QCD matter

Quark matter or QCD matter (see QCD) refers to any of a number of theorized phases of matter whose degrees of freedom include quarks and gluons. These theoretic phases would occur at extremely high temperatures and densities, billions of times higher than can be produced in equilibrium in laboratories. Under such extreme conditions, the familiar structure of matter, with quarks arranged into nucleons and nucleons bound into nuclei and surrounded by electrons, is completely disrupted, and the quarks roam freely. This is analogous to the way that the crystal structure of ice is disrupted by heating or compression, and melts into a liquid of more elementary constituents (water molecules).

In the standard model of particle physics, the strongest force is the strong interaction, which is described by the theory of quantum chromodynamics (QCD). At ordinary temperatures or densities this force just confines the quarks into composite particles (hadrons) of size around 10⁻¹⁵m = 1 femtometer = 1 fm (corresponding to the QCD energy scale Λ_QCD≈200 MeV) and its effects are not noticeable at longer distances. However, when the temperature reaches the QCD energy scale (T of order 10¹²K) or the density rises to the point where the average inter-quark separation is less than 1 fm (quark chemical potential μ around 400 MeV), the hadrons are melted into their constituent quarks, and the strong interaction becomes the dominant feature of the physics. Such phases are called quark matter or QCD matter.

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Occurrence

Natural occurrence

• The early universe. According to the theory of the big bang, at very early times, when the universe was only a few tens of microseconds old, the temperature was so high that all matter took the form of a hot phase of quark matter called the quark-gluon plasma (QGP).
• Compact stars (neutron stars). A neutron star is much cooler than 10¹² K, but it is compressed by its own weight to such high densities that it is reasonable to surmise that quark matter may exist in the interior. Compact stars composed mostly or entirely of quark matter are known as quark stars or strange stars. The nuclear matter component of strange stars, if there is one, is believed to consist only of a tiny surface crust.
• Strangelets. These are hypothetical lumps of strange matter that might populate interstellar space. They only exist if nuclear matter is metastable against decay into quark matter: this is generally regarded as a fairly radical hypothesis.

Artificial occurrence

• Heavy-ion collisions. Physicists can produce small short-lived regions of space whose energy density is comparable to that of the 20-microsecond-old universe. This is achieved by colliding heavy nuclei at high speeds. Extremely powerful accelerators are needed, such as RHIC at Brookhaven National Laboratory in the USA, or the future LHC at CERN in Switzerland/France. There is good evidence that the quark-gluon plasma has been produced at RHIC ^[1].

Thermodynamics

The context for understanding the thermodynamics of quark matter is the standard model of particle physics, which contains six different flavors of quarks, as well as leptons like electrons and neutrinos. These interact via the strong interaction, electromagnetism, and also the weak interaction which allows one flavor of quark to turn into another. Electromagnetic interactions occur between particles that carry electrical charge; strong interactions occur between particles that carry color charge.

The correct thermodynamic treatment of quark matter depends on the physical context. For large quantities that exist for long periods of time (the "thermodynamic limit"), we must take into account the fact that the only conserved charges in the standard model are quark number (equivalent to baryon number), electric charge, the eight color charges, and lepton number. Each of these can have an associated chemical potential. However, large volumes of matter must be electrically and color-neutral, which determines the electric and color charge chemical potentials. This leaves a three-dimensional phase space, parameterized by quark chemical potential, lepton chemical potential, and temperature.

In compact stars quark matter would occupy cubic kilometers and exist for millions of years, so the thermodynamic limit is appropriate. However, the neutrinos escape, violating lepton number, so the phase space for quark matter in compact stars only has two dimensions, temperature (T) and quark number chemical potential μ (see next section). A strangelet is not in the thermodynamic limit of large volume, so it is like an exotic nucleus: it may carry electric charge. A heavy-ion collision is in neither the thermodynamic limit of large volumes nor long times. Putting aside questions of whether it is sufficiently equilibrated for thermodynamics to be applicable, there is certainly not enough time for weak interactions to occur, so flavor is conserved, and there are independent chemical potentials for all six quark flavors. The initial conditions (the impact parameter of the collision, the number of up and down quarks in the colliding nuclei, and the fact that they contain no quarks of other flavors) determine the chemical potentials.

Phase diagram

  The phase diagram of quark matter is not well known, either experimentally or theoretically. A commonly conjectured form of the phase diagram is shown in the figure. It is applicable to matter in a compact star, where the only relevant thermodynamic potentials are quark chemical potential μ and temperature T. For guidance it also shows the typical values of μ and T in heavy-ion collisions and in the early universe. For readers who are not familiar with the concept of a chemical potential, it is helpful to think of μ as a measure of the imbalance between quarks and antiquarks in the system. Higher μ means higher density of quarks.

Ordinary atomic matter as we know it is really a mixed phase, droplets of nuclear matter (nuclei) surrounded by vacuum, which exists at the low-temperature phase boundary between vacuum and nuclear matter, at μ=310MeV and T close to zero. If we increase the quark density (i.e. increase μ) keeping the temperature low, we move into a phase of more and more compressed nuclear matter. Following this path corresponds to burrowing more and more deeply into a neutron star. Eventually, at an unknown critical value of μ, there is a transition to quark matter. At ultra-high densities we expect to find the color-flavor-locked (CFL) phase of color-superconducting quark matter. At intermediate densities we expect some other phases (labelled "non-CFL quark liquid" in the figure) whose nature is presently unknown. They might be other forms of color-superconducting quark matter, or something different.

