EExploring QCD Matter at High Baryon Density
J. D. Brandenburg
Shandong University, Rice University, Brookhaven National LaboratoryE-mail: [email protected]
Abstract.
This contribution presents a brief summary of the recent past efforts toexperimentally explore the QCD phase diagram at high baryon chemical potentials throughheavy-ion collisions. A few measurements are highlighted to present the current status in thesearch for a first-order phase transition, for a possible critical endpoint, and for evidence ofchiral symmetry restoration. Finally, the outlook for the ongoing beam energy scan II programand future experiments at the FAIR complex are discussed.
1. Introduction
The Facility for Anti-proton and Ion Research (FAIR) is a pioneering new accelerator facilitythat will provide access to the exotic types of matter present under extreme temperature anddensity like those that may be found in compact stars, stellar explosions, and in the earlyuniverse [1, 2]. In principle, one could learn everything about the various phases of nuclearmatter from the theory of Quantum Chromodynamics (QCD). However, in practice this is notyet possible since direct QCD calculations are only viable for special cases. Specifically, latticeQCD calculations, which are applicable for large temperatures ( T ) and for low baryon chemicalpotentials ( µ B ), have indicated that hadronic matter transitions (through an analytic cross-overtransition) into a deconfined phase of strongly interacting quarks and gluons above a criticaltemperature ( T C ≈
150 MeV /c ) [3, 4, 5]. However, many other fundamental questions aboutQCD matter still remain that cannot currently be answered by direct theoretical calculations.Therefore, experimental exploration of strongly interacting matter (so-called QCD Matter) isnecessary to address the structure of the QCD phase diagram at moderate temperatures and athigh baryon chemical potentials (See Fig. 1 for a schematic of the QCD phase diagram and themany possible phases of QCD matter).One of the early success of the Relativistic Heavy Ion Collider (RHIC) was the creationof a dense, strongly interacting fluid of deconfined quarks and gluons, now called a quark-gluon plasma (QGP) [7, 8, 9, 10]. Since that time considerable effort has been invested tocharacterize the QGP using high-energy heavy-ion collisions at RHIC and the Large HadronCollider (LHC) [11, 12, 13, 14, 15, 16, 17, 18]. At the nominal collision energies of the RHICand the LHC ( √ s NN = 200 GeV and √ s NN = 2 .
76 TeV), heavy-ion collisions produce atransient state of matter with µ B ≈ b ) and collision energy of heavy-ion collisions can be tuned to produce QCDmatter that follows various trajectories through the phase diagram [20]. Higher values of µ B can be accessed by colliding heavy-ions at lower collision energies (compared to nominal RHICand LHC collision energies). a r X i v : . [ nu c l - e x ] M a y he phase diagram of dense QCD sQGP uSCdSCCFL2SC Critical Point
Quarkyonic MatterQuark-Gluon PlasmaHadronic Phase Color Superconductors ? T e m p e r a t u r e T Baryon Chemical Potential m B I n h o m o g e n e o u s S c B Liquid-Gas
Nuclear Superfluid CFL- K , Crystalline CSCMeson supercurrentGluonic phase, Mixed phase Figure 1.
Conjectured QCD phase diagram with boundaries that define variousstates of QCD matter based on S B patterns.
The chiral transition is a notion independent of the deconfinement transition. Insection 3.2 we classify the chiral transition according to the S B pattern.
