Pairing and condensation in a resonant Bose-Fermi mixture

We study by diagrammatic means a Bose-Fermi mixture, with boson-fermion coupling tuned by a Fano- Feshbach resonance. For increasing coupling, the growing boson-fermion pairing correlations progressively reduce the boson condensation temperature and make it eventually vanish at a critical coupling. Such quantum critical point depends very weakly on the population imbalance and, for vanishing boson densities, coincides with that found for the polaron-molecule transition in a strongly imbalanced Fermi gas, thus bridging two quite distinct physical systems.