Thermomagnetic properties of the strong coupling in the local Nambu–Jona-Lasinio model

Abstract

We study the thermo-magnetic properties of the strong coupling constant G and quark mass M entering the Nambu-Jona-Lasinio model. For this purpose, we compute the quark condensate and compare it to lattice QCD (LQCD) results to extract the behavior of G and M as functions of the magnetic field strength and temperature. We find that at zero temperature, where the LQCD condensate is found to monotonically increase with the field strength, M also increases whereas G remains approximately constant. However, for temperatures above the chiral/deconfinement phase transitions, where the LQCD condensate is found to monotonically decrease with increasing field, M and G also decrease monotonically. For finite temperatures, below the transition temperature, we find that both G and M initially grow and then decrease with increasing field strength. To study possible consequences of the extracted temperature and magnetic field dependence of G and M , we compute the pressure and compare to LQCD results, finding an excellent qualitative agreement. In particular, we show that the transverse pressure, as a function of the field strength, is always negative for temperatures below the transition temperature whereas it starts off being positive and then becomes negative for temperatures above the transition temperature, also in agreement with LQCD results. We also show that for the longitudinal pressure to agree with LQCD calculations, the system should be described as a diamagnet. We argue that the turnover of M and G as functions of temperature and field strength is a key element that drives the behavior of the quark condensate going across the transition temperature and provides clues for a better understanding of the inverse magnetic catalysis phenomenon.

Thermomagnetic evolution of the QCD strong coupling

“…The growth or decrease of the quark condensate would in turn be linked to the corresponding behavior of the coupling at zero or at high temperature, respectively. This scenario has been studied within effective QCD models [3][4][5][6][7][8][9], from the Schwinger-Dyson approach [10], and from the thermomagnetic behavior of the quark-gluon vertex in QCD [11,12]. In the latter, it has been shown that the growth or decrease of the effective QCD coupling, at finite temperature and magnetic field strength, comes from a subtle competition between the color charges of gluons and quarks in such a way that at zero temperature the former is larger than the latter, whereas at high temperature, the coupling receives contributions only from the color charge associated to quarks.…”

On the iterative solution of the gap equation in the Nambu-Jona-Lasinio model

“…Nevertheless, external magnetic field effects are best included through the Schwinger Proper-Time representation of the fermion propagator. This observation has been exploited to address the problem of magnetic catalysis [12] and inverse magnetic catalysis observed in lattice simulations [13,14] and confirmed by several approaches [7,8,15]. Under this environment, the effective coupling of the model can reach very large values, and therefore, exploring the validity of these regularization schemes in this super-strong coupling regime is a natural question to address.…”

“…[6] for a review) and its magnetized extension [7] from a complementary point of view of lattice [8] and other quantum field theoretical approaches [9,10]. Several regularization schemes have been used in literature within the context of NJL model.…”

“…NJL model has been widely used to sketch the quantum chromodynamics (QCD) phase diagram (see, for instance, Ref. [6] for a review) and its magnetized extension [7] from a complementary point of view of lattice [8] and other quantum field theoretical approaches [9,10].…”

“…Nevertheless, up to date, the model continues being used as an effective description of quarks dynamics either as originally proposed, where fermion fields are now regarded as quark fields, or with slightly modifications [3, 4, 5] to account for confinement. NJL model has been widely used to sketch the quantum chromodynamics (QCD) phase diagram (see, for instance, Ref.[6] for a review) and its magnetized extension [7] from a complementary point of view of lattice [8] and other quantum field theoretical approaches [9,10]. Several regularization schemes have been used in literature within the context of NJL model.…”