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QCD matter
QCD matter
QCD matter
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Quark matter or QCD matter (quantum chromodynamic) refers to any of a number of hypothetical phases of matter whose degrees of freedom include quarks and gluons, of which the prominent example is quark-gluon plasma.[1] Several series of conferences in 2019, 2020, and 2021 were devoted to this topic.[2][3][4]

Quarks are liberated into quark matter at extremely high temperatures and/or densities, and some of them are still only theoretical as they require conditions so extreme that they cannot be produced in any laboratory, especially not at equilibrium conditions. Under these extreme conditions, the familiar structure of matter, where the basic constituents are nuclei (consisting of nucleons which are bound states of quarks) and electrons, is disrupted. In quark matter it is more appropriate to treat the quarks themselves as the basic degrees of freedom.

In the Standard Model of particle physics, the strong force is described by the theory of QCD. At ordinary temperatures or densities this force just confines the quarks into composite particles (hadrons) of size around 10−15 m = 1 femtometer = 1 fm (corresponding to the QCD energy scale ΛQCD ≈ 200 MeV) and its effects are not noticeable at longer distances.

However, when the temperature reaches the QCD energy scale (T of order 1012 kelvins) 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.

The strength of the color force makes the properties of quark matter unlike gas or plasma, instead leading to a state of matter more reminiscent of a liquid. At high densities, quark matter is a Fermi liquid, but is predicted to exhibit color superconductivity at high densities and temperatures below 1012 K.

Unsolved problem in 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?
More unsolved problems in physics

Occurrence

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Natural occurrence

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  • According to the Big Bang theory, in the early universe at high temperatures when the universe was only a few tens of microseconds old, the phase of matter took the form of a hot phase of quark matter called the quark–gluon plasma (QGP).[5]
  • Compact stars (neutron stars). A neutron star is much cooler than 1012 K, but gravitational collapse has compressed it to such high densities, that it is reasonable to surmise that quark matter may exist in the core.[6] Compact stars composed mostly or entirely of quark matter are called quark stars or strange stars.
  • QCD matter may exist within the collapsar of a gamma-ray burst, where temperatures as high as 6.7 × 1013 K may be generated.

At this time no star with properties expected of these objects has been observed, although some evidence has been provided for quark matter in the cores of large neutron stars.[7]

  • Strangelets. These are theoretically postulated (but as yet unobserved) lumps of strange matter comprising nearly equal amounts of up, down and strange quarks. Strangelets are supposed to be present in the galactic flux of high energy particles and should therefore theoretically be detectable in cosmic rays here on Earth, but no strangelet has been detected with certainty.[8][9]
  • Cosmic ray impacts. Cosmic rays comprise a lot of different particles, including highly accelerated atomic nuclei, particularly that of iron.

Laboratory experiments suggests that the inevitable interaction with heavy noble gas nuclei in the upper atmosphere would lead to quark–gluon plasma formation.

Laboratory experiments

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Particle debris trajectories from one of the first lead-ion collisions with the LHC, as recorded by the ALICE detector. The extremely brief appearance of quark matter in the point of collision is inferred from the statistics of the trajectories.

Even though quark-gluon plasma can only occur under quite extreme conditions of temperature and/or pressure, it is being actively studied at particle colliders, such as the Large Hadron Collider LHC at CERN and the Relativistic Heavy Ion Collider RHIC at Brookhaven National Laboratory.

In these collisions, the plasma only occurs for a very short time before it spontaneously disintegrates. The plasma's physical characteristics are studied by detecting the debris emanating from the collision region with large particle detectors [11][12]

Heavy-ion collisions at very high energies can produce small short-lived regions of space whose energy density is comparable to that of the 20-micro-second-old universe. This has been achieved by colliding heavy nuclei such as lead nuclei at high speeds, and a first time claim of formation of quark–gluon plasma came from the SPS accelerator at CERN in February 2000.[13]

This work has been continued at more powerful accelerators, such as RHIC in the US, and as of 2010 at the European LHC at CERN located in the border area of Switzerland and France. There is good evidence that the quark–gluon plasma has also been produced at RHIC.[14]

Thermodynamics

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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. 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. (Reference for this section:[15][16]).

Phase diagram

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For application to cosmology, see Cosmological phase transition.
Conjectured form of the phase diagram of QCD matter, with temperature on the vertical axis and quark chemical potential on the horizontal axis, both in mega-electron volts.[15]

Based on rigorous theoretical calculations valid at ultrahigh density and a few experimental ultrarelativistic heavy ion collision experiments, an outline of the phase diagram of quark matter has been worked out as shown in the figure to the right. It is relevant for the understanding the core of neutron stars, where the only relevant thermodynamic potentials are quark chemical potential μ and temperature T.[15]

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 a stronger bias favoring quarks over antiquarks. At low temperatures there are no antiquarks, and then higher μ generally means a 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 = 310 MeV 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.[15][16] 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 = 150 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 (so to say), 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. (Reference for this section:[15][16][17]).

For a complete description of phase diagram it is required that one must have complete understanding of dense, strongly interacting hadronic matter and strongly interacting quark matter from some underlying theory e.g. quantum chromodynamics (QCD). However, because such a description requires the proper understanding of QCD in its non-perturbative regime, which is still far from being completely understood, any theoretical advance remains very challenging.

