  We consider pairing in a three-component gas of degenerate fermions. In
particular, we solve the finite temperature mean-field theory of an interacting
gas for a system where both interaction strengths and fermion masses can be
unequal. At zero temperature we find a a possibility of a quantum phase
transition between states associated with pairing between different pairs of
fermions. On the other hand, finite temperature behavior of the three-component
system reveals some qualitative differences from the two-component gas: for a
range of parameters it is possible to have two different critical temperatures.
The lower one corresponds to a transition between different pairing channels,
while the higher one corresponds to the usual superfluid-normal transition. We
discuss how these phase transitions could be observed in ultracold gases of
fermionic atoms.
