QCD phase diagram in a constant magnetic background

Abstract

Magnetic catalysis is the enhancement of a condensate due to the presence of an external magnetic field. Magnetic catalysis at $$T=0$$ T = 0 is a robust phenomenon in low-energy theories and models of QCD as well as in lattice simulations. We review the underlying physics of magnetic catalysis from both perspectives. The quark-meson model is used as a specific example of a model that exhibits magnetic catalysis. Regularization and renormalization are discussed and we pay particular attention to a consistent and correct determination of the parameters of the Lagrangian using the on-shell renormalization scheme. A straightforward application of the quark-meson model and the NJL model leads to the prediction that the chiral transition temperature $$T_{\chi }$$ T χ is increasing as a function of the magnetic field B. This is in disagreement with lattice results, which show that $$T_{\chi }$$ T χ is a decreasing function of B, independent of the pion mass. The behavior can be understood in terms of the so-called valence and sea contributions to the quark condensate and the competition between them. We critically examine these ideas as well recent attempts to improve low-energy models using lattice input.

Effects of the quark anomalous magnetic moment in the chiral symmetry restoration: magnetic catalysis and inverse magnetic catalysis

“…But a totally different result is observed close to the pseudocritical temperature, where the chiral condensate decreases non monotonically its value as the strong magnetic fields grow, i.e., for 𝑒𝐵 0.2 GeV 2 . This is the well-know inverse magnetic catalysis effect (IMC) [24][25][26], more details can be found in recent reviews [27,28]. Such evaluations are considered with physical pion masses [24], where it is also observed the decreasing of the pseudocritical temperature.…”

Effects of the quark anomalous magnetic moment in the chiral symmetry restoration: magnetic catalysis and inverse magnetic catalysis

“…But a totally different result is observed close to the pseudocritical temperature, where the chiral condensate decreases non monotonically its value as the strong magnetic fields grow, i.e., for eB 0.2 GeV 2 . This is the well-know inverse magnetic catalysis effect (IMC) [24][25][26], more details can be found in recent reviews [27,28]. Such evaluations are considered with physical pion masses [24], where it is also observed the decreasing of the pseudocritical temperature.…”

Magnetic field induced corrections to the NJL model coupling constant from vacuum polarization

“…where Ḡs ij (B) and Ḡij csb (B) were written in Eqs. (18) and (19) and O chsb are the chiral symmetry breaking corrections for the pseudoscalar coupling constants discussed above and neglected from here on. However, the zero magnetic field limit of G s,ps ij (B = 0) contributes for G 0 making the overall normalization of the coupling constant ambiguous and this would have consequences for the calculation of observables for which we are interested, however, in investigating only the magnetic field dependence.…”

“…Usually, global properties of low energies hadrons can be suitably investigated by means of hadron effective models and effective field theories whose use have been extended, more recently, for hadrons in strong magnetic fields [15,1,18,19,20,21,22]. Among the successful QCD effective models, the Nambu-Jona-Lasinio (NJL) model is known to reproduce, and eventually to predict, many observables for the hadron structure and dynamics under different conditions [23,24,25,26,19].…”

“…Usually, global properties of low energies hadrons can be suitably investigated by means of hadron effective models and effective field theories whose use have been extended, more recently, for hadrons in strong magnetic fields [15,1,18,19,20,21,22]. Among the successful QCD effective models, the Nambu-Jona-Lasinio (NJL) model is known to reproduce, and eventually to predict, many observables for the hadron structure and dynamics under different conditions [23,24,25,26,19]. Several approaches have been already employed to describe how the NJL model coupling constant might be obtained in terms of QCD degrees of freedom in the vacuum [27,28,29,30,31,32] or to understand further how those degrees of freedom contribute for the NJL-model parameters [33,34,35].…”