arXiv:1501.06077v1 [nucl-th] 24 Jan 2015 n oa aesi(dtr,Srne ulses 2015 Publishers, Springer (editor), Rafelski Johan and tutr fmte ttmeaue rae than greater temperatures at matter of structure ∗ hudapyt atri h al nvre hi dis- matter. their QCD universe, cold on early focused the mostly in is matter cussion argument to this that apply unconfined very note of should they at composed although matter However, be inter- therefore quarks. should weakly densities and are quark distances large quarks short that at implies asymptotic acting the QCD and that of 1975 Collins model. early freedom with in bootstrap began [3] quandary observation statistical Perry’s this the of resolution in The meaningless was is ino tt fhdoi atrhsasnuaiyat singularity a the in has MeV values 150 matter empirical range with hadronic temperature, of Hagedorn the state of tion state? times? early of such equation at its universe was the What filled 10 that than matter less the of times at MeV 200 µ of experienced tracing excess pos- have in was must By universe it temperatures the times that early model. conclude very to Big-Bang to sible evolution hot cosmic the the back for unambigu- provided evidence cosmic had ous the 1965 of in discovery The background microwave [2]. a cosmology posed for hadrons quandary of its spectrum late with mass [1] growing the model exponentially in bootstrap accessible statistical energies Hagedorn’s 1960s, the at production particle oapa in appear To fe h nta i ag u htwstestructure the was what But Bang. 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I and and at RHIC, predicts, at plasma theory then than SPS, more the finds strangen at the prog first experimental develop at the how help idea, i recall to and experimentally deconfinement effort gluon studied and personal wa my be This here could describe matter. transformation interacting phase strongly temperatu QCD of “critical” phases the ye plasma as 30 pl gluon interpretation than quark-gluon modern more the its transformation into the of with characterization begin and recollections discovery the to erc h eeomnsfo aeonscneto limi a of concept Hagedorn’s from developments the retrace I T < H eateto hsc,Dk nvriy uhm C27708-0 NC Durham, University, Duke Physics, of Department PLASMA < e hs fMte:QakGunPlasma Quark-Gluon Matter: of Phase New A 0 e.Akn htthe what Asking MeV. 200 eodteHgdr rtclTemperature Critical Hagedorn the Beyond rohvnNtoa aoaoy po,N 17,USA 11973, NY Upton, Laboratory, National Brookhaven yRl Hagedorn Rolf by entM¨uller Berndt T H h aeontmeauetu curdtemeaning temperature the critical gluons. acquired and the thus quarks of of temperature plasma Hagedorn colored a a The from to changes hadrons matter the of equa- as gas interacting gas the strongly resonance where in hadronic Hagedorn’s point singularity of the state of to tion interpretation an posed h 90 eas ftelc frlal ahmtclor mathematical QCD. reliable solve of to lack techniques the numerical of because 1970s the discontinuous a undergoes transition. matter interacting strongly of ag hoyadltrfrfl C,md tpossible interacting it strongly of made state QCD, of pure matter full equation the the for for calculate later first to and QCD, theory lattice of gauge function partition the iini h bec fabro xes oee,a However, excess. baryon a of tran- temperature absence phase quasi-critical the discontinuous from in a separated by sition not plasma is quark-gluon resonances the matter hadronic that showed of [5–7], composed result definitive a to converged es fsaitclpyisfrmte ihalrebaryon large a with traditional matter the excess. for physics in statistical transition of phase sense first-order a into turn h ucpiiiyascae ihtesaa ur den- quark – scalar susceptibility the chiral with sity the associated which susceptibility at the temperature the as 1 ml e ayndniyde o xii singularity. o a zero exhibit at not QCD does of density as ha state baryon QCD of transition, net lattice equation tha small fact, phase the fact In that order the shown dual. with second string conclusively (approximate) connected a an but spectrum has to surmised, QCD mass related Parisi growing and not exponentially Cabibbo is the QCD that of know now We trigi h al 90,MneCrosmltosof simulations Monte-Carlo 1980s, early the in Starting h ∗ ψψ ¯ esprtn h arngsadquark- and gas hadron the separating re binitio ab fte“efcl”lqi quark-gluon liquid “perfectly” the of y r g fHgdr’ rgnlconcept original Hagedorn’s of ago ars i saa e tt fmte.My matter. of state new a as asma a rcee ont netgt this investigate to soon proceeded ram olwdb h elzto htthe that realization the by followed s s xeietlsgaue fquark of signatures experimental ess igtmeauefrhdoi matter hadronic for temperature ting ek.Tesot rs-vri xetdto expected is cross-over smooth The peaks. – 1 iheeg ula olsos I collisions. nuclear high-energy n uniaiepeitoswr mosbein impossible were predictions Quantitative te,epcal h erhfra for search the especially ities, fe h ae h experiment the case, the often s hs acltos hc aerecently have which calculations, These . atc C results QCD Lattice 0,UAand USA 305, T T c c ≈ twihtecomposition the which at 5 e a edefined be can MeV 155 r s t 2

