State of matter important in cosmology and particle physics
QCD phase diagram. Adapted from original made by R.S. Bhalerao.[1]
Quark–gluon plasma (QGP orquark soup) is an interacting localized assembly ofquarks andgluons atthermal (local kinetic) and (close to) chemical (abundance) equilibrium. The wordplasma signals that freecolor charges are allowed. In a 1987 summary,Léon Van Hove pointed out the equivalence of the three terms: quark gluon plasma, quark matter and a new state of matter.[2] Since the temperature is above theHagedorn temperature—and thus above the scale of light u,d-quark mass—the pressure exhibits the relativisticStefan–Boltzmann format governed by temperature to the fourth power () and many practically massless quark and gluon constituents. It can be said that QGP emerges to be the new phase of strongly interacting matter which manifests its physical properties in terms of nearly free dynamics of practically massless gluons and quarks. Both quarks and gluons must be present in conditions near chemical (yield) equilibrium with theircolor chargeopen for a new state of matter to be referred to as QGP.
Quark–gluon plasma (QGP) is astate of matter occurring atenergy densities high enough to melt theprotons andneutrons that make up the nuclei of matter. The result is a very low viscosity liquid composed of the elementary particles,quarks and gluons.[3][4] In normal matter quarks areconfined; in the QGP quarks aredeconfined. Quark–gluon plasma is studied to understand the characteristics of the Universe at about 20 μs after theBig Bang. Experimental groups useultrarelativistic beams of ions colliding with other ions or protons to create this plasma inparticle accelerators.[5]
Theories predicting the existence of quark–gluon plasma were developed in the late 1970s and early 1980s.[6] The discovery ofcolor confinement andasymptotic freedom properties ofquantum chromodynamics lead to the realization that quarks would undergo a phase transition at high density.[7] Using an analogy withelectromagnetic plasma, in 1978 E V. Shuryak used the term "hadronic plasma" for matter much more dense than atomic nuclei, matter in which hadrons merge and the quarks act collectively.[8] In his next paper he used "quark-gluon plasma", a name that stuck.[7]: 1125 [9]
Quark–gluon plasma[10][11] was searched for the first time in the laboratory at CERN in the year 2000, where the a press-release discussing the evidence for a new state of matter was issued.[3][12][13] As the authors later wrote:[14] "compelling evidence for the creation of `a new form of matter' had been found but stopped short of claiming unambiguous discovery of the quark-gluon plasma, nor did it comment on its perfectly liquid collective dynamical properties. The latter became only obvious after theory had progressed to a quantitative understanding of the bulk of the very comprehensive and precise experimental data collected at RHIC." Indeed, QGP discovery was announced[15] after the publication of the so-called RHIC White Papers[16][17][18][19] in 2005.
How the quark–gluon plasma fits into the general scheme of physics
QCD is one part of the modern theory ofparticle physics called theStandard Model. Other parts of this theory deal withelectroweak interactions andneutrinos. Thetheory of electrodynamics has been tested and found correct to a few parts in a billion. Thetheory of weak interactions has been tested and found correct to a few parts in a thousand. Perturbative forms of QCD have been tested to a few percent.[20] Perturbative models assume relatively small changes from the ground state, i.e. relatively low temperatures and densities, which simplifies calculations at the cost of generality. In contrast, non-perturbative forms of QCD have barely been tested. The study of the QGP, which has both a high temperature and density, is part of this effort to consolidate the grand theory of particle physics.
The study of the QGP is also a testing ground forfinite temperature field theory, a branch of theoretical physics which seeks to understand particle physics under conditions of high temperature. Such studies are important to understand the early evolution of our universe:the first hundred microseconds or so. It is crucial to the physics goals of a new generation of observations of the universe (WMAP and its successors). It is also of relevance toGrand Unification Theories which seek to unify the three fundamental forces of nature (excluding gravity).
Reasons for studying the formation of quark–gluon plasma
The generally accepted model of the formation of theUniverse states that it happened as the result of theBig Bang. In this model, in the time interval of 10−10–10−6 s after the Big Bang, matter existed in the form of a quark–gluon plasma. It is possible to reproduce the density and temperature of matter existing of that time in laboratory conditions to study the characteristics of the very early Universe. So far, the only possibility is the collision of two heavyatomic nuclei accelerated to energies of more than a hundred GeV. Using the result of a head-on collision in the volume approximately equal to the volume of the atomic nucleus, it is possible to model the density and temperature that existed in the first instants of the life of the Universe.
