Critical temperature of pair condensation in a dilute Bose gas with spin-orbit coupling

We study the Bardeen-Cooper-Shrieffer (BCS) pairing state of a two-component Bose gas with a symmetric spin-orbit coupling. In the dilute limit at low temperatures, this system is essentially a dilute gas of diatomic molecules. We compute the effective mass of the molecule and find that it is anisotropic in momentum space. The critical temperature of the pairing state is about eight times smaller than the Bose-Einstein condensation (BEC) transition temperature of an ideal Bose gas with the same density.