Strangeness at Intermediate Baryon Density

Exploration of the QCD phase diagram has been one of the main programs of contemporary nuclear physics. The intermediate baryon density region covers a broad range of the baryon chemical potential, between 100 and 700 MeV, and is expected to include a possible critial point at the end of a phase equilibrium curve between the hadron gas and quark gluon plasma phases. Experimental programs at the SPS and RHIC facilities have provided valuable insights in this range. These proceedings motivate the exploration of the QCD phase diagram through the use of strangeness. A selection of relevant experimental results from RHIC and SPS beam energy scan programs with associated theoretical predictions is presented along with a discussion of possible physical conclusions and future plans.


Introduction
Finite temperature lattice Quantum Chromodynamics (QCD) calculations predict [1] a cross-over from a hadronic to a QGP phase at a vanishing baryon chemical potential µ B and temperature T = 154 ± 9 MeV [2].Several QCD-based calculations [3,4] show that at lower T and higher µ B a first-order phase transition may take place.The point in the QCD phase diagram, where the first order phase transition ends, is the QCD critical point [5].In the low-T , and low and intermediate µ B phase, interacting hadronic matter in the ground state can be well described in terms of a gas of non-interacting hadrons and resonances -the Hadron Resonance Gas (HRG) model [6].
The availability of more precise experimental data now allows to better discriminate between models.The lattice QCD prediction power is still very limited at non-zero µ B , hence, experimental exploration becomes especially vital.These proceedings will focus on discussion of the intermediate µ B region, which covers a wide µ B range, roughly spanning between 100 MeV and 700 MeV.The intermediate baryon density µ B region is accessible through experiments at Relativistic Heavy Ion Collider (RHIC), Super Proton Synchrotron (SPS), and in the future Facility for Antiproton and Ion Research (FAIR) which will be able to access also high µ B region.Both SPS and RHIC have been running centre-of-mass energy √ s NN and system size scans to fully explore the region.
One of the most important experimental tools to probe the QCD phase diagram is the study of strange particle production.Strange quarks are strongly interacting particles from the second quark flavor generation.In a QGP, strangeness can be easily produced as strange-antistrange quark pairs via gluon-gluon or quark-antiquark fusion [7], where the minimum momentum transfer Q for this e-mail: tlusty@rice.eduprocess is Q ≈ 200 MeV, while the lowest Q process in a hadron gas, n + n −→ n + Λ + K, needs 670 MeV.Strangeness is also abundant since nearly 20% of all energy content of QGP is transferred to the production of strangeness when chemical equilibrium is reached [8].
Studies of strange hadron production in the energy and system size scans help to understand many crucial questions; to name a few: what is the temperature and density of strongly interacting matter formed in heavy ion collisions, what types of phase transitions occur, is there a critical point in the QCD phase diagram, and at which collision energy do the QGP signals turn off.
The next sections will present a selection of experimental results and theoretical calculations relevant to the discussion.].A new calculation has been performed usa hadronic rescattering and freeze-out stage These new predictions [15] are compared to ) and the agreement with the proton shape odynamic picture.This suggests that extra c phase.The difference in the proton yield at the model derives yields from a thermal It is worth to mention that this model also ic flow of identified particles as reported at rated production ratios are observed to be particle species in all centralities suggesting tial µ B is close to zero as expected at LHC res ALICE results with RHIC data in Au-Au 4 i-strange hadrons is enhanced in a comion with higher @ @µ s derivatives, like χ s

