Non-extensive NJL model study of QCD phase structure with chiral imbalance and strong magnetic fields

TL;DR

The paper addresses how non-equilibrium dynamics modify the QCD phase structure of dense quark matter in strong magnetic fields and with chiral imbalance. It employs a two-flavor NJL model augmented by a chiral chemical potential $\mu_5$ and analyzes it within Tsallis statistics, deriving a thermodynamic potential $\Omega(T,\mu_5,B,q)$ and solving the gap equation for the dynamical mass $M$ under a soft-cutoff regularization. The study finds that the pseudocritical temperature $T_{pc}$ decreases as the Tsallis parameter $q$ increases, with magnetic catalysis vs. inverse magnetic catalysis depending on how $\mu_5$ couples to the magnetic field; for $q>1$ the $T_{pc}$ versus $eB$ curve becomes non-monotonic, and thermodynamic observables such as pressure anisotropy and the speed of sound exhibit notable $eB$- and $\mu_5$-dependent modifications. The results indicate that short-time, non-equilibrium dynamics captured by $q>1$ can markedly alter QGP phase transitions and related observables, offering a theoretical lens to interpret heavy-ion collision data in regimes with strong magnetic fields and chiral imbalance.

Abstract

Based on the two-flavor NJL model with Tsallis non-extensive statistics, this work explores the QCD phase structure and thermodynamic properties under strong magnetic fields and chiral imbalance. The Tsallis parameter $q$ captures non-equilibrium effects relevant to heavy-ion collisions. Key findings reveal that the pseudocritical temperature $T_{\textrm{pc}} $ decreases with increasing $q$, indicating that non-equilibrium conditions promote chiral symmetry restoration at lower temperatures. The chiral chemical potential $μ_5 $ significantly alters the magnetic response, with a transition from magnetic catalysis to inverse magnetic catalysis under certain conditions. For $q > 1$, non-monotonic behavior of $T_{\textrm{pc}}$ with magnetic field $eB$ emerges. Pressure becomes anisotropic under strong $eB$, and the speed of sound exhibits a dip near $T_{\textrm{pc}}$, shifting to lower temperatures with larger $q$. These results highlight how non-extensive statistics, chiral imbalance, and magnetic fields collectively influence the QCD phase diagram and thermodynamic observables, offering insights for interpreting heavy-ion collision data.

Figures (7)

• Figure 1: The quark dynamical mass as a function of temperature for three different values of the Tsallis parameter $q$ at zero quark chemical potential. Under magnetic field $eB=0.2 ~\textrm{GeV}^2$, results are shown for two cases of the chiral chemical potential: (a) $\mu_{5}=0.02~\textrm{GeV}$, and (b) $\mu_{5}=0.2~\textrm{GeV}$.
• Figure 2: Dependence of the pseudocritical temperature $T_\textrm{pc}$ on the magnetic field $eB$ under different Tsallis parameters $q$: (a) Comparison between Boltzmann-Gibbs statistics (B.G.) and the case $q = 1.001$, with fixed $\mu_{5} = 0.1~\textrm{GeV}$ and field-dependent $\mu_{5}=0.5\sqrt{eB}$; (b) Behavior under $q = 1.1$ and $1.2$ for the same two choices of $\mu_5$.
• Figure 3: Dependence of the pseudocritical temperature $T_\textrm{pc}$ on the Tsallis parameter $q$ for different values of the chiral chemical potential $\mu_5$.
• Figure 4: Chiral number density $n_5$ as a function of the chiral chemical potential $\mu_5$ for different Tsallis parameters $q$, at a fixed temperature $T=0.15~\textrm{GeV}$ and magnetic field $eB=0.2~\textrm{GeV}^2$.
• Figure 5: Chiral number density $n_5$ as a function of temperature $T$ for different Tsallis parameters $q$. The magnetic field is fixed at $eB=0.2~\textrm{GeV}^2$: (a) $\mu_{5}=0.02~\textrm{GeV}$, (b) $\mu_{5}=0.2~\textrm{GeV}$.