Aplasma is matter in whichcharges arescreened due to the presence of other mobile charges. For example:Coulomb's law is suppressed by the screening to yield a distance-dependent charge,, i.e., the charge Q is reduced exponentially with the distance divided by a screening length α. In a QGP, thecolor charge of the quarks and gluons is screened. The QGP has other analogies with a normal plasma. There are also dissimilarities because the color charge isnon-abelian, whereas theelectric charge is abelian. Outside a finite volume of QGP the color-electric field is not screened, so that a volume of QGP must still be color-neutral. It will therefore, like a nucleus, have integer electric charge.
Because of the extremely high energies involved, quark-antiquark pairs are produced bypair production and thus QGP is a roughly equal mixture of quarks and antiquarks of various flavors, with only a slight excess of quarks. This property is not a general feature of conventional plasmas, which may be too cool for pair production (see howeverpair instability supernova).
One consequence of this difference is that the color charge is too large forperturbative computations which are the mainstay of QED. As a result, the main theoretical tools to explore the theory of the QGP islattice gauge theory.[21][22] The transition temperature (approximately175 MeV) was first predicted by lattice gauge theory. Since then lattice gauge theory has been used to predict many other properties of this kind of matter. TheAdS/CFT correspondence conjecture may provide insights in QGP, moreover the ultimate goal of the fluid/gravity correspondence is to understand QGP. The QGP is believed to be a phase of QCD which is completely locally thermalized and thus suitable for an effective fluid dynamic description.
Production of QGP in the laboratory is achieved by colliding heavy atomic nuclei (called heavy ions as in an accelerator atoms are ionized) at relativistic energy in which matter is heated well above the Hagedorn temperatureTH = 150 MeV per particle, which amounts to a temperature exceeding 1.66 trillionK. This can be accomplished by colliding two large nuclei at high energy (note that175 MeV is not the energy of the colliding beam).Lead andgoldnuclei have been used for such collisions atCERNSPS andBNLRHIC, respectively. The nuclei are accelerated toultrarelativistic speeds (contracting their length) and directed towards each other, creating a "fireball", in the rare event of a collision. Hydrodynamic simulation predicts this fireball will expand under its ownpressure, and cool while expanding. By carefully studying the spherical andelliptic flow, experimentalists put the theory to test.
The cross-over temperature from the normal hadronic to the QGP phase is about156 MeV.[28] The phenomena involved correspond to an energy density of a little less than1 GeV/fm3. Forrelativistic matter, pressure and temperature are not independent variables, so theequation of state is a relation between the energy density and the pressure. This has been found through lattice computations, and compared to bothperturbation theory andstring theory. This is still a matter of active research. Response functions such as thespecific heat and various quark number susceptibilities are currently being computed.