2
, whereas v 1 and v 2 signal the liberated geness from all strange hadrons equally.
r the sake of defining observables which in principle, be measured in experiments, cus on more basic susceptibility combina-.The most attractive quantity to the puris χ f 4 /χ f 2 , since the ratio does not depend e volume.Similar ratios have been proto determine the chemical freeze-out temure independent of any statistical model ptions [18][19][20].Its non-monotic behavior function of the temperature has also been sted as an indicator for the deconfinement ition [21].Fig. 3 shows the T -dependence /χ 2 for light and strange quarks.For ght quark susceptibilities (thus for observrelated to net up+down quark numbers) ion contribution, which is notoriously difto calculate on the lattice, is absent by ition.The figure shows two characterisatures: a) each lattice calculation exhibits k (or peak) at a particular temperature b) this kink coincides with the temperaat which the lattice curve starts to devirom the HRG predictions.Interestingly gh, the separation between the kinks of the avors corresponds to the previously mend ⇡15 MeV.In a scenario, in which the st temperature where the HRG and lattice agree is indicating a "deconfinement" or way.First results from ALICE indicate that the T ch of strange hadrons is about 16 MeV higher than that of light hadrons (164 vs 148 MeV) [7,8].As in the case of the lattice parameters, this sensitivity to the freeze-out temperature, extracted from a statistical hadronization fit, is most pronounced for the multi-strange baryons.
These temperature fits are model-dependent, though, and a direct comparison to the temperatures extracted from quark susceptibilities in lattice QCD likely requires corrections.For example, it was suggested that final state interactions between hadrons might modify the baryon yields [22,23].
A more precise verification, less prone to alternate explanations, can be obtained by using a higher order moment analysis of parti- The T dependence of the susceptibility ratios χ 2 /χ 4 for light and strange quarks in the continuum limit.The lattice data are compared to HRG calculations.Left panel taken from Ref [9] and right panel from Ref [15].
At the Strangeness in Quark Matter conference 2011, the ALICE Collaboration has presented results of particle production ratios [9]: and Ω + /π − , (i.e., ratios of strange-to-light and light-to-light hadrons) together with their thermal statistical model predictions [10,11] at chemical freeze-out temperatures of T ch = 164 and 148 MeV.As shown in Fig. 1 (left panel), the thermal model prediction with T ch = 164 MeV describes the strange-to-light ratios while the prediction with T ch = 148 MeV describes p/π + , p/π − , K + /π + , and K − /π − .This is indicative of a separation of chemical freeze-out temperatures between light and strange quark hadrons.Since the ALICE results came from Pb+Pb collisions at √ s NN = 2.7 TeV, the µ B was nearly 0 and the results are suited for comparisons with lattice QCD calculations of higher order quark number susceptibilities χ n [12][13][14] for light and strange quarks [15].Figure 1 (right panel) shows the dependency of the susceptibility ratios χ 4 /χ 2 for light and strange quarks on temperature T together with corresponding HRG model predictions.The critical temperature T c is assumed to be the temperature where the lattice QCD calculated χ 4 /χ 2 and HRG prediction begin to differ.The choice of susceptibility ratio has two advantages.The susceptibility ratio cancels finite volume effects and is proportional to some experimental observables which will be discussed later.As one can observe from from The STAR Collaboration recently published [16] its results on bulk properties from the RHIC BES. Figure 2 shows the comparison of extracted freeze-out parameters in Au+Au collisions at √ s NN = 39 GeV for a Grand Canonical Ensemble (GCE) using particle yields as input to the THERMUS model [17].Results were compared for four different sets, specified in the legend of Fig. 2, of particle yields used as input for fitting.When only π, K, and p yields are used in the fit, the temperature obtained is lower compared to other sets that include strange hadron yields.

Cumulant Ratios of Net-Particle Multiplicity
Fluctuations of conserved quantities are sensitive observables in the study of phase transitions in the QCD matter and critical point [18].UrQMD model [19] based studies of centrality and energy dependence of various order cumulants and cumulant ratios (up to fourth order) of net-proton, netcharge, and net-kaon multiplicity distributions in Au+Au collisions at √ s NN = 7.7, 11.5, 19.6, 27, 39, 62.4, and 200 GeV were presented in [18].These calculations were compared with the data from RHIC Beam Energy Scan (BES) published in [20,21].
A distribution function can be characterized by the various moments, such as mean M, variance σ 2 , skewness S , and kurtosis κ.The moments products κσ 2 and Sσ are directly related to the ratios of various order susceptibilities as As mentioned in Sect.2.1, using the ratios allows finite volume effects to nearly cancel out and provides for a direct comparison with lattice QCD predictions.lision energies.The monotonic decrease when decreasing energies and strong suppression below unity at low energies are consistent with the effects of the baryon number conservations.