Figure 1 summarizes our state-of-the-art understanding on the phase structure of QCDmatter including conjectures which are not fully established. At present, relatively firmstatements can be made only in limited cases – phase structure at finite T with smallbaryon density ( µ B ⌧ T ) and that at asymptotically high density ( µ B ⇤ QCD ).Below we will take a closer look at figure 1 from a smaller to larger value of µ B inorder. Hadron-quark phase transition at µ B = 0: The QCD phase transition at finitetemperature with zero chemical potential has been studied extensively in the numericalsimulation on the lattice. Results depend on the number of colours and flavours asexpected from the analysis of e↵ective theories on the basis of the renormalizationgroup together with the universality [35, 36]. A first-order deconfinement transitionfor N c = 3 and N f = 0 has been established from the finite size scaling analysison the lattice [37], and the critical temperature is found to be T c '
270 MeV. For N f > u , d and s quark masses [38, 39]. The pseudo-critical temperature T pc , which characterizes thecrossover location, is likely to be within the range 150 MeV
200 MeV as summarizedin section 4.2.Even for the temperature above T pc the system may be strongly correlated andshow non-perturbative phenomena such as the existence of hadronic modes or pre-formed hadrons in the quark-gluon plasma at µ B = 0 [28, 40] as well as at µ B = 0[41, 42, 43]. Similar phenomena can be seen in other strong coupling systems such as Figure 1.
A schematic of a possible QCD phase diagram showing several of the possiblephases of QCD matter along with the phase boundaries separating them [6].This contribution briefly discusses and summarizes some of the important measurements fromthe recent past programs that have expanded our understanding of the QCD phase diagram andset the stage for future facilities like FAIR. The next sections discuss measurements related to1) the search for a first-order phase transition between hadronic matter and a QGP at high µ B , 2) the search for a possible critical endpoint connecting the analytic cross-over transitionat µ B ≈ µ B , and 3) the search forevidence of chiral symmetry restoration at sufficiently high T and µ B . Lastly, the prospectsfor future measurements will be discussed with an emphasis on the ongoing RHIC beam energyscan (BES) II as well as the condensed baryonic matter (CBM) experiment and other FAIRprograms.
2. Search for a First Order Phase Transition and Possible Critical Endpoint
Chiral effective models of QCD have suggested the possibility of a first order phase transitionbetween hadronic matter and a deconfined QGP at finite µ B [6]. Such a first-order phasetransition is characterized by a spinodal region, i.e. a mechanically unstable coexistence regioncorresponding to a softest point in the equation of state. The directed flow of protons atmid-rapidity ( dv /dy | y =0 ), which is sensitive to the compressability of the system, is shown inFig. 2 for several different collision energies from √ s NN =7.7 GeV to √ s NN =200 GeV [21]. Aminimum in the dv /dy | y =0 distribution for p − ¯ p (net-protons) is visible at a √ s NN ≈ − v , other notablemeasurements include quantum correlations (HBT), which can measure the effective size andshape of the emitting source. Pion HBT measurements show a change in the shape of the pionemitting source, from prolate at low energies to oblate at high energies, viewed from beside thebeam, with the transition occurring near the same collision energy as the observed minimum in v [25, 26, 27].If a first order phase transition between hadronic and deconfined matter exists at finite µ B ,then a critical endpoint should connect the smooth cross-over transition (at low µ B ) with the -0.04-0.020 a) antiproton y = / d y | d v b) proton c) net proton DataUrQMD (GeV) NN s √ FIG. 4: Directed flow slope ( dv /dy ) near mid-rapidity ver-sus beam energy for intermediate-centrality Au+Au. Panels(a), (b) and (c) report measurement for antiprotons, protons,and net protons, respectively, along with UrQMD calculationssubject to the same cuts and fit conditions. Systematic un-certainties are shown as shaded bars. Dashed curves are asmooth fit to guide the eye. mum, and for the double sign change in the case of