Theoretical challenges: calculation techniques

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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

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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 < T), and it predicts that the crossover to the quark–gluon plasma will occur around T = 150 MeV [18] However, it cannot be used to investigate the interesting color-superconducting phase structure at high density and low temperature.[19]

Weak coupling theory

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Because QCD is asymptotically free it becomes weakly coupled at unrealistically high densities, and diagrammatic methods can be used.[16] 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

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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

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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.[17]

Other approaches

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Main article: AdS/QCD

There are other methods that are sometimes used to shed light on QCD, but for various reasons have not yet yielded useful results in studying quark matter.

1/N expansion

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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.[15]

Supersymmetry

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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

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Experimentally, it is hard to map the phase diagram of quark matter because it has been rather difficult to learn how to tune to high enough temperatures and density in the laboratory experiment using collisions of relativistic heavy ions as experimental tools. However, these collisions ultimately will provide information about the crossover from hadronic matter to QGP. It has been suggested that the observations of compact stars may also constrain the information about the high-density low-temperature region. Models of the cooling, spin-down, and precession of these stars offer information about the relevant properties of their interior. As observations become more precise, physicists hope to learn more.[15]

One of the natural subjects for future research is the search for 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.[20]

Evidence

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In 2020, evidence was provided that the cores of neutron stars with mass ~2M⊙ were likely composed of quark matter.[7][21] Their result was based on neutron-star tidal deformability during a neutron star merger as measured by gravitational-wave observatories, leading to an estimate of star radius, combined with calculations of the equation of state relating the pressure and energy density of the star's core. The evidence was strongly suggestive but did not conclusively prove the existence of quark matter.

See also

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Sources and further reading

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

QCD matter

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QCD matter, also known as matter, encompasses the various phases of strongly interacting matter where quarks and gluons serve as the fundamental , governed by the of (QCD). This includes the quark-gluon plasma (QGP), a deconfined state of quarks and gluons that emerges at extreme conditions of high (above approximately 150–160 MeV) or high density, contrasting with the confined hadronic phase at lower temperatures and densities where quarks are bound into hadrons like protons and neutrons. In the early , shortly after the , QCD matter existed as a hot QGP before cooling and expanding led to , the process by which quarks and gluons recombine into hadrons. Today, this state is recreated in laboratories through relativistic heavy-ion collisions at facilities such as the Relativistic Heavy-Ion Collider (RHIC) at and the (LHC) at , where colliding heavy nuclei like or lead generate initial energy densities of 12–20 GeV/fm³, producing a transient QGP fireball that expands hydrodynamically before freezing out into observable hadrons. Key properties of QCD matter include deconfinement, where the strong force no longer confines quarks within hadrons, and chiral symmetry restoration, marking the transition from massive to effectively massless quarks at the critical temperature TcT_c. At high densities, such as those in neutron star cores, QCD matter may exhibit exotic phases like color superconductivity, where quarks pair up analogously to superconductivity in condensed matter. Theoretical studies employ lattice QCD simulations for zero baryon density, effective models for finite density, and holographic duality for strongly coupled regimes, while experimental probes include jet quenching, elliptic flow, and particle multiplicity fluctuations to map the QCD phase diagram and search for a critical endpoint.

Fundamentals of QCD

Quarks, Gluons, and Strong Interaction

Quarks are the fundamental fermions that serve as the building blocks of hadronic in (QCD), carrying a non-Abelian that comes in three types: , , or . These color charges are confined to the fundamental representation of the SU(3) gauge group, ensuring that physical particles, such as protons and neutrons, are color singlets formed by combinations of quarks. Gluons are the massless vector bosons responsible for mediating the strong interaction between quarks, analogous to photons in but distinguished by carrying themselves. There are eight gluons, corresponding to the of SU(3), which enables them to couple to both quarks and other gluons. The underlying framework of QCD is a non-Abelian based on the SU(3)c , where the subscript c denotes color. Unlike the Abelian U(1) group of , the non-Abelian structure of SU(3)c introduces self-interactions among gluons through the of the group, leading to three- and four-gluon vertices that are fundamental to the dynamics of the strong force. The dynamics of quarks and gluons are described by the QCD Lagrangian density: LQCD=ψˉ(iγμDμ−m)ψ−14GμνaGaμν,\mathcal{L}_{\rm QCD} = \bar{\psi} (i \gamma^\mu D_\mu - m) \psi - \frac{1}{4} G^a_{\mu\nu} G^{a \mu\nu}, where ψ\psi represents the fields, mm is the mass, Dμ=∂μ−igstaAμaD_\mu = \partial_\mu - i g_s t^a A^a_\mu is the incorporating the strong coupling gsg_s and gluon fields AμaA^a_\mu (with tat^a as the SU(3) generators), and GμνaG^a_{\mu\nu} is the . This form captures both the kinetic and interaction terms for quarks and gluons, with the non-Abelian term −14GμνaGaμν-\frac{1}{4} G^a_{\mu\nu} G^{a \mu\nu} explicitly including gluon self-couplings. Quarks exist in six flavors—up (u), down (d), strange (s), charm (c), bottom (b), and top (t)—each transforming under the same SU(3)c color group but distinguished by their masses, which span more than five orders of magnitude and influence their role in QCD matter. The lighter up, down, and strange quarks have masses on the order of a few MeV, relevant for low-energy hadronic physics, while the heavier charm, bottom, and top quarks have masses of GeV scale, with the top quark being the heaviest at approximately 173 GeV and decaying before forming hadrons.
Quark FlavorMass (MSbar scheme, approximate value)
Up (u)2.2 MeV (at μ = 2 GeV)
Down (d)4.7 MeV (at μ = 2 GeV)
Strange (s)93 MeV (at μ = 2 GeV)
Charm (c)1.27 GeV (at μ = mc)
Bottom (b)4.18 GeV (at μ = mb)
Top (t)172.6 GeV (pole mass)
These masses are running parameters in the modified minimal subtraction (MSbar) scheme unless noted, reflecting the scale-dependent nature of QCD.