VI. SUMMARY
Experimentally, fluctuations of conserved quantities have been applied to probe the signature of the QCD play an important roles.Those will lead to big differ between the cumulants of particles and anti-particl tributions, such as proton, anti-protons and K + , K nally, the comparisons for the cumulant ratios (Sσ of net-proton, net-charge and net-kaon multiplicity butions have been made between the STAR data an UrQMD calculations.Within the statistical unce ties, the net-charge and net-kaon fluctuations mea by STAR experiment can be described by the Ur results.For the net-proton fluctuations, the STAR ion energies.The monotonic decrease when decreasing ergies and strong suppression below unity at low eners are consistent with the effects of the baryon number nservations.

VI. SUMMARY
Experimentally, fluctuations of conserved quantities ve been applied to probe the signature of the QCD play an important roles.Those will lead to big differences between the cumulants of particles and anti-particles distributions, such as proton, anti-protons and K + , K − .Finally, the comparisons for the cumulant ratios (Sσ, κσ 2 ) of net-proton, net-charge and net-kaon multiplicity distributions have been made between the STAR data and the UrQMD calculations.Within the statistical uncertainties, the net-charge and net-kaon fluctuations measured by STAR experiment can be described by the UrQMD results.For the net-proton fluctuations, the STAR mea-  Figure 3 shows the energy dependence of cumulant ratios Sσ, κσ 2 of net-proton, net-charge, and net-kaon multiplicity distributions of the 5% most central Au+Au collisions in RHIC BES energies from the STAR experiment [20,21] and UrQMD calculations [18].The non-monotonic energy dependence of the net-proton κσ predictions.This discrepancy might suggest critical behavior since the critical physics was not implemented in the UrQMD.It is important to reduce uncertainties of these measurements, which is expected in RHIC BES phase II [22], to get to more conclusive results.

Study of the Onset of Deconfinement
Study of onset of deconfinement: K ± /fi ± ratio energy dependence "Horn" structure in Pb+Pb collisions was predicted (SMES) as a signature o At the SPS, measurements of hadron production in a two-dimensional scan in beam momentum (13-158 AGeV/c) and system size (p+p, p+Pb, 7 Be+ 9 Be, Ar+Sc, Xe+La and Pb+Pb) were conducted.New results from p+p and 7 Be+ 9 Be were shown at Quark Matter 2017 conference [23], presenting the energy dependence of the K + /π + multiplicity ratio at mid-rapidity.As shown in Fig. 4, the data from 7 Be+ 9 Be do not show a "horn" structure as data from heavier collision system do (average number of participants in 7 Be+ 9 Be collisions is around 10).This observation constrains size of system to study location of onset of deconfinement energy.The energy dependence of the inverse slope parameter of the transverse mass distribution of charged kaons, as shown in Fig. 5, shows the step structure in both p+p and 7 Be+ 9 Be.The step structure was predicted by the Statistical Model of the Early Stage (SMES) [24] and 3+1 Hydro model [25] as a signature of the onset of deconfinement.
The UrQMD based transport approach [26] provides further insights.It concludes that the "step" is only reproduced if a first order phase transition with a large latent heat is applied or the equation of state is effectively softened due to non-equilibrium effects in the hadronic transport calculation.

