Quark–Gluon Plasma

• Quark–gluon plasma is a deconfined state of matter where quarks and gluons are liberated, formed under extreme temperature and energy conditions.
• Experimental signatures such as elliptic flow, jet quenching, and electromagnetic probes provide robust evidence of QGP formation in heavy-ion collisions.
• Theoretical approaches including lattice QCD, hydrodynamic models, and transport simulations reveal the QGP’s nearly perfect fluidity and low viscosity.

The quark–gluon plasma (QGP) is a state of deconfined quarks and gluons formed at extreme temperatures or energy densities, where color confinement is lifted and chiral symmetry is (at least partially) restored. QGP is relevant for understanding the early universe microseconds after the Big Bang and is experimentally created and studied in ultra-relativistic heavy-ion collisions, notably at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). Its physical properties, formation dynamics, experimental signatures, and theoretical descriptions have been the subject of intense investigation, involving the interplay of non-perturbative quantum chromodynamics (QCD), hydrodynamics, transport theory, lattice simulations, and connections to other domains of strongly coupled matter.

1. Theoretical Foundations and Phase Structure

QCD predicts that, above a critical temperature ($T_c \approx 156-175$ MeV at zero baryon chemical potential), strongly interacting hadronic matter undergoes a crossover transition to a deconfined phase where color-singlet hadrons “melt” into a plasma of quarks and gluons (Braun-Munzinger et al., 2022, Pasechnik et al., 2016, Ploskon, 2018). This prediction is supported by lattice QCD, which shows a sharp increase in the number of active degrees of freedom and the entropy density across $T_c$, as well as restoration of (approximate) chiral symmetry. The equilibrium phase diagram in the $(T, \mu_B)$ plane features a smooth crossover at $\mu_B \sim 0$ and a first-order transition at larger $\mu_B$, with the point of change characterized as a possible QCD critical point.

The QGP is characterized by high parton number density, screening of the color charge (Debye screening), and the rapid dissolution of hadron-like bound states at high $T$. However, quantum simulations and path-integral Monte Carlo calculations demonstrate that the QGP near $T_c$ retains strong interparticle correlations, significant non-perturbative phenomena, and even transient persistence of bound states (Filinov et al., 2010).

2. Creation and Hydrodynamic Evolution in Heavy-Ion Collisions

In ultra-relativistic nuclear collisions, two Lorentz-contracted nuclei collide, creating an energy-dense region with temperatures well above $T_c$ and energy densities $$\varepsilon \gtrsim 0.5~\mathrm{GeV}~\mathrm{fm}^{-3}$$ (Ploskon, 2018, Braun-Munzinger et al., 2022). The produced “fireball” thermalizes rapidly (within $\sim 1$ fm/c) and expands, following longitudinal and transverse collective flow. The hydrodynamic evolution is governed by the conservation of the energy–momentum tensor,

$\partial_\mu T^{\mu\nu} = 0,$

with $T^{\mu\nu}$ typically decomposed into ideal and dissipative (shear/bulk) contributions,

$$T^{\mu\nu} = (\varepsilon + P)u^\mu u^\nu - P g^{\mu\nu} + \pi^{\mu\nu} + \Delta^{\mu\nu} \Pi,$$

where $u^\mu$ is the flow four-velocity, $P$ the pressure, $\pi^{\mu\nu}$ the shear stress tensor, and $\Pi$ the bulk pressure. The acceleration of the fluid is tied to the pressure gradients: $$\dot{u}^\mu = \frac{\nabla^\mu p}{\epsilon+p} = \frac{c_s^2}{1 + c_s^2} \frac{\nabla^\mu \epsilon}{\epsilon},$$ where $c_s$ is the speed of sound.

At freeze-out, the system hadronizes near or just below $T_c$; the final particle yields and spectra are set by the local chemical and kinetic conditions at this stage.