Confinement and Asymptotic Freedom

In (QCD), the strong interaction exhibits two fundamental and contrasting properties: at short distances and confinement at long distances. implies that the effective strength of the interaction between quarks and gluons diminishes as the energy scale increases, allowing perturbative calculations at high energies. This behavior arises from the non-Abelian nature of the SU(3) underlying QCD, where gluons carry and self-interact. The running coupling constant αs(Q)=gs24π\alpha_s(Q) = \frac{g_s^2}{4\pi}, where gsg_s is the strong coupling and QQ is the momentum transfer scale, decreases logarithmically with increasing QQ. This scale dependence is governed by the renormalization group beta function, whose leading-order form is β(g)=−g316π2(113Nc−23Nf)+O(g5)\beta(g) = -\frac{g^3}{16\pi^2} \left( \frac{11}{3} N_c - \frac{2}{3} N_f \right) + \mathcal{O}(g^5), with Nc=3N_c = 3 colors and Nf=6N_f = 6 quark flavors. The negative sign of the first coefficient ensures that αs(Q)\alpha_s(Q) approaches zero in the ultraviolet limit (Q→∞Q \to \infty), enabling quarks and gluons to behave as nearly free particles at sufficiently short distances, on the order of 10−1610^{-16} m or less. The discovery of was independently reported in 1973 by and , and by , resolving a long-standing puzzle in physics by providing a framework for QCD as the theory of hadronic matter. Their work, which demonstrated that a non-Abelian could be asymptotically free while remaining renormalizable, earned them the 2004 . This breakthrough shifted the understanding of the strong force from a to a predictive . In stark contrast, at low energies and large distances (infrared regime), QCD displays confinement, or "infrared slavery," where the αs\alpha_s grows, preventing the isolation of individual quarks or gluons as free particles. Quarks are eternally bound into color-neutral hadrons, such as mesons and baryons, due to the formation of a chromoelectric flux tube between color charges. This leads to a linear interquark potential V(r)∼σrV(r) \sim \sigma r, where rr is the separation and σ≈1\sigma \approx 1 GeV/fm is the string tension, as confirmed by simulations modeling the vacuum as a dual superconductor that squeezes color fields into thin tubes. The interplay between and infrared slavery dictates the dynamics of QCD matter: high-energy processes allow quark-gluon interactions to be treated perturbatively, while low-energy phenomena require methods, culminating in —the irreversible formation of hadrons from deconfined quarks and gluons as the system cools or expands. This dual behavior underpins the transition between free quark-gluon states and confined hadronic matter.

States of QCD Matter

Hadronic Phase

The hadronic phase of QCD matter represents the low-temperature and low-density regime where quarks are confined within color-neutral hadrons due to the interaction's effects. In this phase, observable particles are exclusively color singlets, formed by combinations of quarks and antiquarks that neutralize the SU(3) . Baryons, such as the proton, consist of three quarks (qqq) in a color-antitriplet state that combines to a singlet, while mesons, like the , are quark-antiquark (qqˉ\bar{q}) pairs in a color octet-antioctet configuration yielding a singlet overall. At low temperatures, the hadronic phase is characterized by spontaneous chiral symmetry breaking, where the approximate SU(3)_L × SU(3)_R symmetry of massless QCD is broken to the diagonal SU(3)_V flavor symmetry. This breaking generates a nonzero quark bilinear condensate ⟨qˉq⟩≈−(250MeV)3\langle \bar{q}q \rangle \approx -(250 \mathrm{MeV})^3, representing the vacuum expectation value of the scalar quark density and serving as the order parameter for chiral symmetry. The condensate arises from the dynamical generation of constituent quark masses, on the order of 300-400 MeV, far exceeding the current quark masses (a few MeV), and leads to the emergence of light pseudoscalar mesons as approximate Goldstone bosons, such as the pions with masses around 140 MeV. The QCD vacuum in the hadronic phase exhibits rich non-perturbative structure that underpins confinement, including contributions from s and instantons. s are hypothetical bound states of gluons, predicted as color singlets with the lightest scalar having a around 1.5-1.7 GeV, influencing the glue content of the vacuum and supporting the string-like flux tubes between s. Instantons, as topologically nontrivial configurations, contribute to the and induce by aligning zero modes, with the instanton liquid model describing a dilute ensemble of these objects with average size ρ≈1/600\rho \approx 1/600 MeV−1^{-1} and density n≈1n \approx 1 fm−3^{-3}. As increases toward the pseudocritical scale of approximately 150-170 MeV, the hadronic phase transitions to higher-energy states through the of the condensate, where ⟨qˉq⟩\langle \bar{q}q \rangle decreases rapidly, signaling the restoration of chiral symmetry. This disrupts the bound hadronic structure, allowing quarks to become less confined, though the phase remains dominated by hadronic below the transition.

