Chiral transition with magnetic fields

Abstract

We study the nature of the chiral transition for an effective theory with spontaneous breaking of symmetry, where charged bosons and fermions are subject to the effects of a constant external magnetic field. The problem is studied in terms of the relative intensity of the magnetic field with respect to the mass and the temperature. When the former is the smallest of the scales, we present a suitable method to obtain magnetic and thermal corrections up to ring order at high temperature. By these means, we solve the problem of the instability in the boson sector for these theories, where the squared masses, taken as functions of the order parameter, can vanish and even become negative. The solution is found by considering the screening properties of the plasma, encoded in the resummation of the ring diagrams at high temperature. We also study the case where the magnetic field is the intermediate of the three scales and explore the nature of the chiral transition as we vary the field strength, the coupling constants and the number of fermions. We show that the critical temperature for the restoration of chiral symmetry monotonically increases from small to intermediate values of the magnetic fields and that this temperature is always above the critical temperature for the case when the magnetic field is absent.Comment: 13 pages, 6 figures, added comments. Version to appear in Phys. Rev

Inverse magnetic catalysis in the linear sigma model with quarks

“…They also produce that, for certain values of the model parameters and some temperatures, the effective potential becomes an expansion containing a cubic term in the order parameter signaling that the description goes beyond the mean field approximation (see Ref. [19] for details).…”

“…Nevertheless, it has been shown in Ref. [19] that including the ring diagrams, computed in the presence of the magnetic field, also cures these problems, thereby canceling the new offending infrared terms. In summary, the difference between our approach and previous ones within the context of the linear sigma model is that we have let the particle masses carry its dependence on v and, upon inclusion of the plasma screening effects, have found the self-consistent thermomagnetic effective potential beyond mean field PHYSICAL REVIEW D 91, 016002 (2015) which is then used to perform the analysis to include a thermomagnetic correction to the couplings.…”

“…where we have also included the plasm a screening effects for the boson's mass squared [19]. 2{qB)2k\ + ■ > 2 + k 2 + m2)3J (21) The sum and integrals in 7"^0 are perform ed by means of the M ellin sum m ation technique [23] with the result Figure 4 shows the Feynm an diagrams that contribute to this correction.…”

“…This behavior introduces in turn a dependence of the boson masses on the magnetic field and a decrease of the critical temperature for chiral symmetry breaking/restoration. The essential ingredients for the calculation are the finite temperature effective potential in the presence of a magnetic field together with the proper handling of the plasma screening effects that have been recently consis tently formulated for theories with spontaneous symmetry breaking [19]. The screening effects are included by means of the resummation of the ring diagrams which produce that, for certain values of the model parameters and some temperatures, the effective potential becomes an expansion containing a cubic term in the order parameter signaling that the description goes beyond the mean field approximation.…”

Strongly Interacting Matter in Magnetic Field

“…The magnetic field can reach 10 18−20 Gauss, in the core of magnetars [6,7]. Furthermore, it is indicated that the extremely strong magnetic field, B ∼ 10 23 Gauss, are generated via cosmological electroweak and quark-hadron phase transition [8,9]. Therefore, how the strong magnetic field changes the QCD phase structure becomes an interesting and open question, see [10][11][12] for recent reviews.…”