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The first observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)superconducting state and a subsequent detection of the spin-dependenteffective masses of quasiparticles in the CeCoIn_5 heavy fermion system arecombined into a single theoretical framework. The appearance of the spin-splitmasses extends essentially the regime of temperatures and applied magneticfields, in which FFLO is observable and thus is claimed to be very importantfor the FFLO detectability. We also stress that the quasiparticles composingCooper pair become distinguishable in the nonzero field. The analysis isperformed within the Kondo-lattice limit of the finite-U Anderson-lattice modelcontaining both the mass renormalization and real-space pairing within a singlescheme.

Superconducting BCS versus Fulde-Ferrell-Larkin-Ovchinnikov states of quasiparticles with spin dependent mass and their distinguishability