Conﬁnement and chiral symmetry breaking are two of the most important features of quantum chromodynamics (QCD). The basic constituents of QCD are quarks and gluons that are conﬁned in hadronic matter – this means they only exist in clusters, the simplest ones being the mesons (a quark-antiquark) and the baryons (3 quarks). At high temperatures and/or densities quark deconﬁnement occurs and hadronic matter undergoes a phase transition into a new state of matter, the quark-gluon plasma (QGP). Also as the temperature and/or density increase chiral symmetry should be restored: since the QCD vacuum can be seen as a medium full of quantum ﬂuctuations which are responsible for the generation of non-perturbative quark mass, as the temperatures and/or densities increase the quarks turn bare due to asymptotic freedom, and their mass is approximately zero.
High temperatures conditions in the early universe, just after the big bang, while high matter density conditions can be found in very compact stars.
The QGP state of matter was also created and is still presently studied in current heavy ion collision experiments at the Large Hadron Collider (LHC) at CERN and at the Relativistic Heavy Ion Collider (RHIC) at the Bookhaven National Laboratory.
The very first “QCD” phase diagram was proposed by N. Cabibbo and G. Parisi in 1975 . It shows in a diagram baryonic density-temperature the phases of quark matter: they have conjectured that there is a phase where quarks are confined and another phase where they are unconfined.
Presently, even if the QCD phase diagram of quark matter is not well known, either experimentally or theoretically, based on available theoretical (lattice and model calculations) and phenomenological inputs, the overview of the structure of the QCD phase diagram can be drawn and it proves to be quite complex. In the following diagram some of the possible phases in which quarks occur are indicated. But many more have been proposed.
There are several important questions which have no definitive answer. One of these questions is whether the QCD phase diagram has first order phase transitions (as in boiling water) or the matter forms are smoothly connected in what is called a smooth crossover.
Concerning the chiral phase transition the possible existence of a first order phase transition implies that the transition line will end at a point known as the QCD critical point or critical end point (CEP): the CEP of a first order line is a critical point where the phase transition is of second order.
Water, like most liquids, possesses a critical point. The water boiling transition line ends at temperature T=374ºC and pressure p=218 atm. Along this line the two coexisting phases, water phase and vapor phase, become less and less distinct as the end point is approaching (the density of water decreases and of vapor increases) and the result becomes a single phase at the CEP and beyond.
The chiral CEP for QCD was proposed at the end of the eighties  and its possible existence, with all the implications to the investigation of the QCD phase diagram, is a very timely topic that has drawn the attention of the physics community: by using lattice QCD simulations, Dyson-Schwinger equations and eﬀective models namely the Nambu–Jona-Lasinio type models, there has been an eﬀort to understand the nature of the phase transition and the existence of the CEP (for a review see ).
From the experimental point of view, the location of the CEP is a major goal of several heavy ion collisions programs. At RHIC, the Beam Energy Scan (BES-I) program, ongoing since 2010, is looking for the experimental signatures of the first-order phase transition and the CEP by colliding Au ions at several energies. Also STAR Collaboration presented their measurements on observables relevant to clarify the existence of the CEP. However, so far no definitive conclusions were possible.
With the upcoming BES-II program, it is expected that, if the CEP exists at low baryonic chemical potential quantitative evidence for the presence of the CEP should be obtained.
At CERN SPS the NA49 program has also investigated the CEP’s location in nuclear collisions at 158A GeV without success. Now, the NA61/SHINE program is devoted to the search for the CEP and to investigate the properties of the onset of deconfinement in light and heavy ion collisions.
In the next years, the Facility for Antiproton and Ion Research (FAIR) at GSI and the Nuclotron-based Ion Collider Facility at JINR (NICA) will extend the search of the CEP to even higher densities and definitive conclusions concerning its existence and location are expected (for a review on the experimental search of the CEP see ).
The location of the CEP can be affected by several conditions like the presence of an external magnetic field which has noticeable eﬀects on the QCD phase diagram. Lattice QCD results, together with model calculations, show that the intensity of the magnetic field can drive the CEP to lower densities and, eventually, the crossover at zero density between the two phases becomes a ﬁrst-order chiral phase transition.
The eventual conﬁrmation of the CEP would be one of the ﬁrst discoveries of QCD-like observables in the medium. The implications of its location are vast, in particular concerning the constraints on eﬀective models.
 N. Cabibbo and G. Parisi, Phys. Lett. B59 (1975) 67-69.
 M. Asakawa, K. Yazaki, Nucl. Phys. A504 (1989) 668–684.
 K. Fukushima, T. Hatsuda, Rept. Prog. Phys. 74 (2011) 014001.
 Y. Akiba et al., arXiv:1502.02730 [nucl-ex].
Author: Pedro Costa