Phase diagram of strongly interacting matter: the last 20 years at the CERN SPS

Twenty years ago, on February 10, 2000, the CERN Director General Luciano Maiani announced: The combined data coming from the seven experiments on CERN’s Heavy Ion programme have given a clear picture of a new state of matter. This result verifies an important prediction of the present theory of fundamental forces between quarks. This report briefly reviews studies of the phase diagram of strongly interacting matter with relativistic nuclear collisions at the CERN Super Proton Synchrotron which followed the CERN’s press release on the quark-gluon plasma discovery. An attempt to formulate priorities for future measurements at the CERN SPS closes the paper. The report is dedicated to David Blaschke who celebrated his 60th birthday in 2019. David’s contribution to the studies presented here was very significant.


Introduction
The report is organized along Karl Popper's view of scientific method: where P S1 is an initial problem situation, T T 1 and EE1 stand for tentative theories and error elimination, respectively, and P S2 is a resulting new problem situation. The problem situation emerged after the quark-gluon plasma discovery at the CERN SPS is presented in Section 2. Tentative theories constructed to answer questions motivated by the experimental data are summarized in Section 3. Measurements which were requested to falsify the tentative theories are reviewed in Section 4. A sketch of a new problem situation created by new experimental results closes the paper, Section 5. Left: Artistic sketch of the two phases of strongly interaction matter, hadronresonance gas and quark-gluon plasma. Middle: Phase diagram of QCD in temperature T and baryon chemical potential µB, and the region covered by running or planned experiments [3]. The density range covered by LHC, LHC-FT and SPS experiments is indicated by the shaded areas in the figure. The lower boundary of the grey and blue shaded area follows the chemical freeze-out. The upper boundary relates to the parameters at the early stage of the collisions. The potential deconfinement critical point is labelled with d-CP, the onset of deconfinement with OD. The black line at small temperatures and high densities shows the nuclear liquid-gas transition, also ending in a critical point n-CP. The density range of other experiments is indicated in the bar below the figure. This includes RHIC at BNL, NICA at JINR, SIS100 at FAIR, J-PARC-HI at J-PARC, the Nuclotron at JINR (NUCL), and HIAF at HIRFL. Right: Evolution of a heavy-ion collision at high energies. Successive snapshots of a central collision are shown versus time.

Problem situation around 2000
On February 10, 2000 the CERN Director General Luciano Maiani said: The combined data coming from the seven experiments on CERN's Heavy Ion programme have given a clear picture of a new state of matter. This result verifies an important prediction of the present theory of fundamental forces between quarks. It is also an important step forward in the understanding of the early evolution of the universe. We now have evidence of a new state of matter where quarks and gluons are not confined. There is still an entirely new territory to be explored concerning the physical properties of quark-gluon matter. The challenge now passes to the Relativistic Heavy Ion Collider at the Brookhaven National Laboratory and later to CERN's Large Hadron Collider.
This announcement summarized major achievements [1] of heavy-ion experiments collecting data during the first twenty years of heavy-ion physics at the CERN SPS, for recent review see reference [2]. The measurements were motivated by expectations that matter at very high densities may exist in a state of quasi-free quarks and gluons, the quark-gluon plasma (QGP) and this new state of matter can be created in heavyion collisions at sufficiently high collision energies. Moreover, by changing collision energy and nuclear mass number one changes macroscopic parameters of the created matter -its volume, energy, and net baryon number. This allows to move across the phase diagram of strongly interacting matter, see illustration plots in Figure 1.
The experimental search for a quark-gluon plasma in heavy ion collisions at the CERN SPS was shaped by several model predictions of possible QGP signals: -enhanced production of strange and multi-strange hadrons from the QGP [4], -suppressed production of charmonium states, in particular J/ψ mesons [5], -characteristic radiation of photons and dilepton pairs from the QGP [6].
They were confirmed by the experimental data from the CERN SPS experiments, for detail see reference. [2].
This was in fact the moment when the majority of heavy-ion physicists moved to study heavy-ion collisions at much higher energies at the Relativistic Heavy Ion Collider (RHIC) of Brookhaven National Laboratory (BNL) and prepare measurements at the CERN LHC. Rich and precise results obtained during the period of 2000-2010 at RHIC [7][8][9][10] and 2009-2020 at LHC [11] provided extensive information on the properties of the QGP. There are no doubts about QGP formation at the early stage of nucleus-nucleus (A+A) collisions at the top SPS, and all the more at RHIC and LHC energies.
The situation after the announcement of the QGP discovery in 2000 at CERN was however rather confusing. Many were pretty sure about its formation in central Pb+Pb collisions at the top SPS energy, but unambiguous evidence of the QGP state was still missing. Questions marks concerning the interpretation of the observed effects -the strangeness enhancement and J/ψ suppression -started to accumulate, for detail see reference [2]. Needless to say that the Nobel prize for the QGP discovery was not yet awarded. This may be attributed to the difficulty of obtaining unique and quantitative predictions of the expected QGP signals from the theory of strong interactions, QCD.