The lattice simulations showed that Hagedorn’s model without imposing on him. One puzzling aspect of the ex- of a hadron resonance gas with an exponentially growing perimental observation of thermal particle emission that mass spectrum describes the equation of state of QCD is still occupying theorists today – how a large fraction of matter and many other observables very well for tem- the kinetic energy carried by the incident particles could peratures below Tc. The precision of the lattice QCD be thermalized within a time of order 1 fm/c – led to my simulations is now good enough to distinguish between interest in the chaotic properties of non-abelian gauge the equation of state of a hadron gas made up of the res- theories. I vividly recall Hagedorn’s excitement after he onances tabulated in the Particle Data Book or that of a listened to my talk about our numerical studies of dy- Hagedorn resonance gas. The numerical results point to namical chaos of the Yang-Mills field at the workshop in a continuation of the exponential growth of the hadron Divonne [15]. mass spectrum beyond the reach of direct detection of resonances and thus support Hagedorn’s hadronic boot- strap model [8]. II. PATH TO DISCOVERY OF THE QGP The implied existence of many unknown hadron res- onances may also be present in the strange baryon sec- QGP observables tor [9]. Above Tc the density of states grows much less rapidly and eventually approaches that of a perturba- The biggest challenge on the way to discovery was find- tively interacting quark-gluon plasma composed of mas- ing signatures that could provide evidence that nuclear sive quasiparticles, confirming the notion that the Hage- matter had made the transition to a quark-gluon plasma dorn temperature signals the transition from a hadron for a brief period during the collision. One either had to resonance gas to a new state of matter. look at penetrating probes, such as photons and lepton pairs [16], that could escape from the hot fireball, or at probes that retained their identity under the action of Hot nuclear matter the strong interactions in the final state, such as quark flavor. The next critical step was the realization, arising most Shuryak took the matter further by evoking quark and prominently from discussions in the CERN Theory Di- gluon degrees of freedom in ppreactions and focusing on 2 electromagnetic probes and charm quarks as signatures vision , that temperatures in the range of Tc and even beyond could be created in the laboratory by colliding for the formation of a thermal QCD plasma [17, 18]. heavy atomic nuclei at sufficiently high energies. Rafelski, in collaboration with Hagedorn, Danos, and my- self, focused on strange quarks whose mass is sufficiently The experimental study of relativistic heavy ion colli- low for them to be produced thermally in the quark-gluon sions with stationary targets had commenced at the Be- plasma [19]. valac in the mid-1970s, but the energies available there The strangeness argument was not simply that strange were recognized to be insufficient to reach Tc. The CERN quarks and antiquarks would be produced abundantly at SPS could provide much higher energies, and back-of-the- temperatures above Tc, but that baryons containing mul- envelope calculations suggested that temperatures near tiple strange quarks would be produced copiously and and above Tc would be reached if the nuclear matter in in chemical equilibrium when the quark-gluon plasma the colliding nuclei thermalized rapidly. Hagedorn and hadronizes by recombination of the deconfined quarks Rafelski extended the statistical bootstrap model to mat- into hadrons. A calculation of thermal strange quark pair ter with a baryon excess and found that under certain production in the quark-gluon plasma [20] confirmed that assumptions the equation of state exhibited a first-order flavor equilibrium could, indeed, be reached on the time phase transition [12]. scales of a relativistic heavy ion collision and showed that I had the good fortune of meeting Hagedorn during thermal gluons played a crucial role in the flavor equili- several visits with Johann at CERN during this forma- bration process. tive period in the late 1970s. My conversations with them Following on the recognition of the abundant inspired my own interest in hot QCD and soon thereafter strangeness in quark-gluon plasma, Johann and I em- resulted in our joint work on the thermal properties of the barked on the task of developing a bulk