Physics Letters B 731 (2014) 154–158
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Physics Letters B
www.elsevier.com/locate/physletb
A search for inverse magnetic catalysis in thermal
quark–meson models
E.S. Fraga
a,b,c
, B.W. Mintz
d,∗
, J. Schaffner-Bielich
a
a
Institute for Theoretical Physics, Goethe University, D-60438 Frankfurt am Main, Germany
b
Frankfurt Institute for Advanced Studies, Goethe University, D-60438 Frankfurt am Main, Germany
c
Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro, RJ, Brazil
d
Departamento de Física Teórica, Universidade do Estado do Rio de Janeiro, 20550-013 Rio de Janeiro, RJ, Brazil
article i nfo abstract
Article history:
Received 29 November 2013
Received in revised form 26 January 2014
Accepted 12 February 2014
Availableonline19February2014
Editor: W. Haxton
We explore the parameter space of the two-flavor thermal quark–meson model and its Polyakov loop-
extended version under the influence of a constant external magnetic field B. We investigate the
behavior of the pseudo critical temperature for chiral symmetry breaking taking into account the likely
dependence of two parameters on the magnetic field: the Yukawa quark–meson coupling and the
parameter T
0
of the Polyakov loop potential. Under the constraints that magnetic catalysis is realized
at zero temperature and the chiral transition at B = 0 is a crossover, we find that the quark–meson
model leads to thermal magnetic catalysis for the whole allowed parameter space, in contrast to the
present picture stemming from lattice QCD.
© 2014 The Authors. Published by Elsevier B.V. Open access under CC BY license.
Funded by SCOAP
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1. Introduction
The phase diagram of magnetic quantum chromodynamics
(QCD), i.e. for strong interactions under the influence of an external
classical Abelian magnetic field, is currently under construction.
This phase diagram corresponds to a special case, as it does not
suffer from the Sign Problem, and can be easily simulated on the
lattice. So, from the theoretical point of view, it serves as a crucial
check for effective models of QCD extended to regions not easily
accessible by lattice simulations. From the experimental stand-
point, this setup is also quite remarkable owing to the fact that
strong magnetic fields are relevant in non-central heavy ion col-
lisions, and play a major role in the possibility of observing the
chiral magnetic effect (for a comprehensive review, see Ref. [1]).
The chiral and deconfining transitions under the effect of a
magne
tic background are, of course, amenable also to effective
model descriptions [2,3]. Those models have predicted several out-
standing new features to the thermodynamics of strong interac-
tions, from shifting the chiral and the deconfinement crossover
lines in the phase diagram [4–32] to transforming the vacuum
into a superconducting medium via
ρ-meson condensation [33,34],
for high enough magnetic fields, i.e. a few times m
2
π
. Neverthe-
less, the available lattice data [35–37] contradicted essentially all
predictions regarding the behavior of the pseudo critical lines for
*
Corresponding author.
deconfinement and chiral symmetry restoration coming from chiral
models (including their Polyakov loop extensions). The reason for
this failure is unclear, but the fact that confinement is not prop-
erly captured in such chiral models might play a role [17,38].It
should be noticed that, even though the lattice simulations of [39,
40] point to an increasing pseudo critical temperature as a func-
tion of the applied magnetic field, these results were obtained for
unphysical quark masses.
In this Letter, we explore the parameter space of the two-flavor
thermal
quark–meson (QM) model and its Polyakov loop-extended
version (PQM) under the influence of a constant external magnetic
field B. We investigate the behavior of the pseudo critical temper-
ature for chiral symmetry breaking taking into account the likely
dependence of two parameters on the magnetic field: the Yukawa
quark–meson coupling and the parameter T
0
of the Polyakov loop
potential. We scan an important part of the parameter spaces of
these models, in order to check whether they can accommodate, at
least qualitatively, the trend of inverse magnetic catalysis found in
Ref. [35]. In doing so, we keep two important constraints: (i) that
magnetic catalysis is realized at zero temperature, and (ii) that the
chiral transition at B
= 0 is a crossover. In these two limits, i.e.
zero temperature or zero magnetic field, chiral effective models
usually produce results that are, at least qualitatively, in line with
lattice QCD. We find, nevertheless, that the extensions considered
by introducing a B dependence in the Yukawa coupling and in the
parameter T
0
are not enough to account for the behavior of the
http://dx.doi.org/10.1016/j.physletb.2014.02.028
0370-2693 © 2014 The Authors. Published by Elsevier B.V. Open access under CC BY license. Funded by SCOAP
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