netprotons. Further work towards a more complete theoret-ical understanding of the present observations is needed.To better understand the possible role and relevance ofstopping, measurements as a function of centrality would be helpful, but available event samples are too small forthis purpose. We note that the observations in Fig. 4(b)and (c) qualitatively resemble predicted signatures of afirst-order phase transition between hadronic and decon-fined matter [5–8, 22, 24].In summary, we report directed flow for charged pi-ons, protons and antiprotons in √ s NN = 7.7 - 200 GeVAu+Au collisions in the STAR detector at RHIC. At in-termediate centralities, dv /dy near mid-rapidity for pi-ons and antiprotons is negative at all measured energies,while the proton slope changes sign from positive to neg-ative between 7.7 and 11.5 GeV, shows a minimum be-tween 11.5 and 19.6 GeV, and remains small but negativeup to 200 GeV. In the same centrality region, the net-proton v ( y ) slope also shows a minimum between 11.5and 19.6 GeV, and changes sign twice between 7.7 and 39GeV. These findings are qualitatively different from thepredictions of the UrQMD transport model, which ex-hibits a monotonic trend in the range √ s NN = 7 . − [1] I. Arsene et al. (BRAHMS Collaboration), Nucl. Phys.A , 1 (2005); B. B. Back et al. (PHOBOS Collabo-ration), Nucl. Phys. A , 28 (2005); J. Adams et al. (STAR Collaboration), Nucl. Phys. A , 102 (2005);K. Adcox et al. (PHENIX Collaboration), Nucl. Phys. A , 184 (2005); S. A. Bass et al., Hot & Dense QCDMatter , White Paper submitted to the 2012 Nuclear Sci-ence Advisory Committee.[2] F. Karsch et al. , Nucl. Phys. B Proc. Suppl. , 614(2004); Y. Aoki, G. Endrodi, Z. Fodor, S. D. Katz andK. K. Szabo, Nature , 675 (2006); M. Cheng et al. ,Phys. Rev. D , 074505 (2009) and references therein.[3] S. Ejiri, Phys. Rev. D , 074507 (2008).[4] E. S. Bowman and J. I. Kapusta, Phys. Rev. C ,015202 (2009).[5] D. H. Rischke et al. , Heavy Ion Phys. , 309 (1995).[6] L. P. Csernai and D. Rohrich, Phys. Lett. B , 454 (1999).[7] J. Brachmann et al. , Phys. Rev. C , 024909 (2000).[8] H. St¨ocker, Nucl. Phys. A , 121 (2005).[9] A. M. Poskanzer and S. A. Voloshin, Phys. Rev. C ,1671 (1998).[10] D. Teaney and L. Yan, Phys. Rev. C , 064904 (2011);M. Luzum and J. Y. Ollitrault, Phys. Rev. Lett. ,102301 (2011).[11] J.-Y. Ollitrault, Phys. Rev. D , 229 (1992).[12] U. W. Heinz, in Relativistic Heavy Ion Physics , Landolt-Boernstein New Series, Vol. I/23, ed. R. Stock (SpringerVerlag, New York, 2010).[13] S. A. Bass et al. , Prog. Part. Nucl. Phys. , 225 (1998);M. Bleicher et al. , J. Phys. G , 1859 (1999).[14] H. Sorge, Phys. Rev. Lett. , 2309 (1997).[15] P. Kolb and U. Heinz, nucl-th/0305084; P. Huovinen andP.V. Ruuskanen, Annu. Rev. Nucl. Part. Sci. , 163 Figure 2.
The directed flow ( v )at mid-rapidity ( y = 0) of anti-protons (top), protons (middle), andnet-protons (bottom). The dataare shown in red points with theUrQMD calculations shown in greybands [21] Figure 3.
The κσ for net protonsmeasured from event-by-event protonand anti-proton multiplicities. TheSTAR and HADES data points areshown for two collision centralities [22,23]. The line at unity correspondsto the expected baseline for fluctuationaccording to Poisson statistics.first order phase transition [28]. A critical endpoint is characterized by a divergence in thecorrelation length of the system which is related to a divergence of susceptibilities. Ratios ofsusceptibilities can be accessed experimentally through event-by-event fluctuations in conservedquantities, such as the baryon number. Specifically, the product of the kurtosis and the sigmasquared ( κσ ) of event-by-event net proton multiplicities (net-protons are a proxy to the baryonnumber) has been proposed as an observable sensitive to the critical endpoint. Figure 3 showsthe κσ for net-protons measured by STAR for two different centrality classes along with thesame type of measurement from HADES [23, 22]. The non-monotonic behavior visible in theSTAR 0-5% central data points (specifically the large rise in value near √ s NN = 7 . κσ returns to unity (the Poisson baseline) at lower collisionenergies. Despite being at much lower √ s NN , the HADES measurement from 0-5% central datahas a value similar to the STAR data point at √ s NN = 7 .