The discovery of the perfect liquid was a turning point in physics. Experiments at RHIC have revealed a wealth of information about this remarkable substance, which we now know to be a QGP.[29] Nuclear matter at "room temperature" is known to behave like asuperfluid. When heated the nuclear fluid evaporates and turns into a dilute gas of nucleons and, upon further heating, a gas of baryons and mesons (hadrons). At the critical temperature,TH, the hadrons melt and the gas turns back into a liquid. RHIC experiments have shown that this is the most perfect liquid ever observed in any laboratory experiment at any scale. The new phase of matter, consisting of dissolved hadrons, exhibits less resistance to flow than any other known substance. The experiments at RHIC have, already in 2005, shown that the Universe at its beginning was uniformly filled with this type of material—a super-liquid—which once the Universe cooled belowTH evaporated into a gas of hadrons. Detailed measurements show that this liquid is a quark–gluon plasma where quarks, antiquarks and gluons flow independently.[30]
Schematic representation of the interaction region formed in the first moments after the collision of heavy ions with high energies in the accelerator.[31]
In short, a quark–gluon plasma flows like a splat of liquid, and because it is not "transparent" with respect to quarks, it can attenuatejets emitted by collisions. Furthermore, once formed, a ball of quark–gluon plasma, like any hot object, transfers heat internally by radiation. However, unlike in everyday objects, there is enough energy available so that gluons (particles mediating thestrong force) collide and produce an excess of the heavy (i.e.,high-energy)strange quarks. Whereas, if the QGP did not exist and there was a pure collision, the same energy would be converted into a non-equilibrium mixture containing even heavier quarks such ascharm quarks orbottom quarks.[31][32]
The equation of state is an important input into the flow equations. Thespeed of sound (speed of QGP-density oscillations) is currently under investigation in lattice computations.[33][34][35] Themean free path of quarks and gluons has been computed usingperturbation theory as well asstring theory.Lattice computations have been slower here, although the first computations oftransport coefficients have been concluded.[36][37] These indicate that themean free time of quarks and gluons in the QGP may be comparable to the average interparticle spacing: hence the QGP is a liquid as far as its flow properties go. This is very much an active field of research, and these conclusions may evolve rapidly. The incorporation of dissipative phenomena into hydrodynamics is another active research area.[38][39][40]
The subject was later revived at RHIC. One of the most striking physical effects obtained at RHIC energies is the effect of quenching jets.[47][48][49] At the first stage of interaction of colliding relativistic nuclei, partons of the colliding nuclei give rise to the secondary partons with a large transverse impulse ≥ 3–6 GeV/s. Passing through a highly heated compressed plasma, partons lose energy. The magnitude of the energy loss by the parton depends on the properties of the quark–gluon plasma (temperature, density). In addition, it is also necessary to take into account the fact that colored quarks and gluons are the elementary objects of the plasma, which differs from the energy loss by a parton in a medium consisting of colorless hadrons. Under the conditions of a quark–gluon plasma, the energy losses resulting from the RHIC energies by partons are estimated as. This conclusion is confirmed by comparing the relative yield of hadrons with a large transverse impulse in nucleon-nucleon and nucleus-nucleus collisions at the same collision energy. The energy loss by partons with a large transverse impulse in nucleon-nucleon collisions is much smaller than in nucleus-nucleus collisions, which leads to a decrease in the yield of high-energy hadrons in nucleus-nucleus collisions. This result suggests that nuclear collisions cannot be regarded as a simple superposition of nucleon-nucleon collisions. For a short time, ~1 μs, and in the final volume, quarks and gluons form some ideal liquid. The collective properties of this fluid are manifested during its movement as a whole. Therefore, when moving partons in this medium, it is necessary to take into account some collective properties of this quark–gluon liquid. Energy losses depend on the properties of the quark–gluon medium, on the parton density in the resulting fireball, and on the dynamics of its expansion. Losses of energy by light and heavy quarks during the passage of a fireball turn out to be approximately the same.[50]
In November 2010, CERN announced the first direct observation of jet quenching, based on experiments with heavy-ion collisions.[51][52][53][54]
Thermal photons and dileptons are important electromagnetic probes of the quark–gluon plasma (QGP) formed in relativisticheavy-ion collisions. Unlike hadrons, which predominantly reflect the final stages of the collision, electromagnetic probes are emitted throughout the entire space–time evolution of the fireball, from the early deconfined phase through the hadronic stage up to kinetic freeze-out, when strong interactions cease. Because photons and leptons interact only electromagnetically, their mean free path is much larger than the size of the collision volume, allowing them to escape the medium with minimal final-state interactions. As a result, they provide direct information on the temperature and space–time dynamics of the matter created in the collision.
A key advantage of thermal dileptons over real photons is the presence of an additional kinematic variable: the invariant mass. While real photons are characterized only by their transverse momentum (pT), lepton pairs are described by both invariant mass (M) and transverse momentum. For thermal radiation, transverse-momentum spectra are sensitive to a combination of temperature and collective expansion velocity (radial flow), which complicates their interpretation. By contrast, the invariant mass is Lorentz invariant and largely insensitive to flow effects, making the dilepton mass spectrum a particularly clean and largely model-independent observable for extracting the true thermal temperature of the emitting medium.
