Strong coupling theory for the superfluidity of Bose-Fermi mixtures

We develop the strong coupling theory for the superfluidity of fermion $s$-wave pairing state in a Bose-Fermi mixture. Dynamical screening, self-energy renormalization, and pairing gap function are included self-consistently in the regime where the phonon velocity is smaller than the Fermi velocity. Analytical form for the transition temperature ($T_c$) is derived within reasonable approximations. In typical $^{40}$K-$^{87}$Rb mixtures, the obtained $T_c$ is several times larger than that in the weak coupling theory and can be as high as several percents of Fermi temperature.