3. Search for Chiral Symmetry restoration
Theoretical predictions have indicated that the critical temperature for the transition fromhadronic matter (with chiral symmetry broken) to a phase of matter with chiral symmetryrestored may be roughly equal to the critical temperature for the deconfinement transition at low µ B [28]. At higher values of µ B these two phase transitions may not coincide, making room for aphase of matter with chiral symmetry restored but still confined, a so-called Quarkyonic form ofQCD matter. However, observing direct unambiguous evidence for chiral symmetry restoration RTICLES
NATURE PHYSICS previously been observed in Super Proton Synchrotron/CERN (European Centre for Particle Physics) and Relativistic Heavy-Ion Collider/Brookhaven National Laboratory experiments. With the high-precision μ + μ − data taken by the NA60 Collaboration in In + In collisions it could be shown that thermal medium radia-tion, with invariant masses below 1 GeV c –2 , can be understood as radiation originating from strongly modified ρ -meson states formed and propagating in a hot hadronic environment. Such a strong modification had been conjectured before and explained as being due to the coupling of the ρ meson to baryons . The good sta-tistics of the NA60 data, even for invariant masses beyond the low-mass vector-meson pole region ( M ee > c –2 ), enabled us to extract an average source temperature of kT = ±
12 MeV (ref. ), pointing to a mostly partonic medium as the source of this radiation (compare Fig. 1).Low-mass dilepton emission at beam energies around 1 GeV per nucleon in elementary and in light heavy-ion collision sys-tems has so far been studied by the DLS and High Acceptance Dielectron Spectrometer (HADES) experiments. The common striking feature observed at these energies is an enhanced yield of e + e − pairs above the contribution from η Dalitz decays and a strong isospin dependence in both η production and nucleon–nucleon (NN) bremsstrahlung . Emission of e + e − from the internal charged pion exchange line—contributing only in n + p colli-sions—has been proposed to be responsible for the isospin effect . In the following, we will call these contributions ‘conventional sources’. First indications for radiation beyond the conventional sources described above were found for the 48% most central Ar + KCl collisions with a mean number of participating nucleons 〈 A part 〉 = ). The HADES experiment
The experiment was performed with HADES at GSI using a beam of accelerated Au ions impinging on a stack of Au foils. A photograph and a cross-sectional view of the set-up are exhibited in Supplementary Figs. 1 and 2, respectively. A description of the relevant components (mini drift chamber, ring-imaging Cherenkov (RICH), time of flight and resistive plate chamber) can be found in Methods.Using the measured momenta of electrons and positrons forming correlated e + e − pairs, various pair observables such as invariant mass, rapidity and transverse momentum were con-structed and investigated. To obtain the signal-pair yield, the con-tribution of uncorrelated pairs was subtracted from the spectra of total pair yield. The signal spectrum was furthermore cor-rected for detector inefficiencies. Details of the analysis procedures are explained in Methods.The resulting invariant-mass distribution of signal dielectrons, derived for the 40% most central Au + Au collisions, is shown in Fig. 2. The precision of the measurement is demonstrated by quoting the 1 σ statistical uncertainty (s.d.) and our estimator for the systematic uncertainty (see Methods for details). The signal yield is normalized to the number of produced neutral pions to remove a trivial system-size dependence of the signal-pair yield. The pion multiplicities are found to scale linearly with 〈 A part 〉 . For the centrality class presented here 〈 A part 〉 amounts to 173. At low invariant masses a contribution from three-body π Dalitz decays is visible. Above M ee ≃ c –2 , the spectrum drops nearly exponentially over almost four orders of magnitude until it runs out of statistics around 1 GeV c –2 . Also shown are the expected yields attributed to mesons ( π , η , ω , ρ , ϕ ) decaying after they have decoupled from the fireball. Although dileptons radiated from this stage are not considered part of the thermal emission from the fireball, they still contribute to the total reconstructed signal-pair yield. Likewise, non-equilibrium contributions from baryonic sources (NN bremsstrahlung, Δ Dalitz decay), which contribute significantly at SIS18 energies , are also accounted for. This yield is approximated by the NN reference spectrum (open dark-blue squares) derived from measured p + p and n + p data as d N NNref d M ee ¼ :
54 d N pp d M ee þ :
46 d N np d M ee ! " h A part i ð Þ with prefactors reflecting the isospin composition of the Au + Au collision system. Note that the η contribution has already been removed from the NN reference, since this contribution is taken care of by the mesonic cocktail. While the Au + Au signal-pair yield and NN reference agree in the π Dalitz region ( M ee < c –2 ) as expected, they differ strikingly for masses M ee > c –2 . In this region, the yield from Au + Au collisions exceeds the NN reference and mesonic cocktail substantially, clearly indi-cating the presence of excess radiation originating from the dense hadronic medium.