In the intermediate-mass region (IMR), with invariant mass above about 1 GeV, hadronic resonance contributions become small and the electromagnetic spectral function is expected to be approximately flat, as in the black-body case. In this regime, thermal dilepton emission exhibits a nearly exponential, 'Planck-like' mass spectrum, providing direct access to the average temperature of the emitting medium and sensitivity to radiation from the deconfined QGP phase.
The first experimental evidence for thermal dilepton production in relativistic heavy-ion collisions was obtained by theCERES experiment at theCERN Super Proton Synchrotron (SPS), which observed an enhancement of low-mass lepton pairs above known hadronic decay sources. ,[55],[56],[57],[58].[59]These measurements established dileptons as sensitive probes of hot and dense strongly interacting matter and of in-medium modifications of vector mesons.
A major advance was achieved by theNA60 experiment at the SPS, which measured thermal dilepton radiation with unprecedented mass resolution and statistical precision for heavy-ion collisions.
In the low-mass region (M < 1 GeV), NA60 demonstrated that the dilepton excess is dominated by hadronic radiation, primarily π+π− annihilation mediated by a strongly broadened in-medium ρ meson. The measurements provided direct experimental access to the in-medium ρ spectral function and resolved a long-standing controversy regarding its modifications in hot and dense matter. The observed strong broadening, without a significant mass shift, revealed the mechanism related to chiral symmetry restoration near theQCD phase boundary, offering experimental insight into how hadron properties are modified as chiral symmetry is restored in the medium. In addition, the data exhibited clear signatures of collective radial flow, linking the dilepton signal to the dynamics of the expanding fireball and to the evolution of the strongly interacting medium.
In the intermediate-mass region (M ≳ 1.1 GeV), NA60 observed a nearly exponential mass spectrum consistent with thermal radiation from a source with a flat electromagnetic spectral function. Fits to the IMR mass spectrum yielded temperatures exceeding 200 MeV (e.g.T = 205 ± 12 MeV for 1.1 <M < 2.0 GeV andT = 230 ± 10 MeV for 1.1 <M < 2.4 GeV), well above the QCD critical temperatureTc of 155 MeV as determined by lattice QCD. Because invariant mass is Lorentz invariant, these results provide a direct, flow-independent measurement of the medium temperature.
Independent analyses of transverse-mass spectra revealed a characteristic change aroundM = 1 GeV: the effective slope parameter increases with mass in the LMR, consistent with hadronic emission boosted by radial flow, but drops and becomes approximately constant in the IMR, withTeff values around 200 MeV. This behaviour indicated early emission with comparatively little collective flow (i.e. little or no blue shift). NA60 also measured the angular distributions of the excess dileptons and found them to be consistent with isotropy, with vanishing polarization coefficients, supporting an interpretation of the excess as thermal radiation from a randomized medium rather than from strongly directed annihilation processes.,[60],[61],[62],[63],[64].[65]
Taken together, the measured dilepton mass spectra, transverse-momentum distributions, and angular distributions provide a largely model-independent signature of thermal radiation from the hot and dense medium created in heavy-ion collisions and establish thermal dileptons as an experimental thermometer for quark–gluon matter.[66]
Since 2008, there is a discussion about a hypothetical precursor state of the quark–gluon plasma, the so-called "Glasma", where thedressed particles are condensed into some kind of glassy (or amorphous) state, below the genuine transition between the confined state and the plasma liquid.[67] This would be analogous to the formation of metallic glasses, or amorphous alloys of them, below the genuine onset of the liquid metallic state.
