Which equations of QCD are the QGP (Quark Gluon Plasma) and QCD phase diagram coming from?

Question

Which equations of QCD are the QGP (Quark Gluon Plasma) and QCD phase diagram coming from ?

Are there derivation formulas ?

Answer 1

The existence of quark-gluon plasma has been predicted in some form since the 1970s. About a decade beforehand, there were two predominant classes of theories that attempted to explain the characteristics of the spectrum of hadrons. "Bootstrap" theories did not assume the existence of any elementary particles and did not rely on field theory, and attempted to explain the hadron spectrum just by assuming some very general things about the strong interaction S-matrix, while field theories relied on the existence of at-the-time-undiscovered elementary constituents of hadrons. Rolf Hagedorn, while working on statistical bootstrap theory, found in 1967 that by examining the hadron spectrum, one finds a "limiting temperature" of around 160 to 170 MeV, an energy density at which hadrons are no longer stable (aptly named the Hagedorn temperature; see https://cerncourier.com/a/the-tale-of-the-hagedorn-temperature/ for further information).

After quarks were discovered, bootstrap theory fell out of favor and QCD became the predominant explanation for the strong interaction. Two other theorists, Cabibbo and Parisi, offered a re-interpretation of the Hagedorn temperature in 1975: it wasn't just a limiting temperature for a hadron gas, it was actually a phase transition between a hadron gas and some kind of as-yet-undiscovered quark matter (see http://inspirehep.net/record/99714?ln=en). So the idea of the existence of QGP came, in a way, from reinterpreting a result from statistical bootstrap theory.

The "equations of QCD that QGP comes from" aren't really known. Most of the things we know about QCD are in the perturbative regime, where the strong interaction is weak enough and particles are diffuse enough that we can use our usual mathematical tools from quantum field theory to obtain meaningful results. However, for low energies or high densities, the strong interaction fails to be perturbative, and so our normal tools don't actually work. Any quark confined inside a hadron or QGP is subject to non-perturbative QCD.

Since there aren't really very many analytical ab initio results regarding non-perturbative QCD, most of the things that we know about it come from one of two sources:

• matching up experimental data with phenomenological models that don't claim to be fundamental, or
• simulating QCD on a lattice.

Depending on what in particular you're looking to understand about QGP, the source of our understanding is different (for example, lattice QCD is attempting to locate the hadron gas-QGP phase transition, among other things, while phenomenological models are used to explain, for example, hadron production in QGP and how jets interact with the medium through which they propagate). Different phenomenological models/lattice techniques are used for different properties, and so the "equations" largely depend on what you want to know - and who you ask.

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As for the "equations" of the QCD phase diagram: we don't have them. We don't currently know where most of the phase boundary is, and we don't even have the right kind of data yet to look for it (it turns out that creating matter at extremely high temperature and high density is expensive and quite tricky). Here is some of what we do know:

• Lattice QCD results work well at zero net baryon density (i.e. equal amounts of matter and antimatter). They tell us that there is an analytical crossover on the y-axis of the phase diagram; in other words, there isn't a phase transition below some critical density. This means that the phase diagram has a critical point somewhere. We don't know precisely where it is, though various models agree on its general location.
• Experiments like Brookhaven National Lab's Beam Energy Scan II (BES II) at the Relativistic Heavy Ion Collider (RHIC) and the Compressed Baryon Matter (CBM) experiment at the Facility for Antiproton and Ion Research (FAIR) will hopefully collect data that will help to locate the critical point by colliding ions at a range of energies (creating a range of temperatures and densities).
• Lattice QCD can also tell us the derivatives of the crossover at zero density. The higher the statistics, the higher the derivatives which are accessible and the more we can constrain the behavior of the phase diagram from the left side.
• Working in the infinite-density limit, a phase transition to some kind of matter with color superconducting properties is predicted. Since the density required is around the density found in the core of neutron stars, there is no terrestrial experimental data for behavior in this regime. Data from nuclear astrophysics (especially regarding the behavior of neutron stars) may eventually support this prediction. Once again, we don't know where the phase transition is.