Excess radiation
To isolate this excess radiation we first subtract the contributions from conventional sources (compare equation (2) and Fig. 2). We further apply a mass-dependent acceptance correction factor in analogy to the efficiency correction explained in Methods. The resulting dilepton excess radiation is presented in Fig. 3. It exhibits a near-exponential fall-off. A fit of d N /d M ee ∝ ( M ee ) exp( − M ee / T ) (black-body spectral distribution) to the data gives a satisfac-tory overall description of the distribution and yields an inverse slope parameter of kT = ± χ /ndf = Π em / M is constant M ee (GeV c –2 )0 0.2 0.4 0.6 0.8 1.0 1.2 / N π d N c o rr / d M ee [ ( G e V c –2 ) –1 ] − − − − − − − − = 2.42 GeV s NN Au + Au 0–40%Au + Au back trackingAu + Au ring-finderNN reference π → γ e + e – η → γ e + e – ω → π e + e – ω → e + e – ϕ → e + e – Fig. 2 |
Reconstructed e + e − mass distribution from Au ! + ! Au collisions.
Signal-pair invariant-mass distributions obtained from two different analysis strategies explained in the Methods: back tracking and ring-finder. The data are efficiency corrected and normalized to the number of neutral pions produced. Statistical (s.d.) and systematic uncertainties of the measurements are shown as vertical bars and boxes, respectively. The systematic uncertainties include uncertainties from subtraction of the CB, efficiency corrections, normalization to the number of π and uncertainties of the cocktail components. Curves represent the π , η and ω Dalitz components, as well as ω and ϕ direct decays after decoupling from the fireball. Blue open squares show the NN reference spectrum. The sum of the two is the conventional sources contributing to the total signal yield. NATURE PHYSICS
Figure 4.
