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BCS-BEC Crossover and Stability in a Nambu-Jona-Lasinio Model with Diquark-Diquark Repulsion

We investigate the equation of state (EoS) along the BCS-BEC crossover for a quark system described by a Nambu-Jona-Lasinio model with multi-fermion interactions. Together with attractive channels for particle-antiparticle ($\Gs$) and particle-particle ($\Gd$) interactions, a multi-fermion channel with coupling $λ$ that accounts for the diquark-diquark repulsion is also considered. The chiral and diquark condensates are found in the mean-field approximation for different values of the coupling constants. The parameter values where the BCS-BEC crossover can take place are found, and the EoS is used to identify the stability region where the BEC regime has positive pressure. We discuss how the particle density and the repulsive diquark-diquark interaction affect the stability window in the $\Gs-\Gd$ plane and find the profile of the pressure versus the density for various values of $λ$ and $\Gd$. The effects of $λ$ and $\Gd$ in the BCS-BEC crossover tend to compensate each other, allowing for a feasible region of densities where the crossover can occur with positive pressure. These results, although mainly qualitative, should serve as a preliminary step in the microscopic analysis required to determine the feasibility of the BCS-BEC crossover and its realization in more realistic models of dense QCD that can be relevant for applications to neutron stars.