3. Experimental Signatures and Probes

Multiple experimental observables provide evidence for QGP creation and its properties:

• Elliptic flow ($v_2$): The most direct evidence for strong collectivity is the large value of the second Fourier coefficient $v_2$ of the azimuthal hadron distribution relative to the reaction plane,

$$v_2(y, p_T; b) = \left\langle \cos(2\phi_p) \right\rangle.$$

The conversion of initial spatial anisotropy into momentum anisotropy through hydrodynamic expansion is near the ideal hydrodynamic limit (i.e., with minimal viscosity), especially in central collisions (0810.5529). Heavy flavors (charm, bottom) also exhibit flow, underscoring the strong coupling of the QGP.

• Jet quenching: High-$p_T$ parton energy loss via medium-induced gluon radiation (with strong Landau–Pomeranchuk–Migdal suppression) leads to phenomena such as the disappearance of away-side jets and the suppression of high-$p_T$ hadrons. The jet quenching parameter,

$\hat{q} = \frac{d\langle k_T^2 \rangle}{dL},$

and the nuclear modification factor $R_{AA}$ are measured to quantify the medium’s opacity, with $R_{AA} \ll 1$ at intermediate $p_T$ indicating substantial parton energy loss (Braun-Munzinger et al., 2022, Ploskon, 2018).

• Electromagnetic probes: Real photons and dileptons ($e^+e^-, \mu^+\mu^-$) provide penetrating insight, as they decouple from the system throughout its evolution. Invariant-mass spectra of dilepton pairs are used to extract temperatures at various stages: the low-mass region reflects the later stage (chemical freeze-out, $T \sim 170$ MeV), while the intermediate-mass region is sensitive to the earliest QGP temperature ($T \sim 300$ MeV) (Collaboration, 3 Feb 2024).
• Flavor and strangeness observables: Enhanced production of multi-strange baryons and non-equilibrium strangeness content are robust indicators of QGP formation (Rafelski, 2019). Ratios such as $K^+/\pi^+$ exhibit non-monotonicity (“horn”) near the onset of deconfinement.
• Quarkonium suppression and recombination: Suppression of heavy quark bound states (e.g., $J/\psi$, $\Upsilon$) is attributed to color screening, but statistically significant regeneration via recombination of thermalized heavy quarks at the phase boundary also occurs (Braun-Munzinger et al., 2022, Yao et al., 2019).

4. Transport Properties and Nearly Perfect Fluidity

Hydrodynamic modeling and Bayesian analysis of flow observables yield extremely low values for the specific shear viscosity $\eta/s$, close to the conjectured universal lower bound,

$\frac{\eta}{s} = \frac{1}{4\pi} \approx 0.08.$

Experimental data constrain $\eta/s \lesssim 0.2$ near $T_c$ (0810.5529, Braun-Munzinger et al., 2022, Pasechnik et al., 2016). The bulk viscosity to entropy ratio $\zeta/s$ peaks sharply above $T_c$, consistent with the sharp change in the QCD interaction measure $I = \epsilon - 3P$.

The QGP thus qualifies as a nearly perfect fluid, with collective behavior characteristic of liquids rather than gases. Viscous corrections are mandatory for precision modeling; the reduction of $v_2$ and damping of high-frequency hydrodynamic modes scale with $\eta/s$. Recent studies on jet–medium interactions also incorporate generalized dielectric response and chromohydrodynamics (Jiang et al., 2014), with polarization energy loss strongly damped by higher viscosity.

Quantum simulations confirm that, at coupling parameter $\Gamma \sim O(1)$, the QGP is a strongly coupled Coulomb liquid with quantum effects (e.g., Kelbg regularization, quantum statistics) essential for reproducing the equation of state and microscopic structure (pair distribution functions) observed on the lattice (Filinov et al., 2010). The persistence of anti-ferromagnetic color correlations and string-like binding just above $T_c$ support a quantum liquid picture.

