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/α s ∼ ln(eB/ 2 QCD ) for large values of B.
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
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