hadronization QCD vacuum [13] and on particle production with exact model that would enable us to make quantitative predic- symmetry in proton-antiproton annihilation [14]. What tions for the strange antibaryon signature of the quark- impressed me most on these occasions was Hagedorn’s gluon plasma. Our effort grew over two years, in col- willingness to share his thoughts with a young scientist laboration with Peter Koch, into a Physics Reports ar- ticle [21]. Among the highlights of this work is the development of the recombination and fragmentation- recombination models of quark-gluon hadronization that 2 What distinguished these discussions from other theoretical spec- ulation in the mid-1970s was that the focus was on thermal prop- in slightly modified form remain in use today [22]. We en- erties of strongly interacting matter, rather than properties of forced conservation laws, assured increase of entropy, and compressed baryonic matter (see e.g. Lee [10, 11].) quantified the production of strange (anti-)baryons with 3 their strangeness content. These developments set clear and thermal equilibrium. Because the matter is already experimental goals for the forthcoming SPS strangeness expanding very rapidly when the transition to a hadron experiments which are further discussed below and in the gas occurs, many observables are nearly unaffected by contribution of Emanuele Quercigh. final-state interactions among hadrons. The low viscosity of the liquid quark-gluon plasma implies that the interac- tions among quarks and gluons contained in it are strong. SPS results Other observations, such as the strong suppression of high-momentum hadrons and of charmonium, support The heavy ion experiments at the SPS, which com- this conclusion (for early reviews, see: [39, 40]). menced in 1986/87, impressively confirmed these ideas. The chemical composition of the hadrons emitted from the collisions can be well described by a chemical near Experiments at LHC equilibrium gas at a temperature close to Tc and a baryon chemical potential that varies strongly with the collision Experiments at even higher energies at the LHC have energy [23]. The strong enhancement and full chemi- impressively confirmed the nature of QCD matter above cal equilibration of baryons and anti-baryons containing Tc as a strongly coupled, liquid quark-gluon plasma [41]. multiple strange quarks [24, 25] could only be explained A careful analysis of the LHC data revealed that the aver- if hadrons containing valence quarks of all three light fla- age strong coupling at the higher energy density reached vors were “born” into thermal abundances [26–28]. at LHC is slightly weaker than at RHIC [42], in accor- However, the SPS data did not provide other corrob- dance with the running of αs with temperature. The orating evidence for the existence of a thermal phase reduced coupling is also reflected in a somewhat larger of matter at temperatures above Tc from which these shear viscosity-to-entropy density ratio [43]. hadrons formed by statistical emission. The (unpub- In addition to consolidating the insights gained at lished) CERN announcement of a new state of matter [29] RHIC, the much higher energy available at LHC permit in 2000 was thus greeted with skepticism by many physi- more detailed studies of the event-by-event fluctuations cists. Experiments with heavy ion collisions at much of the collective flow pattern, which reflect the quantum higher energies were needed to resolve this issue. fluctuations of the initial energy density distribution. En- abled by the design of the LHC detectors, the higher en- ergy also allows for precise studies of the phenomenon Experiments at RHIC of jet quenching that was first discovered at RHIC. And finally, the large yield of primordially produced charm Commencing at RHIC in year 2000, these experiments quarks at LHC results in abundant late-stage recombina- allowed to access a new kinematic domain, in which the tion of charm-anticharm quark pairs into charmonium, produced matter is imprinted from the start with a nearly providing additional evidence for the deconfinement of boost invariant longitudinal flow profile. An analyti- quarks in the QCD plasma phase. cal solution of relativistic hydrodynamics for this initial condition had been found by Bjorken [30], and it pro- vided the basis for a systematic investigation of the col- Beam energy scan at RHIC lective properties of the matter formed in the nuclear collisions [31–34]. The fact that the transverse geometric How far down in beam energy does the phenomenology profile of the reaction zone and the initial energy density discovered and established at RHIC persist? Where is the fluctuations from event to event could be correlated with threshold below which no quark-gluon plasma is formed? the patterns observed in the collective flow