Coupling strength induced BCS-BEC crossover on phase boundary of pion superfluid

Coupling strength effect on the quark matter with finite isospin chemical potential is studied in a Pauli-Villars regularized NJL model. A BCS-BEC crossover occurs along the phase boundary of pion superfluid phase transition, as increasing coupling strength $G$. For strong coupling cases, the critical isospin chemical potential for pion superfluid phase transition $\mu_I^c$ is exactly the same as pion mass in vacuum $M_\pi$. Around the critical point $\mu_I^c$, the pion superfluid quark matter is in BEC state, associated with a fast increase of pion condensate. For weak coupling cases, we obtain $\mu_I^c<M_\pi$, and a mass jump of the Goldstone boson at the critical point $\mu_I^c$. The pion superfluid quark matter is in BCS state even around $\mu_I^c$, accompanied by a slow increase of pion condensate. Note that $\mu_I^c$ is a non-monotonic function of coupling strength $G$. On the other hand, coupling strength effect changes the bulk properties of quark matter. In strong (weak) coupling cases, the EoS of quark matter at finite isospin chemical potential is stiff (soft). Therefore, the compact stars composed of strong (weak) coupling pion superfluid quark matter has a heavier (lighter) mass and larger (smaller) radius.