Tentative theories
Difficulties in interpretation of the QGP signatures forced scientists to rethink the QGP-hunt strategy. The emerging new strategy was similar to the one followed by physics studying molecular liquids and gases. In these essentially simpler and familiar cases it is also sometimes difficult to distinguish the properties of a dense gas from those of a liquid. It is much easier to identify the effects of the liquid-gas transition. Thus, if one believes that the QGP is formed in central Pb+Pb collisions at the top SPS energy one should observe qualitative signals of the transition to the QGP at a lower collision energy. Several such signals were predicted within the statistical model of the early stage [12]. Their observation would serve as strong evidence of QGP creation in heavy-ion collisions at high enough collision energies.
These arguments motivated some of us to propose in 1997 the collision energy scan at the CERN SPS with the aim to search for the onset of deconfinement [13,14]. It was the beginning of the search for the critical structures in heavy-ion collisions, for detail see references [2,15].
Some years later the workshop Tracing the onset of deconfinement in nucleusnucleus collisions, ECT* Trento, April 24-29, 2004, summarized the results from the energy scan programme at the CERN SPS and concluded that future measurements in the SPS energy range are needed [22]. The goal is to search for the deconfinement critical point and study system size dependence of the onset of deconfinement. Possibilities to perform these measurements at the CERN SPS, FAIR SIS300 and RHIC were discussed. The event initiated a series of the Critical point and onset of   The experimental search for the d-CP in A+A collisions at the CERN SPS was shaped by several model predictions (for detail see Ref. [23]) of its potential signals: -characteristic multiplicity fluctuations of hadrons [23][24][25][26], -enhanced fluctuations of (pion multiplicity)-(transverse momentum) [27].
The signals were expected to have a maximum in the parameter space of collision energy and nuclear mass number of colliding nuclei -the hill of fluctuations [28], see Figure 2 (bottom).   [29], see text for details and more references.

Error elimination
at 40A GeV. The data were registered by NA49, NA45, NA50 and NA57. In 2000 a beam at 80A GeV was delivered to NA49 and NA45. The program was completed in 2002 by runs of NA49 and NA60 at 20 and 30A GeV. Thus, together with the previously recorded data at 158A GeV, NA49 gathered data at five collision energies. Other experiments collected data at two (NA50, NA57) or three (NA45, NA60) energies. In 2010 the beam energy scan programme BES started at RHIC with the aim of covering the low energy range overlapping with the CERN SPS and providing important consistency checks on the measurements.
Results on the collision energy dependence of hadron production in central Pb+Pb collisions from the onset-of-deconfinement search programme at the CERN SPS [30,31] appeared to be consistent with the predicted signals (for review see Ref. [20]): -The average number of pions per wounded nucleon, N π / W , in low energy Pb+Pb collisions is smaller that this value in p+p reactions. This relation is however changed to the opposite at collision energies larger than ≈30A GeV, the so-called kink structure.
-The collision energy dependence of the K + / π + ratio shows the so-called horn structure. Following a fast rise the ratio passes through a maximum in the SPS range, at approximately 30A GeV, and then decreases and settles to a plateau value at higher energies. This plateau was found to continue up to the RHIC and LHC energies.
-The collision energy dependence of the inverse slope parameter of the transverse mass spectra, T * , of charged kaons shows the so-called step structure. Following a fast rise the T * parameter passes through a stationary region (or even a weak minimum for K − ), which starts at the low SPS energies, approximately 30A GeV, and then enters a domain of a steady increase above the top SPS energy. Figure 3 shows examples of the most recent plots [29] illustrating the observation of the onset-of-deconfinement signals. As seen data from the RHIC BES I programme (2010-2014) and LHC (see Ref. [29] for references to original experimental papers) confirm the NA49 results and their interpretation.  interactions at six beam momenta in the range from 13A GeV/c to 158A GeV/c. In the following years data on Be+Be, Ar+Sc, Xe+La and Pb+Pb collisions were recorded, see Figure 4 (left) for an overview.
Many experimental results have already been obtained within the d-CP search programmes at SPS, for a recent review see reference [35]. In particular, the hill of fluctuations was expected in the collision momentum -nuclear mass number plane (see Fig. 2 (bottom)). Measurements of (pion multiplicity)-(transverse momentum) fluctuations from NA61/SHINE shown in Figure 4 (right) do not show this feature [34]. The analysis of the recorded data continues, various fluctuation quantities predicted to be sensitive to d-CP are studied. Thus many new results from the programme are expected in the years to come.
In parallel to the d-CP search at the CERN SPS a search is carried out at BNL RHIC, for recent reviews see references [35,36].

