• QCD
• pseudocritical temperature
• magnetic catalysis
• magnetic background
• confinement
• QCD phase diagram

Quantum Chromodynamics (QCD) is the quantum theory that describes strong interactions. It is a non-Abelian gauge theory with gauge group SU(3). The quanta of the SU(3) gauge field are called gluons, while the matter content of the theory consists of quarks.
The latter are fermions that differentiate into six different flavours, each of them assigned to the fundamental representation of the local gauge group.
Recently, many studies have been performed in order to understand how the properties of strong interactions get modified by intense electromagnetic backgrounds, with field values comparable to the QCD scale Λ_{QCD} ∼ 200MeV. This physical situation has great phenomenological importance: in non-central heavy ion collision experiments conducted at LHC and RHIC, charged ion beams produce strong magnetic impulses, which can reach the value of sqrt(eB) ∼ 0.5 GeV. Large magnetic background fields, of the order of sqrt(eB) ∼ 1.5 GeV, may have been produced at the time of the cosmological electroweak phase transition. In addition, the subsequent evolution of the Universe and, in particular, the transition from deconfined to confined matter, may have been influenced by the presence of such strong backgrounds. Finally, some neutron stars called magnetars posses strong magnetic dipole fields ( sqrt(eB) ∼ 1 MeV).
The study of these physical phenomena, which manifest many of their prominent features in the low energy regime, cannot be approached by means of perturbative techniques. In this framework, lattice simulations represent a research tool of primary importance: Monte Carlo simulations allow us to carry out an in-depth analysis of non-perturbative strong dynamics effects from first principles.
At zero baryon chemical potential, a crossover divides the QCD phase diagram in two distinct regions, namely the Quark-Gluon Plasma (QGP) and the Hadron Gas phases.
The pseudocritical temperature T c corresponding to the crossover of deconfinement and chiral restoration represents one of the most important aspects of strong interactions. It is well established that the position of the pseudocritical point is influenced by the presence of a static magnetic field. In particular, the study has found that T C is a monotonic decreasing function of the background field strength. This result is in contrast with the naive expectation based on the so-called magnetic catalysis (i.e. the enhancement of chiral symmetry breaking due to the presence of a background magnetic field) and earlier numerical simulations, performed with larger than physical quark masses and unimproved action. At the same time, the magnetic field has been found to cause the suppression around the pseudocritical temperature of the chiral condensate, that is an approximate order parameter for the chiral transition. This phenomenon has been called inverse magnetic catalysis.
In this context we can state that, by understanding the origin of the discrepancy in the conclusions obtained in the above-mentioned studies, we can move a significantly step forward towards the comprehension of the physical mechanism which leads to the decreasing behaviour of T_C with respect to the magnetic field strength and the inverse magnetic catalysis phenomenon. An interesting direction to investigate emerges from the study of the static quark-antiquark potential at finite B: the authors found that the confining properties of QCD are suppressed due to the presence of a magnetic field, and this phenomenon turns out to be dominant with respect to the impact on the chiral condensate.
On this basis, we hypothesize that the modification of the confining properties may play a dominant role in the mechanism that determines the trend of T C (B). If this is the case, we expect that the decreasing behaviour of the pseudocritical temperature with respect to the magnetic field strength is preserved for larger than physical quark masses. In order to verify this assumption, we simulate N f = 2 + 1 QCD with improved gauge action, stout smeared rooted staggered fermions and N t = 6 for three different larger than physical pion masses, in particular M_{π_0} = 343,440,664MeV.
We obtained that the pseudocritical temperature T c corresponding to the crossover of deconfinement and chiral restoration decreases with B in the explored pion mass range.
In addition, we found that the inverse magnetic catalysis phenomenon in the up+down chiral condensate is no more present for sufficiently heavy quarks, i.e. for a pion mass that exceed a threshold located in between 440−664MeV. In contrast with the conjecture made in, the results obtained in the present study support the idea that the decreasing behaviour of the pseudocritical temperature on the field strength B is a consequence of the effect of the magnetic background on the confining properties of QCD, in accordance with the point of view proposed in of deconfinement catalysis.
The pseudocritical temperature as a function of the background magnetic field strength can be parametrized as T C (B) = T_C(0)(1 − υ_B(|e|B)^2+ O(B^4)) where T_C(0) is the pseudocritical temperature at B = 0 and υ_B is the curvature coefficient.
In the present study we have analysed the dependence of υ B on the pion mass. The results indicates that υ B goes to zero asymptotically as M^α_{π_0} with α ∼ −0.7, even if α = −1 is not excluded.
Further development of this work may include the measurements of some key observables, such as the chiral condensate and susceptibility and the Polyakov loop, on lattices with finer lattice spacing. In order to do so, it is necessary to perform the same simulations carried out in the present work on lattices with a larger temporal extension (N t = 8,10). In fact, this would allow us to continuum extrapolate the observables of interest and check whether the results obtained in the present work are recovered in the limit in which the lattice spacing goes to zero.