Ratios of The Freeze-out Parameters
The experimental results of ratios of the freeze-out parameters µ S /µ B and µ B /T (µ S is strange chemical potential) from the NA57 experiment [27] and the STAR experiment [28] can be reproduced by Study of onset of deconfinement: transverse momentum spectra properties Plateau ("step") in the inverse slope parameter of m T spectra at the SPS energies observed in Pb+Pb was predicted (SMES) as a signature of phase transition Step-like structure visible in p+p for K ≠ Step in Be+Be slightly above p+p a HRG model, as discussed in [29].The HRG model prediction is in better agreement with lattice QCD calculations [29] if additional (strange) hadron resonances are included which are predicted by the quark model [30,31] but until today unobserved (such a setup of the HRG model is denoted as QM-HRG).The µ S /µ B and µ B /T ratios were obtained by a statistical thermal model [32] fitting data for strange-baryon ratios Λ/Λ, Ξ + /Ξ − , and Ω + /Ω − and are shown in Fig. 6 together with lattice QCD predictions, and HRG predictions.One HRG predictions assumes only experimentally discovered hadrons (PDG-HRG) and another is the QM-HRG.As Fig. 6 presents, the QM-HRG predictions match the experimental data and the lattice QCD at the temperatures consistent with the lattice QCD and the data while the PDG-HRG matches at temperatures significantly higher.Hence, it appears that additional, experimentally yet-to-be observed strange hadrons become thermodynamically relevant in the vicinity of the QCD crossover.

Summary and Future Plans
Recent results shown at this conference have underlined once again the relevance of the study of strangeness at intermediate µ B .There are indications of flavor hierarchy with respect to the chemical freeze-out [33].Hadrons containing strange quarks appear to hadronize earlier than the hadrons containing only quarks from the first generation.This has been predicted by lattice QCD at µ B = 0 and experimentally observed by the ALICE Collaboration [9] as well as at the intermediate µ B by the STAR Collaboration [16].
In order to describe the freeze-out parameter ratios consistently with the experimental results from STAR and NA57, a Hadron Resonance Gas needs to assume additional, yet-to-be observed strange hadrons.The experimental results are also predicted by lattice QCD.
The NA61 Collaboration has shown intriguing results from 7 Be+ 9 Be collisions.A comparison with its results on K + /π + ratios shows a remarkably similar structure, which departs from the "horn".
The RHIC BES Phase II is scheduled in years 2019 and 2020.It will provide substantially higher statistics thanks to the accelerator upgrades [22].Detector upgrades will further reduce systematic uncertainties of measurements.The fixed target program at STAR will allow for the QCD phase raland to ze-ð5Þ the ical nly not in a expected from Fig. 3, the QM-HRG predictions are in good agreement with lattice QCD results and lead to almost identical values for T f .The PDG-HRG-based analysis, however, results in freeze-out temperatures for strange baryons that are larger by about 8 (5) MeV for the smaller (larger) value of T f .
Conclusions.-Bycomparing lattice QCD results for various observables of strangeness fluctuations and correlations with predictions from PDG-HRG and QM-HRG models, we have provided evidence that additional, experimentally unobserved strange hadrons become thermodynamically relevant in the vicinity of the QCD crossover.We have also shown that the thermodynamic relevance of  space diagram exploration to be extended to µ B 720 MeV.At the SPS, NA61 will upgrade its data acquisition system to allow for a 1 kHz readout.This is expected to be ready in 2020 and will allow a high statistics beam momentum scan with Pb+Pb collisions for precise measurement of multi-strange hyperon production.All these upgrades will help further constrain the search for a critical point, and the type of phase transition in the intermediated baryon density region.

2. 1
Flavor Hierarchy in the Deconfinement Transition of QCD la printed on December 1the 0-5% most central Pb-Pb uction ratios compared to thermal model predic- FIG. 3.The T -dependence of the χ 4 /χ 2 ratio for light and strange quarks in the continuum limit.The lattice data are compared to HRG calculations.

