Pionic BEC-BCS crossover at finite isospin chemical potential

Abstract

We study the character change of the pionic condensation at finite isospin chemical potential ${\ensuremath{\mu}}_{\mathrm{I}}$ by adopting the linear sigma model as a nonlocal interaction between quarks. At low $|{\ensuremath{\mu}}_{\mathrm{I}}|$ the condensation is purely bosonic, then the Cooper pairing around the Fermi surface grows gradually as $|{\ensuremath{\mu}}_{\mathrm{I}}|$ increases. This $q\mathrm{\text{\ensuremath{-}}}\overline{q}$ pairing is weakly coupled in comparison with the case of the $q\mathrm{\text{\ensuremath{-}}}q$ pairing that leads to color superconductivity.