding energies the spectrum is characterized by a semi-coherent repulsive polaron and an incoherent molecule, which is the lowest-energy feature in the single-particle spectrum. The previously predicted attractive polaron seems not to exist for strong binding.