Quark-Gluon Plasma

The quark-gluon plasma (QGP) is a deconfined state of (QCD) matter at high temperatures, where quarks and gluons propagate freely as partons over distances exceeding the typical scale of approximately 1 fm. This phase emerges because renders the strong coupling weak at short distances, suppressing confinement effects and allowing the fundamental color charges to exist unbound. The QGP was first proposed theoretically by Collins and Perry in , who recognized that at sufficiently high temperatures, the perturbative nature of QCD would permit a plasma of asymptotically free quarks and gluons, analogous to the ionized state of electromagnetic plasmas. Deconfinement in the QGP is quantified by the order parameter known as the Polyakov loop, a gauge-invariant Wilson line in the temporal direction whose ⟨L⟩≈1\langle L \rangle \approx 1 signals the restoration of the Z(3) center symmetry and the absence of confinement. In this state, the active consist of quarks with 2 spin states, 3 colors, and NfN_f flavors, alongside gluons with 2 transverse polarizations and 8 color-octet states, yielding a total degeneracy that approaches the Stefan-Boltzmann limit for thermodynamic quantities. Specifically, the follows ϵ=π230g∗T4\epsilon = \frac{\pi^2}{30} g_* T^4, where the effective number of relativistic g∗≈47.5g_* \approx 47.5 for Nf=3N_f = 3 massless quark flavors (up, down, and strange), reflecting the bosonic contribution from gluons (16) and the fermionic contribution from quarks adjusted by the factor 7/87/8. The QGP manifests as a nearly ideal fluid, characterized by an extraordinarily low shear viscosity-to-entropy density ratio η/s≈0.1\eta/s \approx 0.1, approaching the universal lower bound conjectured from gauge/gravity duality and indicating minimal dissipation during collective expansion. Indirect signatures of this deconfined medium include jet quenching, the energy loss of hard partonic jets traversing the plasma via medium-induced radiation and , which suppresses high-transverse-momentum yields relative to fragmentation. Complementing this, elliptic flow quantifies the anisotropic pressure gradients in the expanding plasma, producing a second-order Fourier coefficient v2v_2 in particle azimuthal distributions that reflects the medium's rapid thermalization and hydrodynamic response.

Exotic Phases at High Density

At high densities and low temperatures, (QCD) predicts the emergence of exotic phases of matter distinct from the -gluon plasma, characterized by novel forms of pairing and partial deconfinement. These phases arise in the cold, dense regime of the QCD , where the strong interaction leads to states with superconducting properties or hybrid confinement-deconfinement behaviors, potentially realized in the cores of stars. Color superconductivity represents one such exotic phase, where quarks form Cooper pairs analogous to the Bardeen-Cooper-Schrieffer (BCS) mechanism in conventional superconductors, but mediated by exchange. In the color-flavor-locked (CFL) phase, up, down, and strange s pair in a way that locks color and flavor symmetries, breaking them spontaneously to a diagonal and generating a gap Δ∼10−100\Delta \sim 10{-}100 MeV in the spectrum. This pairing leads to color Meissner effects, expelling magnetic fields, and renders the ground state a superfluid with both color and electromagnetic . The CFL phase is favored at asymptotically high densities where perturbative QCD applies, but at moderate densities, mismatched Fermi surfaces due to unequal quark masses can lead to alternative patterns like the 2SC phase, where only up and down s pair. Quarkyonic proposes another paradigm for high-density QCD, featuring a deconfined Fermi sea at the core surrounded by a shell of confined ic excitations. At large chemical μB≳1\mu_B \gtrsim 1 GeV, the pressure is dominated by near the Fermi surface, while confinement persists for excitations above it, preventing free s but allowing a large . This state reconciles at short distances with confinement at long distances, emerging in the large-NcN_c limit of QCD where NcN_c is the number of colors. Model calculations indicate quarkyonic stiffens the equation of state compared to pure hadronic , influencing the structure of compact stars. Recent theoretical advances, including model studies up to 2025, suggest intermediate states between the hadronic phase and full quark-gluon plasma at high density, exhibiting non-conformal behaviors such as speed-of-sound variations exceeding the conformal limit cs2=1/3c_s^2 = 1/3. These proposals, motivated by effective models and analogies from in related theories, describe phases with partial chiral restoration or quarkyonic-like transitions, potentially bridging confined and deconfined regimes without sharp boundaries. Hybrid stars, incorporating quark cores amid hadronic mantles, provide an astrophysical context for these exotic phases, with observations of massive stars (M≳2M⊙M \gtrsim 2 M_\odot) constraining the transition density to matter around 2-5 times nuclear saturation. Calculations using perturbative QCD or Nambu-Jona-Lasinio models yield stable hybrid configurations where color-superconducting cores occupy 10-20% of the star's radius, enhancing maximum masses and altering cooling via emission from paired quarks. These structures highlight the role of high-density QCD in explaining timing and signals.