Now, imagine starting at the bottom left corner of the phase diagram, in the vacuum where μ=T=0. If we heat up the system without introducing any preference for quarks over antiquarks, this corresponds to moving vertically upwards along the T axis. At first, quarks are still confined and we create a gas of hadrons (pions, mostly). Then around T=170 MeV there is a crossover to the quark gluon plasma: thermal fluctuations break up the pions, and we find a gas of quarks, antiquarks, and gluons, as well as lighter particles such as photons, electrons, positrons, etc. Following this path corresponds to travelling far back in time, to the state of the universe shortly after the big bang (where there was a very tiny preference for quarks over antiquarks).

The line that rises up from the nuclear/quark matter transition and then bends back towards the T axis, with its end marked by a star, is the conjectured boundary between confined and unconfined phases. Until recently it was also believed to be a boundary between phases where chiral symmetry is broken (low temperature and density) and phases where it is unbroken (high temperature and density). It is now known that the CFL phase exhibits chiral symmetry breaking, and other quark matter phases may also break chiral symmetry, so it is not clear whether this is really a chiral transition line. The line ends at the "chiral critical point", marked by a star in this figure, which is a special temperature and density at which striking physical phenomena (analogous to critical opalescence) are expected (see "open questions" below).

Theoretical challenges: calculation techniques

The phase structure of quark matter remains mostly conjectural because it is difficult to perform calculations predicting the properties of quark matter. The reason is that QCD, the theory describing the dominant interaction between quarks, is strongly coupled at the densities and temperatures of greatest physical interest, and hence it is very hard to obtain any predictions from it. Here are brief descriptions of some of the standard approaches.

Lattice gauge theory

The only first-principles calculational tool currently available is lattice QCD, i.e. brute-force computer calculations. Because of a technical obstacle known as the fermion sign problem, this method can only be used at low density and high temperature (μ[2] However, it cannot be used to investigate the interesting color-superconducting phase structure at high density and low temperature ^[3].

Weak coupling theory

Because QCD is asymptotically free it becomes weakly coupled at unrealistically high densities, and diagrammatic methods can be used ^[4]. Such methods show that the CFL phase occurs at very high density. At high temperatures, however, diagrammatic methods are still not under full control.

Models

To obtain a rough idea of what phases might occur, one can use a model that has some of the same properties as QCD, but is easier to manipulate. Many physicists use Nambu-Jona-Lasinio models, which contain no gluons, and replace the strong interaction with a four-fermion interaction. Mean-field methods are commonly used to analyse the phases. Another approach is the bag model, in which the effects of confinement are simulated by an additive energy density that penalizes unconfined quark matter.

Effective theories

Many physicists simply give up on a microscopic approach, and make informed guesses of the expected phases (perhaps based on NJL model results). For each phase, they then write down an effective theory for the low-energy excitations, in terms of a small number of parameters, and use it to make predictions that could allow those parameters to be fixed by experimental observations ^[5].

Other approaches

There are other methods that are sometimes used to shed light on QCD, but for various reasons turn out not to be particularly useful in studying quark matter.

• 1/N expansion. Treat the number of colors N, which is actually 3, as a large number, and expand in powers of 1/N. It turns out that at high density the higher-order corrections are large, and the expansion gives misleading results.

• Supersymmetry. Adding scalar quarks (squarks) and fermionic gluons (gluinos) to the theory makes it more tractable, but the thermodynamics of quark matter depends crucially on the fact that only fermions can carry quark number, and on the number of degrees of freedom in general.

Experimental challenges

Experimentally, it is hard to map the phase diagram of quark matter because it is impossible to achieve high enough temperatures and densities in the laboratory. Heavy-ion collisions provide information about the crossover from hadronic matter to QGP. Observations of compact stars may provide information about the high-density low-temperature region. Studies of the cooling, spin-down, and precession of these stars have already given information about the properties of their interior. As observations become more precise we hope to learn more.

One of the natural subjects for future research is the exact location of the chiral critical point. Some ambitious lattice QCD calculations may have found evidence for it, and future calculations will clarify the situation. Heavy-ion collisions might be able to measure its position experimentally, but this will require scanning across a range of values of μ and T ^[6], a project that may be undertaken in future experiments.

See also

• Quantum chromodynamics
• Quark-gluon plasma
• Lattice QCD
• 1/N expansion
• Strange matter
• quark star

Further reading

• S. Hands, "The phase diagram of QCD" Contemp. Phys. 42, 209 (2001)

References

1. ^ B. Müller "Quark Matter 2005 -- Theoretical Summary", arxiv.org:nucl-th/0508062
2. ^ U. Heller, "Recent progress in finite temperature lattice QCD", PoS (LAT2006) 011
3. ^ C. Schmidt, "Lattice QCD at Finite Density", PoS (LAT2006) 021
4. ^ D. Rischke, "The quark-gluon plasma in equilibrium", Prog. Part. Nucl. Phys. 52, 197 (2004)
5. ^ T. Schäfer, "Quark matter", arxiv.org:hep-ph/0304281
6. ^ K. Rajagopal, "Mapping the QCD Phase Diagram", Nucl.Phys. A661 (1999) 150-161