of the emit- Did the SPS experiments produce a quark-gluon plasma? ted hadrons made it possible to pin down the transport In order to address these open questions, RHIC has re- properties of the expanding matter, which was shown to cently collided heavy ions at lower energies, down to have an extraordinarily low shear viscosity, relative to its √sNN =7.7 GeV. An extensive analysis of the data gath- entropy density [35–37]. The matter was thus shown to ered in this beam energy scan is now available [44, 45]. It be a liquid at temperatures well above Tc. shows that the matter produced in collisions down to the A detailed study of the subtle variations of the flow top SPS energy, √sNN = 19.6 GeV, exhibits some of the profile between different hadron species revealed that same characteristics as that produced at the top RHIC these variations disappeared when all hadrons were as- energy, √sNN = 200 GeV. sumed to be formed by recombination of deconfined, col- However, there are noticeable differences. Matter pro- lectively flowing quarks when the matter cooled below duced at the lower beam energies contains a larger excess Tc [38]. Together, these observations provided strong ev- of baryons resulting in a different chemical composition idence for the notion that the matter formed in nuclear of the emitted hadrons; energetic hadrons are no longer collisions at RHIC is, indeed, a plasma of deconfined suppressed at lower energies; and no direct photon sig- quarks and gluons, which behaves as a nearly inviscid nal has been observed. Thus it is quite likely that the liquid and decays by the emission of hadrons in chemical CERN experiments succeeded in breaking through the 4 thermal barrier of the Hagedorn temperature, but it is will study the transport of c and b quarks in the plasma still unclear what kind of baryon-rich matter they pro- in great detail and hopefully detect clues to its internal duced and whether it exhibited collective behavior at the structure. Jets explore multiple length scales as they parton level. Theoretical models that can more reliably develop inside the matter after the initial hard scattering describe nuclear reactions at these lower energies will be event. Extensive jet measurement programs, which are needed to finally address this issue. already underway at the LHC, are planned for RHIC in the decade ahead [48].

Next steps III. OUTLOOK AND CONCLUSIONS Where do we go from here? Two major questions re- main to be answered: (1) Is there a critical point in the Our understanding of the structure and properties of phase diagram of QCD matter where the cross-over from hadronic matter at high energy density has made tremen- hadron resonance gas to the quark-gluon plasma turns dous progress since the days when the question first arose into a true phase transition, and where is it located in in full urgency in the late 1960s, and remarkable discover- T and µ? (2) What are the effective constituents of the ies have been made along the way. We have established liquid quark-gluon plasma? that Hagedorn’s gas of hadron resonances turns into a The first question will be addressed in a second, high liquid quark-gluon plasma when heated above 155 MeV, statistics beam energy scan that is planned to be carried quite an extraordinary phenomenon in itself. We have out in 2018–19 at RHIC after a luminosity upgrade of discovered a liquid that comes very close to the quantum the collider at low beam energies. Physicists will then bound on the shear viscosity imposed by unitarity. And look for telltale signs of a phase transition, including we have learned that the statistical and collective proper- critical fluctuations in baryon number or large event-by- ties of the flowing quark-gluon plasma get imprinted onto event fluctuations caused by spinodal decomposition of the emitted hadrons in a characteristic way that makes the matter at the phase boundary. A recent discussion it possible to experimentally determine the thermal and of the theoretical and experimental challenges of locating chemical properties of the QCD phase boundary. Rolf the QCD critical point can be found in [47]. Hagedorn would surely be satisfied to witness that the Addressing the second question requires probes that questions he helped pose fifty years ago have proved to are sensitive to the structure of the quark-gluon plasma be so extraordinarily fertile. at shorter than thermal length scales. Two such probes Acknowledgement: I thank W. A. Zajc, J. Rafelski, are heavy quarks and jets. The experiments at LHC and and U. Heinz for constructive comments. This work was now at RHIC are equipped with powerful vertex detectors supported by Grant no. DE-FG02-05ER41367 from the that can identify hadrons containing heavy quarks. They U. S. Department of Energy.

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