Occurrence and Production

Cosmological Contexts

In the standard model, the early transitioned through a quark-gluon plasma (QGP) phase shortly after the , where quarks and gluons existed in a deconfined state due to high temperatures. This phase dominated from approximately 10−1210^{-12} seconds, corresponding to temperatures around 100 GeV near the electroweak scale, to about 10−510^{-5} seconds at temperatures of roughly 150 MeV, marking the onset of the . During this interval, the expanded rapidly while cooling, with the QGP serving as the primordial state of matter before . The shift from the electroweak era to the QCD-dominated QGP occurred as temperatures dropped from about 100 GeV to 150 MeV, a period spanning roughly 10−1210^{-12} to 10−510^{-5} seconds. simulations indicate that the at this scale is a smooth crossover rather than a sharp first-order event, involving gradual confinement of quarks into hadrons without significant or bubble nucleation. This crossover influences processes, as transitions—key to generating the observed —remain active until the electroweak scale but can be modulated by the evolving QCD dynamics, potentially affecting the efficiency of lepton-to-baryon conversion in extensions of the . The also impacts cosmological relic abundances by introducing potential density fluctuations during , which occur post-QGP at temperatures below 150 MeV. These inhomogeneities, arising from the release of and changes in the equation of state, could alter distributions on small scales, influencing the subsequent (BBN) around 1 MeV. For instance, even in a crossover scenario, such effects might subtly modify the predicted abundances of light elements like and formed after full , though current observations constrain significant deviations. In inflationary cosmology, the reheating phase following the rapid expansion driven by the field can produce a primordial QGP if the reheating temperature exceeds the QCD scale of approximately 150 MeV, restoring and populating the with deconfined quarks and gluons. This process, occurring at temperatures potentially up to 10^{15} GeV or higher depending on the model, ensures the hot conditions necessary for the QGP era, with non-equilibrium dynamics facilitating fast thermalization into the plasma state.

Astrophysical Environments

In the cores of neutron stars, where densities exceed several times the nuclear saturation density ρ0≈0.16\rho_0 \approx 0.16 fm−3^{-3}, the conditions may favor the formation of quark matter, potentially transitioning from hadronic matter to deconfined quark-gluon states at densities greater than 5–10 ρ0\rho_0. This transition is theorized to stiffen the equation of state (EOS), allowing neutron stars to support masses up to approximately 2 solar masses (M⊙M_\odot) or higher, as softer purely hadronic EOS would otherwise lead to collapse. Observational evidence from pulsar timing and supports the existence of such stiff EOS in massive neutron stars, consistent with hybrid configurations featuring quark cores. The strange quark matter hypothesis posits that a mixture of up, down, and strange quarks could form the absolute ground state of baryonic matter, with stable strangelets—small clumps of this matter—having an energy per baryon lower than that of iron (around 930 MeV), rendering ordinary nuclei unstable against conversion. Proposed originally by Witten, this idea suggests that neutron star remnants from supernovae could convert to strange quark stars if the surface energy barrier is overcome, potentially explaining compact objects with unusual cooling or mass-radius relations. Stability analyses within chiral quark models confirm that such matter remains bound at zero pressure, unlike neutron matter. Phenomena in magnetars, highly magnetized neutron stars, such as giant flares and spin glitches, may serve as indirect probes of in their interiors. Sudden energy releases during flares could arise from magnetic field rearrangements triggering a hadron-to-quark , releasing and altering the star's rotation. Glitches, observed as abrupt spin-ups, might similarly reflect density fluctuations or superfluid responses near a phase boundary, providing constraints on the EOS stiffness. Recent analyses incorporating gravitational wave data from have tightened constraints on hybrid star models, favoring those with quark cores that match the observed tidal deformability while accommodating massive pulsars like PSR J0740+6620 (∼2.08M⊙\sim 2.08 M_\odot). By 2025, multimessenger observations, including updated radius measurements from NICER, have tightened constraints on the EOS, excluding soft purely hadronic models and favoring stiffer hadronic or hybrid scenarios with matter components for stars above 1.4 M⊙M_\odot, though nonstrange cores remain viable alternatives to . Recent 2025 NICER measurements of pulsars like PSR J0437-4715 and PSR J0614-3329 have further constrained radii to ~12-13 km for 1.4 M⊙M_\odot stars, supporting stiffer EOS consistent with hybrid -hadron configurations. These constraints highlight the role of astrophysical environments in testing QCD at extreme densities.