Although the experimental high temperatures and densities predicted as producing a quark–gluon plasma have been realized in the laboratory, the resulting matter doesnot behave as a quasi-ideal state of free quarks and gluons, but, rather, as an almostperfect dense fluid.[68] Actually, the fact that the quark–gluon plasma will not yet be "free" at temperatures realized at present accelerators was predicted in 1984, as a consequence of the remnant effects of confinement.[69][70]
A quark–gluon plasma (QGP)[72] or quark soup[73][74] is astate of matter in quantum chromodynamics (QCD) which exists at extremely hightemperature and/ordensity. This state is thought to consist ofasymptotically freestrong-interacting quarks and gluons, which are ordinarily confined bycolor confinement inside atomic nuclei or other hadrons. This is in analogy with the conventional plasma where nuclei and electrons, confined insideatoms byelectrostatic forces at ambient conditions, can move freely. Experiments to create artificial quark matter started at CERN in 1986/87, resulting in first claims that were published in 1991.[75][76] It took several years before the idea became accepted in the community of particle and nuclear physicists. Formation of a new state of matter in Pb–Pb collisions was officially announced at CERN in view of the convincing experimental results presented by the CERNSPS WA97 experiment in 1999,[77][27][78] and later elaborated byBrookhaven National Laboratory'sRelativistic Heavy Ion Collider.[79][80][26] Quark matter can only be produced in minute quantities and is unstable and impossible to contain, and will radioactively decay within a fraction of a second into stable particles throughhadronization; the produced hadrons or their decay products andgamma rays can then be detected. In thequark matter phase diagram, QGP is placed in the high-temperature, high-density regime, whereas ordinary matter is a cold and rarefied mixture of nuclei and vacuum, and the hypotheticalquark stars would consist of relatively cold, but dense quark matter. It is believed that up to a few microseconds (10−12 to 10−6 seconds) after the Big Bang, known as thequark epoch, the Universe was in a quark–gluon plasma state.
The strength of thecolor force means that unlike the gas-like plasma, quark–gluon plasma behaves as a near-idealFermi liquid, although research on flow characteristics is ongoing.[81] Liquid or even near-perfect liquid flow with almost no frictional resistance or viscosity was claimed by research teams at RHIC[82] and LHC'sCompact Muon Solenoid detector.[83] QGP differs from a "free" collision event by several features; for example, its particle content is indicative of a temporarychemical equilibrium producing an excess of middle-energystrange quarks vs. a nonequilibrium distribution mixing light and heavy quarks ("strangeness production"), and it does not allow particle jets to pass through ("jet quenching").
Experiments at CERN's Super Proton Synchrotron (SPS) begun experiments to create QGP in the 1980s and 1990s: the results led CERN to announce evidence for a "new state of matter"[84] in 2000.[85] Scientists at Brookhaven National Laboratory's Relativistic Heavy Ion Collider announced they had created quark–gluon plasma by colliding gold ions at nearly the speed of light, reaching temperatures of 4 trillion degrees Celsius.[86] Current experiments (2017) at theBrookhaven National Laboratory's Relativistic Heavy Ion Collider (RHIC) on Long Island (New York, USA) and at CERN's recentLarge Hadron Collider near Geneva (Switzerland) are continuing this effort,[87][88] by colliding relativistically accelerated gold and other ion species (at RHIC) or lead (at LHC) with each other or with protons.[88] Three experiments running on CERN's Large Hadron Collider (LHC), on the spectrometersALICE,[89]ATLAS andCMS, have continued studying the properties of QGP. CERN temporarily ceased collidingprotons, and began collidinglead ions for the ALICE experiment in 2011, in order to create a QGP.[90] A new record breaking temperature was set byALICE: A Large Ion Collider Experiment at CERN in August 2012 of about 5.5 trillion (5.5×1012) kelvin as claimed in their Nature PR.[91]
The formation of a quark–gluon plasma occurs as a result of astrong interaction between thepartons (quarks, gluons) that make up the nucleons of the colliding heavy nuclei called heavy ions. Therefore, experiments are referred to as relativistic heavy ion collision experiments. Theoretical and experimental works show that the formation of a quark–gluon plasma occurs at the temperature of T ≈ 150–160 MeV, the Hagedorn temperature, and an energy density of ≈ 0.4–1 GeV / fm3. While at first a phase transition was expected, present day theoretical interpretations propose a phase transformation similar to the process of ionisation of normal matter into ionic and electron plasma.[92][93][94][95][26]
The central issue of the formation of a quark–gluon plasma is the research for theonset of deconfinement. From the beginning of the research on formation of QGP, the issue was whetherenergy density can be achieved in nucleus-nucleus collisions. This depends on how much energy each nucleon loses. An influential reaction picture was the scaling solution presented byBjorken.[96] This model applies to ultra-high energy collisions. In experiments carried out at CERN SPS and BNL RHIC more complex situation arose, usually divided into three stages:[97]
Primary parton collisions and baryon stopping at the time of complete overlapping of the colliding nuclei.
