Two-flavor color superconductivity in the Fierz-transfromed Nambu--Jona-Lasinio model

Abstract: The color superconducting phase of two-flavor quark matter is studied under a Fierz-transformed Lagrangian. In the Fierz-transformed Lagrangian both the quark-antiquark and quark-quark channel are included. Two parameters $\alpha$ and $\beta$ are introduced to weight the Fierz-transformed quark-antiquark Lagrangian and quark-quark Lagrangian, respectively. The couplings of different interaction channel are thus fixed by the two coefficients other than five free parameters. The interplay between chiral symmetry restoration and the formation of color superconducting phases are discussed. It is found that the increase of $\alpha$ leads the chiral phase transition from first order to crossover. The calculated specific heat shows jump at critical temperature which confirms the phase transition. The increase of $\beta$ leads the pseudo-critical chemical potential reduce. With large $\beta$ the superconductors gap $\Delta$ can be larger than the typical value and the well-known BCS relation between critical temperature and gap is well fitted.