5. Microscopic Parton Energy Loss, Scaling Laws, and Gluon Emission

Parton energy loss in QGP is dominated by medium-induced gluon radiation, whose rate is calculated via the AMY formalism—resumming multi-scattering diagrams and including Landau–Pomeranchuk–Migdal effects (Suryanarayana, 2010). The emission spectrum exhibits universal scaling when expressed in terms of a dynamically determined variable,

$x = z_1 / k^{2.35}, \qquad z_1 = |(p-k) p k / T|,$

with all systematics collapsing onto a single emission function $g(x)$ for different processes ($g \to gg, q \to gq, g \to q\bar{q}$). This universality drastically simplifies parton energy loss calculations and facilitates quantitative jet quenching predictions.

Advanced theoretical work connects jet attenuation and energy loss to strong coupling physics via holographic dualities. For instance, in $\mathcal{N}=4$ supersymmetric Yang–Mills plasma, an energetic gluon beam is attenuated over a distance $d_{\text{att}} \sim q^{1/3}/(\pi T)^{4/3}$, but the angular and momentum distribution of the beam remains tightly collimated, in close correspondence with LHC observations of jet quenching (Chesler et al., 2011).

6. Non-Perturbative and Topological Aspects

Non-perturbative effects, including gluon condensates of mass dimension two and four, persist in the deconfined phase and can significantly modify the effective equation of state. The separation of the gluon field into soft non-perturbative (condensate) and hard (perturbative) components, with the latter treated via mean-field approximations, allows analytic derivation of the EOS beyond the MIT bag model. The interplay between condensates (softening EOS) and hard gluons (stiffening, especially at high density) has critical implications for compact stellar objects (Fogaça et al., 2010).

Additionally, effective field theories that bosonize the QGP response indicate that, near $T_c$, the QGP exhibits topological order akin to topological fluids in condensed matter (Luo, 2014). The dominance of topological terms (e.g., BF and $\theta$-terms in the effective action) below a QCD gap ensures incompressibility, small viscosity, and fractionalization of charge, with dyonic structure (mixed electric and magnetic response) providing a natural explanation for nearly perfect fluidity and some of the exotic transport properties observed at RHIC.

The finite baryon density QGP can behave as a paramagnet once polarized by a magnetic field, with a persistent medium-induced splitting in the damping rates of probe quarks of different spin along the field, extending the influence of the magnetic field—observable in strange quark polarization and $\Lambda$ hyperon spin asymmetries (Dong et al., 19 Mar 2024).

7. Ongoing Developments and Future Perspectives

Experimentally, challenges remain in mapping the full QCD phase diagram, isolating cold nuclear matter effects from true QGP signatures, and extracting transport coefficients (e.g., jet transport parameter $\hat{q}$, $\eta/s$, $\zeta/s$, $D$) with reduced theoretical/model uncertainty (Braun-Munzinger et al., 2022, Ploskon, 2018). The ongoing RHIC Beam Energy Scan targets the potential critical point at finite $\mu_B$. Jet substructure, heavy flavor (open and hidden charm), and electromagnetic observables continue to be refined for greater sensitivity to QGP properties and its evolution.

On the theory side, dynamical models have matured, integrating microscopic transport, matched hydro–kinetic stages, and explicit partonic degrees of freedom (see, e.g., PHSD and UrQMD hybrid approaches) (Bleicher et al., 20 Apr 2025). The interplay between partonic and hadronic dynamics is essential to describe a broad range of observables, from early thermalization (glasma/CGC) to chemical freeze-out.

Lattice QCD, quantum simulations, effective field theories, and AdS/CFT methods remain crucial in elucidating the non-perturbative regime and guiding model development. Recent advances in extracting real-time dynamics, spectral functions, and transport parameters from lattice calculations are increasingly relevant for establishing ab initio benchmarks for phenomenology.

In sum, the QGP is a unique state of matter blending features of a quantum, strongly coupled liquid with collective, topological, and non-perturbative phenomena. Its theoretical, experimental, and computational exploration continues to shape contemporary understanding of QCD under extreme conditions.