Redistribution of particle energy and new particles born in the QGP fireball.
The fireball of QGP matter equilibrates and expands before hadronizing.
More and more experimental evidence points to the strength of QGP formation mechanisms—operating even in LHC-energy scale proton-proton collisions.[24]
Shuryak, Edward (2024).Quark-Gluon Plasma, Heavy Ion Collisions and Hadrons. World Scientific Lecture Notes in Physics. Vol. 85. Singapore: World Scientific.doi:10.1142/13570.ISBN978-981-128234-8.
Damjanovic, Sanja; Metag, Volker; Schukraft, Jürgen (2024). "Research at the CERN accelerators from 1983 onwards – ultra-relativistic heavy-ion physics: searching for the quark–gluon plasma". In Damjanovic, Sanja; Metag, Volker; Schukraft, Jürgen (eds.).Hans Joachim Specht – Scientist and Visionary. Springer Biographies. Cham: Springer Nature. pp. 58–93.doi:10.1007/978-3-031-92353-1.ISBN978-3-031-92352-4.
Review articles with a historical perspective of the field
Kajantie, K.; Miettinen, H. I. (1981). "Temperature measurement of quark-gluon plasma formed in high-energy nucleus-nucleus collisions".Zeitschrift für Physik C: Particles and Fields.9 (4). Springer:341–348.Bibcode:1981ZPhyC...9..341K.doi:10.1007/BF01548770.
^Bhalerao, Rajeev S. (2014). "Relativistic heavy-ion collisions". In Mulders, M.; Kawagoe, K. (eds.).1st Asia-Europe-Pacific School of High-Energy Physics. CERN Yellow Reports: School Proceedings. Vol. CERN-2014-001, KEK-Proceedings-2013–8. Geneva: CERN. pp. 219–239.doi:10.5170/CERN-2014-001.ISBN978-92-9083-399-4.OCLC801745660.S2CID119256218.
^Heinz, Ulrich; Jacob, Maurice (2000-02-16). "Evidence for a New State of Matter: An Assessment of the Results from the CERN Lead Beam Programme".arXiv:nucl-th/0002042.
^Collaboration, STAR; Adams, J. (2005-04-26), "Experimental and theoretical challenges in the search for the quark–gluon plasma: The STAR Collaboration's critical assessment of the evidence from RHIC collisions",Nuclear Physics A,757 (1–2):102–183,arXiv:nucl-ex/0501009,Bibcode:2005NuPhA.757..102A,doi:10.1016/j.nuclphysa.2005.03.085
^A. Bazavov, H.-T. Ding, P. Hegde, O. Kaczmarek, F. Karsch, N. Karthik, E. Laermann, Anirban Lahiri, R. Larsen, S.-T. Li, Swagato Mukherjee, H. Ohno, P. Petreczky, H. Sandmeyer, C. Schmidt, S. Sharma, P. Steinbrecher,Chiral crossover in QCD at zero and non-zero chemical potentials,Physics Letters B,Volume 795,2019,Pages 15–21,ISSN 0370-2693,https://doi.org/10.1016/j.physletb.2019.05.013.
^"Celebrating a Decade of Brewing Perfection".Brookhaven National Laboratory. 26 June 2015.Archived from the original on 28 June 2017. Retrieved2020-04-15.Berndt Müller, Brookhaven Lab's Associate Laboratory Director for Nuclear and Particle Physics.
^Letter from Berndt Müller to Johann Rafelski, reproduced in "Discovery of Quark–Gluon Plasma: Strangeness Diaries". The European Physical Journal Special Topics. 229 (1): pp.40–41doi:10.1140/epjst/e2019-900263-x. ISSN 1951-6401.
^Adcox, K.; Adler, S.S.; Afanasiev, S.; Aidala, C.; Ajitanand, N.N.; Akiba, Y.; Al-Jamel, A.; Alexander, J.; Amirikas, R.; Aoki, K.; Aphecetche, L. (2005). "Formation of dense partonic matter in relativistic nucleus–nucleus collisions at RHIC: Experimental evaluation by the PHENIX Collaboration".Nuclear Physics A.757 (1–2):184–283.arXiv:nucl-ex/0410003.Bibcode:2005NuPhA.757..184A.doi:10.1016/j.nuclphysa.2005.03.086.S2CID119511423.