Laboratory Creation

QCD matter, particularly the quark-gluon plasma (QGP), is primarily created in laboratory settings through high-energy collisions at particle accelerators, where extreme temperatures and densities briefly recreate conditions akin to the early universe. The (RHIC) at initiated gold-gold (Au-Au) heavy-ion collisions in 2000, producing a hot, dense medium interpreted as QGP in central collisions, with the initial overlap volume estimated at approximately 10 fm³. Similarly, the (LHC) at began lead-lead (Pb-Pb) collisions in November 2010 at a center-of-mass energy per nucleon pair of √s_{NN} = 2.76 TeV, generating even hotter and denser QGP states within comparable local volumes of about 10 fm³. These collisions involve relativistic heavy ions, where the Lorentz-contracted nuclei overlap to form a deconfined plasma that expands and cools rapidly over femtoseconds. To map the QCD phase diagram, particularly at finite chemical potential (μ_B), RHIC's Beam Energy Scan () program systematically varies collision energies from low values up to √s_{NN} = 200 GeV, allowing probes of increasing μ_B up to around 400 MeV in the most central Au-Au events. This multi-phase effort, launched in 2010, has collected extensive datasets across energies like 7.7, 11.5, 19.6, 27, 39, and 200 GeV, enabling studies of the transition from hadronic matter to QGP and potential critical points. In parallel, smaller systems such as proton-lead (p-Pb) and proton-proton (pp) collisions at the LHC have revealed signatures of mini-QGP droplets, where high-multiplicity events produce compact, transient deconfined regions with volumes orders of magnitude smaller than in heavy-ion collisions, yet exhibiting collective behaviors indicative of QGP formation. Future facilities will extend these investigations to higher baryon densities. The Facility for Antiproton and Ion Research (FAIR) at GSI Helmholtz Centre, with construction advancing since 2018, anticipates first heavy-ion beams for QCD experiments in 2028 using the SIS100 accelerator to probe dense matter at μ_B up to 1 GeV. Likewise, the Nuclotron-based Ion Collider fAcility (NICA) at the (JINR) in , under development since the early , is slated for operational heavy-ion collisions around 2025, focusing on high-density QCD probes in Au-Au interactions at √s_{NN} up to 11 GeV to explore the high-μ_B regime. These accelerators will complement RHIC and LHC by accessing longer-lived, denser QCD matter states.

Phase Diagram

Temperature and Chemical Potential Axes

The phase diagram of (QCD) matter is conventionally mapped in the plane defined by TT and baryon chemical potential μB\mu_B, which together parameterize the thermodynamic conditions of strongly interacting systems in . The TT, measured in such as MeV, represents the scale available to excitations, with relevant QCD scales spanning from near zero up to several hundred MeV, comparable to the QCD scale ΛQCD≈200\Lambda_\mathrm{QCD} \approx 200 MeV. The baryon chemical potential μB\mu_B, also in MeV, controls the net number density and extends from zero (corresponding to baryon-symmetric matter with equal numbers of and antibaryons) to values around 1 GeV, the approximate scale of the mass, where dense matter relevant to astrophysical objects like stars becomes accessible. For quark-level descriptions, the quark chemical potential is μq=μB/3\mu_q = \mu_B / 3, reflecting the tripling of for three-quark constituents. Lattice QCD simulations provide the primary non-perturbative tool for exploring this diagram, particularly along the μB=0\mu_B = 0 axis, where the pseudo-critical temperature for the transition from confined to deconfined matter is determined to be Tpc=156.5±1.5T_\mathrm{pc} = 156.5 \pm 1.5 MeV for physical quark masses. At finite μB\mu_B, direct simulations face the severe sign problem: the fermion determinant in the path integral becomes complex for real μB≠0\mu_B \neq 0, preventing efficient Monte Carlo sampling and requiring alternative approaches such as analytic continuation from imaginary chemical potentials μB=iμI\mu_B = i \mu_I, where the determinant remains real and positive. This workaround exploits the periodicity and analyticity of the partition function in imaginary μ\mu, allowing extrapolations to real values, though with increasing uncertainty at larger μB/T\mu_B / T. In the TT-μB\mu_B plane, the low-TT, low-μB\mu_B region describes a of confined within color-neutral mesons and , while high TT at moderate μB\mu_B yields a quark-gluon plasma of asymptotically free partons. At high μB\mu_B and low TT, exotic phases such as color-superconducting emerge due to instabilities in dense fermionic systems. The zero-μB\mu_B line thus serves as a reference for symmetric , with deviations probing net densities encountered in heavy-ion collisions and compact .

Phase Transitions and Critical Points

In the QCD phase diagram, the transition from the hadronic phase to the quark-gluon plasma at zero baryon chemical potential μB=0\mu_B = 0 manifests as a rapid crossover rather than a sharp . Lattice QCD simulations determine the pseudocritical temperature for this chiral crossover at Tc≈155T_c \approx 155 MeV for physical quark masses with 2+1 flavors. This smooth behavior arises because explicit due to nonzero light quark masses prevents a true second-order transition, consistent with expectations from the O(4) in the chiral limit where a second-order transition would occur at a lower Tc≈132T_c \approx 132 MeV. At higher baryon densities, the crossover is expected to evolve into a phase transition line, terminating at a critical endpoint (CEP) where the transition becomes second-order. Theoretical predictions from effective models and holographic approaches place the CEP at μB∼600\mu_B \sim 600 MeV and T∼100T \sim 100 MeV, marking the boundary between the crossover region and the regime. This point belongs to the 3D Ising universality class, influencing observables like number fluctuations near the transition. The chiral transition, associated with the restoration of approximate chiral symmetry SU(2)_L × SU(2)_R, aligns closely with the pseudocritical line at low μB\mu_B but weakens into a crossover due to explicit breaking by masses. At imaginary chemical potentials μ=iμI\mu = i \mu_I, QCD exhibits Roberge-Weiss periodicity with period 2πT/32\pi T / 3 in μI/T\mu_I / T, arising from the Z(3) center symmetry of pure Yang-Mills theory, leading to phase transitions between different Polyakov loop sectors that intersect with the chiral transition line. Recent lattice QCD studies in 2025, leveraging improved algorithms for continuum extrapolation and handling finite-volume effects under strangeness neutrality, provide hints on the CEP location by excluding its presence at μB<450\mu_B < 450 MeV at the 2σ\sigma level, suggesting it resides at higher densities consistent with model predictions. These advances refine the phase boundary mapping, enhancing constraints on the diagram's structure without direct sign problem resolution.

