  We study by diagrammatic methods a mixture of single-component bosons and
fermions, 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.