^Adams, J.; Aggarwal, M.M.; Ahammed, Z.; Amonett, J.; Anderson, B.D.; Arkhipkin, D.; Averichev, G.S.; Badyal, S.K.; Bai, Y.; Balewski, J.; Barannikova, O. (2005). "Experimental and theoretical challenges in the search for the quark–gluon plasma: The STAR Collaboration's critical assessment of the evidence from RHIC collisions".Nuclear Physics A.757 (1–2):102–183.arXiv:nucl-ex/0501009.Bibcode:2005NuPhA.757..102A.doi:10.1016/j.nuclphysa.2005.03.085.S2CID119062864.
^Back, B.B.; Baker, M.D.; Ballintijn, M.; Barton, D.S.; Becker, B.; Betts, R.R.; Bickley, A.A.; Bindel, R.; Budzanowski, A.; Busza, W.; Carroll, A. (2005). "The PHOBOS perspective on discoveries at RHIC".Nuclear Physics A.757 (1–2):28–101.arXiv:nucl-ex/0410022.Bibcode:2005NuPhA.757...28B.doi:10.1016/j.nuclphysa.2005.03.084.
^Agakichiev, G.; et al. (CERES) (1995). "Enhanced production of low mass electron pairs in 200 GeV/u S–Au collisions at the CERN SPS".Physical Review Letters.75:1272–1275.doi:10.1103/PhysRevLett.75.1272.
^G. Agakichiev et al. (CERES/NA45 Collaboration) (1998). "Low-mass e+e− pair production in 158 AGeV Pb–Au collisions at the CERN SPS and its dependence on multiplicity and transverse momentum".Physics Letters B.422:405–412.arXiv:nucl-ex/9712008.doi:10.1016/S0370-2693(98)00083-5.{{cite journal}}: CS1 maint: numeric names: authors list (link)
^G. Agakichiev et al. (CERES Collaboration) (2005). "e+e− pair production in Pb–Au collisions at 158 GeV per nucleon".European Physical Journal C.41 (4):475–513.arXiv:nucl-ex/0506002.doi:10.1140/epjc/s2005-02272-3.
^Arnaldi, R.; et al. (NA60 Collaboration) (2009). "Evidence for the production of thermal-like muon pairs with masses above 1 GeV/c2 in 158 A GeV indium–indium collisions".The European Physical Journal C.59:607–623.doi:10.1140/epjc/s10052-008-0857-2.
^Damjanovic, Sanja; Ruben Shahoyan; Hans J. Specht; et al. (NA60 Collaboration) (2009)."NA60: In hot pursuit of thermal dileptons".CERN Courier. Vol. 49, no. 11. CERN. pp. 31–34.
^Damjanovic, Sanja; Volker Metag; Jürgen Schukraft (2024). "Research at the CERN accelerators from 1983 onwards – ultra-relativistic heavy-ion physics: searching for the quark–gluon plasma". In Damjanovic, Sanja; Metag, Volker; Schukraft, Jürgen (eds.).Hans Joachim Specht – Scientist and Visionary. Springer Biographies. Cham: Springer Nature. pp. 58–93.doi:10.1007/978-3-031-92353-1.ISBN978-3-031-92352-4.
^Bohr, Henrik; Nielsen, H. B. (1977). "Hadron production from a boiling quark soup: quark model predicting particle ratios in hadronic collisions".Nuclear Physics B.128 (2): 275.Bibcode:1977NuPhB.128..275B.doi:10.1016/0550-3213(77)90032-3.
^Müller, Berndt (2016), "A New Phase of Matter: Quark-Gluon Plasma Beyond the Hagedorn Critical Temperature", in Rafelski, Johann (ed.),Melting Hadrons, Boiling Quarks - from Hagedorn Temperature to Ultra-Relativistic Heavy-Ion Collisions at CERN, Springer International Publishing, pp. 107–116,arXiv:1501.06077,doi:10.1007/978-3-319-17545-4_14,ISBN978-3-319-17544-7,S2CID119120988
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