Importance of asymptotic freedom for the pseudocritical temperature in magnetized quark matter

Although asymptotic freedom is an essential feature of QCD, it is absent in effective chiral quark models like the Nambu–Jona-Lasinio and linear sigma models. In this work we advocate that asymptotic freedom plays a key role in the recently observed discrepancies between results of lattice QCD simulations and quark models regarding the behavior of the pseudocritical temperature $T_{pc}$ for chiral-symmetry restoration in the presence of a magnetic field $B$. We show that the lattice predictions that $T_{pc}$ decreases with $B$ can be reproduced within the Nambu–Jona-Lasinio model if the coupling constant $G$ of the model decreases with $B$ and the temperature. Without aiming at numerical precision, we support our claim by considering a simple ansatz for $G$ that mimics the asymptotic-freedom behavior of the QCD coupling constant $1/{\alpha }_s\sim ln(eB/{\Lambda }_{\text{QCD}}^2)$ for large values of $B$.

Figure 1

The condensate average as a function of the temperature. Data points are from the lattice simulations of Ref. [13].

Figure 2

The condensate difference as a function of temperature. Data points are from the lattice simulations of Ref. [13].

Figure 3

The normalized thermal susceptibility as a function of the temperature for different values of the magnetic field $B$.

Figure 4

The pseudocritical temperature for the chiral transition of magnetized quark matter as a function of magnetic field.