QCD matter

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 theoretical 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 familiarstructure of matter, with quarks arranged into nucleons andnucleons bound into nuclei and surrounded by electrons, iscompletely disrupted, and the quarks roam freely in what is called a quark gluon plasma.This is analogous to the way that the crystalstructure of ice is disrupted by heating or compression, and meltsinto a liquid of more elementary constituents (water molecules).

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

unsolved|physics|QCD in the non-perturbative regime:quark matter. The equations of QCD predict that a sea of quarks and gluons should be formed at high temperature and density. What are the properties of this phase of matter?

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.
* Cosmic Ray Impacts. High speed protons (now believed to have originated from "nearby" active galactic nuclei based on recent results of the Pierre Auger cosmic ray observatory) routinely impact earth with center of momentum energies much greater than today's Particle colliders

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 LHC at CERN in Switzerland/France. There is good evidence that the quark-gluon plasma has been produced at RHIC [B. Müller "Quark Matter 2005 -- Theoretical Summary", [http://www.arxiv.org/abs/nucl-th/0508062 arxiv.org:nucl-th/0508062] ] .

Thermodynamics

The context for understanding the thermodynamics of quark matter isthe standard model of particle physics, which contains six different
flavors of quarks, as well as
leptons like electrons and neutrinos. Theseinteract via the strong interaction, electromagnetism, andalso the weak interaction which allows one flavor of quark to turninto another. Electromagnetic interactions occur between particlesthat carry electrical charge; strong interactions occur betweenparticles that carry color charge.

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

In compact stars quark matter would occupy cubic kilometers andexist for millions of years, so the thermodynamic limit isappropriate. However, the neutrinos escape, violating lepton number, so the phase space forquark matter in compact stars only has twodimensions, 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 carryelectric charge.A heavy-ion collision is in neither the thermodynamic limit of large volumes nor long times. Putting aside questions of whetherit is sufficiently equilibrated for thermodynamics to be applicable,there is certainly not enough time for weak interactions to occur, so flavoris conserved, and there are independent chemical potentials for all sixquark flavors. The initial conditions (the impact parameter of the collision, the number of up and down quarksin the colliding nuclei, and the fact that they contain no quarks ofother flavors) determine the chemical potentials.

Phase diagram


frame|right|Conjectured form of the phasediagram of QCD matter|Conjectured form of the phasediagram of QCD matterThe phase diagram of quark matter is not well known, eitherexperimentally or theoretically. A commonly conjectured form of thephase diagram is shown in the figure [M. Alford, K. Rajagopal, T. Schäfer, A. Schmitt, "Color superconductivity in dense quark matter", [http://arxiv.org/abs/0709.4635 arXiv:0709.463] , Reviews of Modern Physics (to be published)] . It is applicableto matter in a compact star, where the only relevant thermodynamic potentialsare quark chemical potential μ and temperature T. For guidanceit 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 ofμ as a measure of the imbalance between quarks and antiquarks inthe system. Higher μ means higher density of quarks.

Ordinary atomic matter as we know it is really a mixed phase, dropletsof nuclear matter (nuclei) surrounded by vacuum, which exists at thelow-temperature phase boundary between vacuum and nuclear matter, atμ=310MeV and T close to zero. If we increase the quark density(i.e. increase μ) keeping the temperature low, we move into a phaseof more and more compressed nuclear matter. Following this pathcorresponds 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 findthe color-flavor-locked (CFL) phase of
color-superconducting quark matter. Atintermediate densities we expect some other phases (labelled "non-CFL quark liquid" in the figure) whose nature ispresently unknown. They might be other forms of color-superconductingquark 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 withoutintroducing any preference for quarks over antiquarks, this corresponds to moving vertically upwardsalong the T axis. At first, quarks are still confined and we create a gas of hadrons (pions, mostly). Thenaround 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 asphotons, electrons, positrons, etc. Following this path corresponds to travelling far back in time, to the state of the universe shortlyafter the big bang (where there was a very tiny preference forquarks over antiquarks).

The line that rises up from the nuclear/quark matter transition andthen bends back towards the T axis, with its end marked by a star,is the conjectured boundary betweenconfined and unconfined phases. Until recently it was alsobelieved to be a boundary between phases where chiral symmetry isbroken (low temperature and density) and phases where it is unbroken(high temperature and density). It is now known that the CFL phaseexhibits chiral symmetry breaking, and other quark matter phasesmay also break chiral symmetry, so it is not clear whether this is really a chiral transitionline. The line ends at the "chiral critical point", marked bya star in this figure, which is a specialtemperature 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 becauseit is difficult to perform calculations predicting the properties ofquark matter.The reason is that QCD, the theory describing the dominant interaction between quarks, is strongly coupled at the densities andtemperatures of greatest physical interest, and hence it is veryhard to obtain any predictions from it. Here are brief descriptionsof 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 (μU. Heller, "Recent progress in finite temperature lattice QCD", [http://www.arxiv.org/abs/hep-ph/0610299 PoS (LAT2006) 011] ] However, it cannot be used to investigate the interesting color-superconducting phase structure at high density and low temperature [C. Schmidt, "Lattice QCD at Finite Density", [http://www.arxiv.org/abs/hep-lat/0610116 PoS (LAT2006) 021] ] .

Weak coupling theory

Because QCD is asymptotically free it becomesweakly coupled at unrealistically high densities, and diagrammaticmethods can be used [ D. Rischke, "The quark-gluon plasma in equilibrium", [http://www.arxiv.org/abs/nucl-th/0305030 Prog. Part. Nucl. Phys. 52, 197 (2004)] ] . 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 easierto manipulate. Many physicists use Nambu-Jona-Lasinio models,which contain no gluons, and replace the strong interaction witha four-fermion interaction. Mean-field methods are commonly usedto analyse the phases. Another approach is the bag model, in which the effects of confinement are simulated by an additive energy densitythat penalizes unconfined quark matter.

Effective theories

Many physicists simply give up on a microscopic approach, andmake informed guesses of the expected phases (perhaps based on NJLmodel results). For each phase, they then write down an effectivetheory for the low-energy excitations, in terms of a small number ofparameters, and use it to make predictions that could allow thoseparameters to be fixed by experimental observations [T. Schäfer, "Quark matter", [http://www.arXiv.org/abs/hep-ph/0304281 arxiv.org:hep-ph/0304281] ] .

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 usefulin 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 matterbecause it is impossible to achieve high enough temperaturesand densities in the laboratory. Heavy-ion collisions provideinformation about the crossover from hadronic matter to QGP.Observations of compact stars may provide information about thehigh-density low-temperature region. Studies of the cooling,spin-down, and precession of these stars have already giveninformation about the properties of their interior. Asobservations 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 tomeasure its position experimentally, but this will requirescanning across a range of values of μ and T [K. Rajagopal, "Mapping the QCD Phase Diagram", [http://www.arxiv.org/abs/hep-ph/9908360 Nucl.Phys. A661 (1999) 150-161] ] , a project that may be undertaken in future experiments.

ee also

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

Further reading

* S. Hands, "The phase diagram of QCD" [http://www.arXiv.org/abs/physics/0105022 arXiv:physics/0105022] Contemp. Phys. 42, 209 (2001).

References


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