Hot QCD at finite isospin density: Confronting the SU(3) Nambu–Jona-Lasinio model with recent lattice data

Extending our recently published SU(2) results for zero temperature, we now compute the QCD equation of state for finite isospin density within the three-flavor Nambu–Jona-Lasinio (NJL) model in the mean field approximation, motivated by the recently obtained lattice QCD results for both zero and finite temperatures. Like our previous study, here also we have considered both the commonly used traditional cutoff regularization scheme and the medium separation scheme. Our results are compared with recent high-precision lattice simulations as well as previously obtained results in two-flavor Nambu–Jona-Lasinio model. The agreement between the lattice results and the predictions from three-flavor NJL model is very good for low values of ${\mu }_I$ (for both zero and finite temperatures). For larger values of ${\mu }_I$, the agreement between lattice data and the two-flavor NJL predictions is surprisingly good and better than with the three-flavor predictions.

Figure 1

Chiral and pion condensates as functions of ${\mu }_I$ at $T=0$, evaluated according to Eqs. (3.1) and (3.2), for TRS and MSS.

Figure 2

Normalized pressure $p_N$ as a function of ${\mu }_I$ at $T=0$, for SU(2) (solid and dot-dashed lines) and SU(3) (dashed and dotted lines) comparing TRS, MSS, and lattice results from Ref. [54] (small dots).

Figure 3

Isospin density $n_I$ as a function of ${\mu }_I$ at $T=0$, for SU(2) (solid and dot-dashed lines) and SU(3) (dashed and dotted lines) comparing TRS, MSS, and lattice results from Ref. [54] (small dots).

Figure 4

Comparison of the energy density scaled by the Stefan-Boltzmann limit for zero temperature and finite isospin chemical potential. The pQCD results for higher values of ${\mu }_I/m_{\pi }$ are obtained using the expressions from Ref. [72].

Figure 5

Normalized interaction measure ($\mathrm{\Delta }I$) as a function of ${\mu }_I$ for SU(2) (solid and dot-dashed lines) and SU(3) (dashed and dotted lines) comparing TRS, MSS, and lattice results from Refs. [54, 66] (small dots).

Figure 6

SU(3) chiral and pion condensates as functions of the temperature $T$ with ${\mu }_I=0.206\mathrm{GeV}$ for TRS and MSS.

Figure 7

Normalized pressure $p_N$ as a function of ${\mu }_I$ for different temperatures $T$, for TRS and MSS, comparing SU(2) and SU(3) to lattice results from Refs. [49, 52, 64, 65].

Figure 8

Isospin density $n_I$ as a function of ${\mu }_I$ for different temperatures $T$, for TRS and MSS, comparing SU(2) and SU(3) to lattice results from Refs. [49, 52, 64, 65].

Figure 9

Normalized trace anomaly or interaction measure ($\mathrm{\Delta }I$) as a function of ${\mu }_I$ for different temperatures $T$, for TRS and MSS, comparing SU(2) and SU(3) to lattice results from Ref. [66].

Figure 10

$T-{\mu }_I$ phase diagram within NJL model, implementing both TRS and MSS and comparing SU(2) and SU(3) to lattice results from Refs. [49, 52, 64, 65].