$T-\mu$ quark matter phase transitions and critical endpoint in nonlocal PNJL models under a strong magnetic field

We study the $T-\mu$ phase diagram of quark matter under the influence of a strong uniform magnetic field in the framework of a nonlocal extension of the Polyakov–Nambu–Jona-Lasinio model (PNJL). The existence of a critical endpoint (CEP) is found for the whole considered range of the magnetic field (up to $1{\mathrm{GeV}}^2$). We analyze the location of this CEP as a function of the external field and discuss the presence of inverse magnetic catalysis for nonzero chemical potentials. Our results show that the temperature of the CEP decreases with the magnetic field, in contrast to the behavior observed in local NJL/PNJL models.

Figure 1

Behavior of $\overline{\sigma }$ as a function of $\mu$ for different values of the temperature and the magnetic field.

Figure 2

Flavor-averaged chiral condensate as a function of $eB$ for different representative values of the temperature and the quark chemical potential.

Figure 3

Behavior of the chiral and PL susceptibilities as a function of temperature for $eB=0$ and $eB=0.5{\mathrm{GeV}}^2$.

Figure 4

Upper: chiral critical temperatures $T_c$ at $\mu =0$ as functions of the predicted value for the chiral quark condensate $-⟨qq{⟩}^{1/3}$, for different values of $eB$. Lower: normalized critical temperatures as functions of $eB$ for various model parametrizations. Solid (dashed) lines correspond to first-order (crossover) transitions. For comparison, three-flavor LQCD results from Ref. [36] are indicated by the gray band.

Figure 5

Chiral restoration critical temperature as a function of $eB$ for some representative values of the quark chemical potential.

Figure 6

Phase diagram in $\mu -T$ plane for different values of $eB$. Solid and dashed lines correspond to first-order and crossover transitions, respectively. The gray band indicates the locations of the critical endpoints.

Figure 7

Phase diagram in $\mu -eB$ plane for different temperatures. Solid and dashed lines represent first-order and crossover transitions, respectively. The gray band indicates the locations of the critical endpoints.