Figure 1 .
Figure 1.Left panel: Hadron-production ratios from Pb+Pb collisions at √ s NN = 2.76 TeV compared to the statistical hadronization model predictions with parameters T = 148, 164 MeV and µ B = 1 MeV.Right Panel:The T dependence of the susceptibility ratios χ 2 /χ 4 for light and strange quarks in the continuum limit.The lattice data are compared to HRG calculations.Left panel taken from Ref[9] and right panel from Ref[15].

Fig. 1 (
right panel), the T c ≈ 160 MeV for strange quarks differ from the T c ≈ 145 MeV for the light quarks and both are very close to the corresponding T ch from the thermal statistical model predictions for the ALICE data.This suggests a flavor hierarchy in the deconfinement transition of QCD.The previous paragraph introduces a flavor hierarchy in the deconfinement transition of QCD at low µ B .At intermediate µ B a pattern has been observed similar to ALICE's observations at low µ B .

Figure 2 .
Figure 2. Extracted chemical freeze-out temperature for GCE using particle yields as input for THERMUS model.Results are compared for Au+Au collisions at √ s NN = 39 GeV for four different sets of particle yields used in fitting.Figure taken from Ref [16].

FIG. 10 :
FIG. 10: Energy dependence of cumulant ratios(Sσ, κσ 2 ) of net-proton, net-charge and net-kaon multipliity distributio Au+Au collision at √ sNN =7.7 to 200 GeV.The solid markers represent the results from STAR measurement, the open m represent results from UrQMD calculation.The dashed lines denote the Poisson expectations for the STAR data.

G. 10 :
Energy dependence of cumulant ratios(Sσ, κσ 2 ) of net-proton, net-charge and net-kaon multipliity distributions for +Au collision at √ sNN =7.7 to 200 GeV.The solid markers represent the results from STAR measurement, the open markers resent results from UrQMD calculation.The dashed lines denote the Poisson expectations for the STAR data.

Figure 3 .
Figure 3. Energy dependence of cumulant ratios Sσ (left panel), κσ 2 (right panel) of net-proton, net-charge, and net-kaon multiplicity distributions for the Au+Au collision at √ s NN = 7.7 to 200 GeV.The solid markers represent the results from the STAR measurement, the open markers represent results from the UrQMD calculation.The dashed lines denote the Poisson expectations for the STAR data.Figure taken from Ref [18].

2 KFigure 4 .
Figure 4. Energy dependence of the positively charged kaon multiplicity divided by corresponding charged pion multiplicity at mid-rapidity.Figure taken from Ref[23]

FIG. 4 (
FIG. 4 (color online).Values of (μ fS =μ f B , μ f B =T f ) extracted from fits to multiple strange hadrons yields (see text) are compared to μ S =μ B predictions, obtained by imposing strangeness neutrality, from lattice QCD calculations (shaded bands) as well as from QM-HRG (solid lines) and PDG-HRG (dotted lines) models.The predictions are shown for μ B =T ¼ μ f B =T f .For each case, the temperature ranges are chosen such that the predicted values reproduce μ f S =μ f B .

Figure 6 .
Figure 6.Values of µ S /µ B and µ B /T extracted from fits to multiple strange hadrons yields (blue circle at √ s NN = 39 GeV, red square at √ s NN = 17.3 GeV) are compared to the lattice QCD calculations (shaded bands) as well as to the QM-HRG (solid lines) and PDG-HRG (dotted lines) models.Figure taken from Ref [29].
2and net-kaon Sσ contrasts with the monotonic behavior of UrQMD [23]re 5. Energy dependence of the inverse slope parameter of the transverse mass distribution at mid-rapidity for charged kaons.The NA61/SHINE results on p+p interactions (full blue circles) and new results on Be+Be (full green diamonds) collisions are compared with world data on p+p and heavy ion (Pb+Pb and Au+Au) reactions.Figure taken from Ref[23]