Thermodynamic Properties

Equation of State

The equation of state (EOS) of QCD matter describes the thermodynamic relations between pressure PP, energy density ε\varepsilon, temperature TT, and chemical potentials μ\mu, such as P=P(T,μ)P = P(T, \mu). Lattice QCD simulations provide non-perturbative calculations of the EOS at zero or small chemical potentials, revealing a smooth crossover transition from hadronic matter to quark-gluon plasma (QGP) around the pseudocritical temperature Tc≈155T_c \approx 155 MeV for μ=0\mu = 0. For instance, the normalized pressure reaches P/T4≈0.2P/T^4 \approx 0.2 (relative to the Stefan-Boltzmann limit) at T=155T = 155 MeV and μ=0\mu = 0, indicating partial deconfinement with interactions suppressing the pressure below the ideal gas value. In the high-temperature limit, QCD matter approaches the conformal limit of a massless ideal gas, where ε=3P\varepsilon = 3P, corresponding to the trace anomaly vanishing as ε−3P→0\varepsilon - 3P \to 0. Deviations from this relation arise from quark masses, non-perturbative effects near TcT_c, and residual interactions, with lattice results showing ε/T4≈0.6\varepsilon/T^4 \approx 0.6 at T=155T = 155 MeV, leading to ε≈2.8P\varepsilon \approx 2.8 P. At higher temperatures, say T>300T > 300 MeV, the closely tracks the Stefan-Boltzmann values for 2+1 flavors, with P/T4P/T^4 approaching unity in normalized units. The squared, defined as cs2=dP/dεc_s^2 = dP/d\varepsilon, provides insight into the stiffness and exhibits a characteristic dip near the transition due to the softening of the medium. Lattice calculations show cs2≈0.2c_s^2 \approx 0.2 near TcT_c, reflecting interactions and the latent heat-like behavior in the crossover, before rising toward the conformal value of 1/31/3 in the QGP phase at T≳200T \gtrsim 200 MeV. This minimum highlights the transition's impact on hydrodynamic evolution in heavy-ion collisions. At high densities, relevant for the cores of neutron stars, the is probed by effective models since direct lattice calculations are challenging due to the problem. These models, such as the Nambu-Jona-Lasinio (NJL) approach or perturbative QCD, predict a stiff for deconfined matter, with cs2c_s^2 approaching or exceeding 1/31/3 at densities ≳5n0\gtrsim 5 n_0 (where n0n_0 is nuclear saturation density), enabling support for massive compact stars up to 2 solar masses.

Transport Coefficients

Transport coefficients describe the dissipative response of QCD matter, such as the quark-gluon plasma (QGP), to external gradients, playing a key role in its hydrodynamic evolution. In the QGP phase, these include shear viscosity η, which governs momentum diffusion; bulk viscosity ζ, related to volume changes; electrical conductivity σ, characterizing charge transport; and baryon diffusion coefficient D_B, describing net propagation. These properties arise from interactions among quarks and gluons, with values determined theoretically via , effective models, and dualities like AdS/CFT, and constrained by collective flow in heavy-ion collisions. Shear viscosity η quantifies the fluid's resistance to shear deformations, often normalized as the η/s to the density s for . The AdS/CFT correspondence predicts a universal lower bound η/s ≥ 1/(4π) ≈ 0.08 for strongly coupled relativistic fluids, derived from gravitational perturbations in anti-de Sitter spacetime dual to conformal field theories. In the QGP, this bound is nearly saturated, with hydrodynamic analyses of heavy-ion collision data yielding η/s ≈ 0.1–0.5, indicating a low-, nearly behavior distinct from the ideal limit where η = 0 as per the equation of state. Bulk viscosity ζ measures resistance to uniform compression or expansion and vanishes in conformally invariant theories but is nonzero in QCD due to scale from the running coupling and masses. Near the pseudocritical T_c ≈ 155 MeV, where conformal invariance is most violated during the hadron-QGP transition, ζ exhibits a pronounced peak, with computations showing ζ/s reaching ~1, far exceeding shear in this regime. This enhancement reflects rapid changes in the trace anomaly and across the crossover. Electrical conductivity σ and diffusion D_B are derived from linear response theory via Kubo formulas, relating them to low-frequency limits of retarded functions of conserved currents. For σ, the Kubo relation σ = (1/3) lim_{ω→0} (1/ω) Im G^R_{ii}(ω,0), where G^R is the electromagnetic current correlator, yields values of σ/T ≈ 0.1–0.4 in the QGP at temperatures above T_c, scaling with the strong coupling. Similarly, D_B emerges from the current correlator, with recent lattice results indicating D_B T ≈ 1–2 at high temperatures, decreasing near finite density due to enhanced scattering. Recent 2025 hydrodynamic studies of heavy-ion collisions provide stringent lower bounds on these coefficients, confirming η/s ≳ 0.08 from flow suppression patterns and aligning with AdS/CFT predictions, while constraining ζ/s < 0.5 away from T_c to match expansion dynamics.

