The role of asymptotic freedom for the pseudocritical temperature in magnetized quark matter

Abstract

Abstract.Motivated by discrepancies observed between lattice QCD simulations and quark models regarding the behavior of the pseudo critical temperature for chiral symmetry restoration as a function of the magnetic field B, we investigate the effects of a running the quark coupling constant G with temperature T and the magnetic field B in the context of the Nambu-JonaLasinio model(NJL). Our point that when asymptotic freedom, an essential feature of QCD and absent in the model, is included through a running of G with T and B results from the NJL model can be brought in qualitative agreement with lattice QCD simulations. IntroductionRecently much effort has been devoted to the understanding of the effects produced by a magnetic field in the phase diagram of Quantum Chromodynamics (QCD). The motivation is due to the fact that strong magnetic fields may be produced in non central heavy ion collisions [1,2,3,4]. Other scenarios that strong magnetic fields are also important are in the phenomenology of stars, in particular in magnetars [5,6], and in the physics of the early universe [7]. Lattice QCD simulations [8,9] predict that at zero baryon density and zero magnetic field there is a crossover transition at a pseudo critical temperature T pc . More recent lattice simulations show that this crossover persists if we include the effects of external strong magnetic fields [10,11,12,13]. At zero temperature the lattice results confirm the existence of the phenomenon of magnetic catalysis (MC) [14,15,16], where the chiral order parameter is enhanced with the increase of the magnetic field. At finite temperature, lattice results are in agreement with effective models [17,18,19,20,21]. However, recent lattice results of Refs. [12,13], that consider physical values of quark masses, predict an inverse magnetic catalysis (IMC), in that the pseudo critical temperature T pc for the crossover decrease with B, in total disagreement with all effective model calculations in the literature [17,18,19,22,23,24].Many efforts have been dedicated to understand the disagreement between lattice and models in the behavior of T pc with B; see e.g. Refs. [25,26,34,27]. Very sophisticated versions of quark

Thermodynamics of PNJL at zero temperature in a strong magnetic field

“…In literature, the Fock-Schwinger propertime method [42] is applied to a thermal field theory to obtain the exact expression of the effective potential with B-dependent divergent part in the vacuum regularization [43][44][45]. Another equivalent method is the magnetic field independent vacuum regularization (MFIR), which is widely employed in the recent work [46][47][48][49][50][51][52]. In this paper, we adopt the second regularization scheme.…”

Nambu--Jona-Lasinio model with a fractal inspired coupling

“…The studies on properties of compact stars and the experiments with heavy-ion collisions have indicated the possibility of having very intense magnetic fields affecting the quark matter. This idea inspired some modifications of the standard NJL model in order to access the effects of strong magnetic fields in quark matter [14][15][16][17] and on the pion properties [18,19]. Deconfinement and chiral phase transition in quark matter under strong electric field [20], the magnetic field-dependence of the neutral pion mass in the linear sigma model coupled to quarks [21] and the anisotropy in the equation of state of strongly magnetized quark matter [22] were also studied recently with effective models.…”