QCD phase diagram at finite baryon and isospin chemical potentials

Abstract

The phase structure of two-flavor QCD is explored for thermal systems with finite baryon- and isospin-chemical potentials, ${\ensuremath{\mu}}_{\mathrm{B}}$ and ${\ensuremath{\mu}}_{\mathrm{iso}}$, by using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. The PNJL model with the scalar-type eight-quark interaction can reproduce lattice QCD data at not only ${\ensuremath{\mu}}_{\mathrm{iso}}={\ensuremath{\mu}}_{\mathrm{B}}=0$, but also ${\ensuremath{\mu}}_{\mathrm{iso}}>0$ and ${\ensuremath{\mu}}_{\mathrm{B}}=0$. In the ${\ensuremath{\mu}}_{\mathrm{iso}}$-${\ensuremath{\mu}}_{\mathrm{B}}$-$T$ space, where $T$ is temperature, the critical endpoint of the chiral phase transition in the ${\ensuremath{\mu}}_{\mathrm{B}}$-$T$ plane at ${\ensuremath{\mu}}_{\mathrm{iso}}=0$ moves to the tricritical point of the pion-superfluidity phase transition in the ${\ensuremath{\mu}}_{\mathrm{iso}}$-$T$ plane at ${\ensuremath{\mu}}_{\mathrm{B}}=0$ as ${\ensuremath{\mu}}_{\mathrm{iso}}$ increases. The thermodynamics at small $T$ is controlled by $\sqrt{{\ensuremath{\sigma}}^{2}+{\ensuremath{\pi}}^{2}}$ defined by the chiral and pion condensates, $\ensuremath{\sigma}$ and $\ensuremath{\pi}$.