Theoretical Approaches

Lattice QCD Simulations

Lattice QCD offers a rigorous, non-perturbative approach to investigating the properties of QCD matter by discretizing the theory on a hypercubic lattice in four-dimensional Euclidean spacetime, allowing numerical simulations via Monte Carlo methods. The continuum QCD action S=∫d4x LS = \int d^4x \, \mathcal{L}, where L\mathcal{L} includes gluon and quark kinetic terms, is replaced by a discrete sum over lattice sites separated by spacing aa, with the continuum limit recovered as a→0a \to 0. Gluons are represented by SU(3) link variables Uμ(x)U_\mu(x) on the links, while quarks are described using fermion discretizations such as Wilson fermions or staggered fermions. Wilson fermions incorporate a non-derivative Wilson term to eliminate the 15 unphysical doubler modes that arise in naive discretizations, ensuring a single continuum fermion species per flavor, though at the cost of explicit chiral symmetry breaking that requires careful tuning. Staggered fermions, by contrast, preserve a remnant chiral symmetry and reduce doublers to four "tastes" per flavor, which must be taken to the fourth root in the action to match the continuum with NfN_f degenerate flavors, enabling efficient simulations of light quarks. These formulations allow computation of thermodynamic observables, such as the pressure and energy density, from the partition function Z=∫DU det⁡M e−SgZ = \int \mathcal{D}U \, \det M \, e^{-S_g}, where SgS_g is the pure gauge action (e.g., the plaquette or improved actions) and MM the fermion matrix. Phase transitions in QCD matter are identified through lattice observables sensitive to symmetry changes. Deconfinement, associated with the breaking of Z(3) center symmetry in the pure gauge limit, is probed via the renormalized Polyakov loop ⟨L⟩\langle L \rangle, whose non-zero value above the transition signals quark liberation; the corresponding susceptibility χL=∂2ln⁡Z/∂β2\chi_L = \partial^2 \ln Z / \partial \beta^2 (with β=6/g2\beta = 6/g^2) exhibits a peak marking the pseudocritical temperature. Chiral symmetry restoration is monitored by the quark chiral condensate ⟨ψˉψ⟩\langle \bar{\psi} \psi \rangle, which acts as an order parameter in the chiral limit and decreases rapidly near the transition, with its susceptibility providing another indicator of the crossover. A major challenge in lattice simulations of QCD matter arises at finite baryon chemical potential μB≠0\mu_B \neq 0, where the fermion determinant det⁡M(μ)\det M(\mu) becomes complex due to the imaginary part from the chemical potential term, leading to the infamous sign problem that renders standard Monte Carlo importance sampling inefficient as the phase factor oscillates wildly. This issue is addressed through indirect methods, such as Taylor expansion of observables (e.g., pressure) in powers of μB/T\mu_B / T around μB=0\mu_B = 0, where coefficients are computed directly, or reweighting techniques that use configurations at μB=0\mu_B = 0 to estimate ratios at small finite μB\mu_B, though both approaches have limitations in convergence radius and computational cost. Recent advances in lattice QCD, including highly improved staggered quark actions, multi-level integration algorithms, and exascale computing resources, have facilitated precise continuum extrapolations on finer lattices with physical quark masses. These efforts have refined the pseudocritical temperature for the chiral-deconfinement crossover at zero chemical potential to Tc=156.5±1.5T_c = 156.5 \pm 1.5 MeV, consistent with features of the QCD phase diagram such as the absence of a critical point at low μB\mu_B.

Perturbative QCD and Weak Coupling

At temperatures T≫ΛQCD≈200T \gg \Lambda_\mathrm{QCD} \approx 200 MeV, where ΛQCD\Lambda_\mathrm{QCD} is the intrinsic QCD scale setting the onset of non-perturbative effects, the running strong coupling g(T)g(T) becomes weak due to asymptotic freedom, enabling a perturbative expansion of QCD matter properties using Feynman diagrams and weak-coupling techniques. This regime corresponds to the quark-gluon plasma phase at asymptotically high temperatures, where the deconfined quarks and gluons behave as a weakly interacting gas, but collective plasma effects necessitate resummations to handle infrared sensitivities arising from long-range interactions. Naive perturbative calculations encounter infrared divergences from soft modes with momenta of order gTgT, which are resolved through the hard thermal loop (HTL) resummation scheme. HTL perturbation theory reorganizes the expansion by resummed self-energies into effective propagators and vertices that capture the leading plasma physics, such as Debye screening of static electric fields. The resulting Debye screening mass is mD∼gTm_D \sim gT, specifically mD=gTNc/3m_D = gT \sqrt{N_c/3}
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