Problem situation around 2020
Understanding charm production. Data on charm quark production at the CERN SPS collision energies are very sparse. Systematic results are crucial to understand precise results on charmonia production by NA38, NA50 and NA60 in the context of the onset of deconfinement. Moreover, a collision energy scan in the onset of deconfinement region to measure open and hidden charm production in Pb+Pb collisions and establish the impact of the onset on the heavy quark sector is essential.
This requires high statistics data collected with detectors optimized for open and hidden charm measurements. Charm measurements are planned by NA61/ SHINE [37], NA60+ [38] at the CERN SPS, they are considered by MPD [39] at NICA and JHITS [40] at J-PARC-HI MR.
Detailed physics arguments and possible experimental set-ups are presented in references [37,38].
Understanding system size dependence. Measurements of the system size dependence of hadron production properties at different collision energies were carried out by NA61/SHINE to search for the d-CP and to establish system size dependence of effects related to the onset of deconfinement. As a result an unexpected phenomenon has been discovered. Its presentation requires a brief introduction.  5. Measurements of the K + /π + ratio in p+p, Be+Be, Ar+Sc and Pb+Pb collisions: system size dependence at 150A GeV/c [44] (left) and collision energy dependence [29] (right). Predictions of the Wounded Nucleon Model [42] and Hadron-Resonance Gas Model [45] are shown for comparison (left). There are two models often used to obtain reference predictions concerning the system-size dependence of hadron production properties [41] -the Wounded Nucleon Model (WNM) [42] and the Statistical Model (SM) [43]. For the K + /π + ratio at the CERN SPS energies they are: -The WNM prediction: the K + /π + ratio is independent of the system size (number of wounded nucleons).
-The SM prediction: in the canonical formulation incorporating global quantum number conservation the K + /π + ratio increases monotonically with the system size and approaches the limit given by the grand canonical approximation of the model. The rate of this increase is the fastest for small systems.

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The European Physical Journal Special Topics    6 show the unexpected result [44,46]. The K + /π + ratio in Figure 5 and the scaled variance of the multiplicity distribution at 150A GeV/c in Figure 6 are similar in inelastic p+p interactions and in central Be+Be collisions, whereas they are different in central Ar+Sc collisions which are close to central Pb+Pb collisions. Both reference models, WNM and SM (represented here by the Hadron-Resonance Model [45]), qualitatively disagree with the data. The WNM seems to work in the collisions of light nuclei (up to Be+Be) and becomes qualitatively wrong for heavy nuclei (like Pb+Pb). On the contrary, the SM is approximately valid for collisions of heavy nuclei. However, its predictions disagree with the data on p+p to Be+Be collisions.
The rapid change of hadron production properties when moving from Be+Be to Ar+Sc collisions is referred to as the onset of fireball. From Figure 5 (right) follows that the increase of the K + /π + ratio depends on the collision energy. On the other hand, the scaled variance ω of the multiplicity distribution shows only weak collision energy dependence (see Fig. 6 (right)). The physics behind the onset of fireball is under discussion [45].
NA61/SHINE has started a discussion on possibilities to perform systematic measurements of the effect by conducting a detailed two dimensional scan with low and medium mass nuclei at the CERN SPS. Figure 7 presents a draft of the beam request for the data taking period after the CERN Long Shutdown 3.
David Blaschke turned 60 in 2019. Over many years David explored synergies between theoretical and experimental physics, between heavy-ion collisions and astroparticle physics, between cultures of many countries, see Figure 8. In particular, David has played an import role in theoretical studies of the onset of deconfinement [47][48][49][50]. He was the key organizer of CPOD 2010 Workshop in JINR, Dubna and CPOD 2016 Workshop in Wroclaw. Very importantly, David enthusiastically creates the physics programme of NICA -the new heavy-ion facility in JINR, Dubna [51,52]. I wish David to continue running his Universe for many years to come.
Open Access funding enabled and organized by Projekt DEAL. The work was supported by the the National Science Centre Poland grant 2018/30/A/ST2/00226 and the German Research Foundation grant GA1480/8-1.
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