  The first observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)
superconducting state and a subsequent detection of the spin-dependent
effective masses of quasiparticles in the CeCoIn_5 heavy fermion system are
combined into a single theoretical framework. The appearance of the spin-split
masses extends essentially the regime of temperatures and applied magnetic
fields, in which FFLO is observable and thus is claimed to be very important
for the FFLO detectability. We also stress that the quasiparticles composing
Cooper pair become distinguishable in the nonzero field. The analysis is
performed within the Kondo-lattice limit of the finite-U Anderson-lattice model
containing both the mass renormalization and real-space pairing within a single
scheme.
