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

TL;DR

This paper investigates how coupling strength influences the BCS-BEC crossover in pion superfluid quark matter, revealing phase transition behaviors and their effects on the properties of compact stars.

Contribution

It demonstrates the coupling strength-induced BCS-BEC crossover on the phase boundary of pion superfluidity within a NJL model, linking microscopic phase changes to macroscopic star properties.

Findings

Strong coupling leads to BEC state with $ ext{μ}_I^c = M_ ext{π}$.

Weak coupling results in BCS state with $ ext{μ}_I^c < M_ ext{π}$.

Coupling strength affects the stiffness of the quark matter equation of state.

Abstract

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.