Strongly interacting Bose-Fermi mixtures in $4-\epsilon$ dimensions

Thermodynamically stable low-temperature phases of the Bose-Fermi mixtures composed of bosons and spinless fermions close to four dimensions are considered. In the regime, where the only boson-fermion two-body interaction is present and tuned to unitary limit, the properties of a system solely depend on the mass and number ratios of constituent atoms. In addition to the phase with the dimers (boson-fermion shallow bound states), we identified one more state of the mixture with the coexistence of fermionic dimers and trimers. The universal physics of these phases, the characteristic feature of is absence of the Bose-Einstein condensate, is discussed.