A critical endpoint in QCD is a kind of holy grail in nuclear physics. It has been theorized as a point where deconfinement occurs and hadronic matter leaves place to some kind of plasma of quarks and gluons. We know that the breaking of chiral symmetry is something that people has proposed several years ago and we recently gave a proof of existence of such a transition (see here). But here the situation is more complex: We have essentially two physical variables to describe the phase diagram and these are temperature and chemical potential. This makes lattice computations a kind of nightmare. The reason is the sign problem. Some years ago Zoltan Fodor and Sandor Katz come out with a pioneering paper (see here) doing lattice computation and seeing the chemical potential taking an imaginary factor: The infamous sign problem. Discretization implies it but a theoretical physicist can happily lives just ignoring it. Fodor and Katz evaded the problem just taking an absolute value but this approach was criticized casting doubt on their results at chemical potential different from zero. It should be said that they gave evidence of existence for the critical point and surely their results are unquestionably correct with zero chemical potential in close agreement with my and others findings. A lucid statement of the problems of lattice computations for finite temperatures and densities was recently given by Philippe de Forcrand (see here).

So far, people has produced several results just working around with phenomenological model like a Nambu-Jona-Lasinio or sigma model. This way of work arises from our current impossibility to manage QCD at very low energies but, on the other side, we are well aware that these models seem to represent reality quite well. The reason is that a Nambu-Jona-Lasinio is really the low-energy limit for QCD but I will not discuss this matter here having done this before (see here). Besides, the sigma model arises naturally in the low-energy limit interacting with quarks. The sigma field is a true physical field that drives the phase transitions in low-energy QCD.

While the hunt for the critical point in the lattice realm is already open since the paper by Fodor and Katz, the experimental side is somewhat more difficult to exploit. The only facility we have at our disposal is RHIC and no much proposals are known to identify the critical point from the experimental data were available since a fine proposal by Misha Stephanov a few years ago (see here and here). The idea runs as follows. At the critical point, fluctuations are no more expected to be Gaussian and all the correlations are extended to all the hadronic matter as the correlation length is diverging. Non-Gaussianity implies that if we compute cumulants, linked to higher order moments of the probability distribution, these will depend on the correlation length with some power and, particularly, moments like skewness and kurtosis, that are a measure of deviation from Gaussianity, start to change. Particularly, kurtosis is expected to change sign. So, if we are able to measure such a deviation in a laboratory facility we are done and we get evidence for a critical point and critical behavior of hadronic matter. We just note that Stephanov accomplishes his computations using a sigma model and this is a really brilliant hindsight.

At RHIC a first evidence of this has been obtained by STAR Collaboration (see here). These are preliminary results but further data are expected this year. The main result is given in the following figureWe see comparison with data from lattice as red balls for Au+Au collisions and the kurtosis goes down to negative values! The agreement with lattice data is striking and this is already evidence for a critical endpoint. But this is not enough as can be seen from the large error bar. Indeed further data are needed to draw a definitive conclusion and, as said, these are expected for this year. Anyhow, this is already a shocking result. Surely, we stay tuned for this mounting evidence of a critical endpoint. This will represent a major discovery for nuclear physics and, in some way, it will make easier lattice computations with a proper understanding of the way the sign problem should be settled.

Marco Frasca (2011). Chiral symmetry in the low-energy limit of QCD at finite temperature arXiv arXiv: 1105.5274v2

Z. Fodor, & S. D. Katz (2001). Lattice determination of the critical point of QCD at finite T and \mu JHEP 0203 (2002) 014 arXiv: hep-lat/0106002v2

Philippe de Forcrand (2010). Simulating QCD at finite density PoS (LAT2009)010, 2009 arXiv: 1005.0539v2

M. A. Stephanov (2008). Non-Gaussian fluctuations near the QCD critical point Phys.Rev.Lett.102:032301,2009 arXiv: 0809.3450v1

Christiana Athanasiou, Krishna Rajagopal, & Misha Stephanov (2010). Using Higher Moments of Fluctuations and their Ratios in the Search for

the QCD Critical Point Physical review D arXiv: 1006.4636v2

Xiaofeng Luo (2011). Probing the QCD Critical Point with Higher Moments of Net-proton

Multiplicity Distributions arXiv arXiv: 1106.2926v1