The invariant-mass distri-butions of signal e + e − pairs obtainedfrom two different analysis strategies(See [29]) measured by the HADEScollaboration in Au+Au collisions at √ s NN =2.42 G e V. (GeV) NN sCollision Energy I n t e r a c t i on R a t e ( H z ) SIS100 CBM
HIAF CEEHADES
BM@N
NICA MPDSTAR FXT
BES-II
NA61/SHINESPS NA60+J-PARC-HI ALICEsPHENIXSTAR F i x ed - T a r ge t C o lli de r Fig. 2. Interaction rates achieved by existing andplanned heavy-ion experiments as a function ofcenter-of-mass energy. Red symbols show col-lider mode, black and grey symbols show fixed-target mode. Solid curve show running facili-ties / experiments [22, 23, 24, 25], long-dashed – ap-proved [26, 27, 28, 29], short-dashed – in a conceptualdesign [30, 31, 32]. accelerators, SIS100 and SIS300. The space for this second accelerator is already foreseen in the ringtunnel building [20]. Addition of a higher rigidity synchrotron (500 Tm) would greatly enhance the physicspotential of CBM experiment and would also enhance parallel operation.The Compressed Baryonic Matter ( CBM ) experiment is a fixed-target multi-purpose detector, designed toidentify hadrons, electrons and muons in elementary and heavy-ion collisions over the full FAIR beamenergy range [21]. Variation of e.g. z-position of the sub-systems and the magnetic rigidity of the dipolefield enable mid-rapidity coverage for relevant observables down to √ s NN = e V. The measurements willbe performed at event rates of 100 kHz up to 10 MHz. To accomplish this ambitious goal, the complexinterplay of the detector systems with their free-streaming read-out electronics and the fast online eventreconstruction and selection under realistic experiment conditions at interaction rates of 10 MHz has to becommissioned and tested. The demonstrator (mini-CBM [33]) for the full CBM data taking and analysischain is currently being installed at SIS18. Furthermore, important tests of newly developed CBM detectorcomponents and data analysis tools will be realized in running experiments (HADES [34], STAR [35],BM@N, NA61 / SHINE). These are also known as FAIR Phase-0 activities, marking the beginning of theFAIR era. Installation and commissioning of the CBM at SIS100 without beam is planned during 2021 − HADES ) [36] is installed at GSI Darmstadt and provideshigh-quality data to establish a thorough understanding of the dielectron and strangeness production inelementary and heavy-ion collisions at the SIS18 energy range. Further experiments on baryon rich matterwill be realized at SIS18 during FAIR Phase-0. To enhance the performance of the spectrometer, an upgradeprogram has been conducted. In cooperation with CBM, the multi-anode PMT-based RICH UV-detector wasinstalled and will provide substantially improved e ± detection e ffi ciency. An electromagnetic calorimeterwas added and will enable photon measurements, as well as improving the e ± identification. The 2018 − x experiment campaign [34] will start with medium-heavy collision system at the maximum energy of SIS18(Ag + Ag at √ s NN = e V) and pion induced reactions ( π − + N / A at various pion beam momenta). HADEScan serve as ideal spectrometer to provide an important reference measurements (p + p and p + A) at SIS100. @ N and MPD at NICA
The Nuclotron-based Ion Collider fAcility (
NICA ) is now under construction at JINR (Dubna, Ru-ssia) [37]. NICA comprises an injector complex, superconducting synchrotrons (Booster and Nuclotron)and a Collider composed of two superconducting rings with two beam intersection points for heavy-ionsand spin physics. The new heavy-ion injector Linac is in operation since 2016. The assembling of Boostersynchrotron started in 2018. Ions accelerated in the Booster are extracted and transported to the Nuclotronin a superconducting beam transport system. The Nuclotron is in operation since 1993 and has been recentlyupgraded. Beams from the Nuclotron are extracted to a fixed-target station or injected and post-accelerated
T. Galatyuk / Nuclear Physics A 982 (2019) 163–169
Figure 5.
The interaction rate versus center-of-mass collision energy of current and futurefacilities. Red points show collider modeexperiments while black points show fixed-targetexperiments [30].is far from trivial. One proposed method is to observe the “melting” of the ρ meson spectraldistribution through measurements of lepton pairs [31]. Recently the HADES collaborationhas conducted precision measurements of the dielectron spectrum in Au+Au collisions at √ s NN = 2 .
42 GeV (see Fig. 4) which are useful for constraining the ρ meson spectral functionand for pristine measurement of the temperature of the produced fireball [29, 32]. However, anunambiguous observation of chiral symmetry restoration via dileptons requires, in addition tothe ρ meson, measurement of its chiral partner, the a . Since the a cannot be easily observeddirectly, the mixing between the vector and axial-vector may provide an alternative route fordirectly observing chiral symmetry restoration. Though, current experiments are not capable ofreaching the statistical and experimental accuracy needed for such a measurement.
4. Looking Forward
While progress has been made, definitive quantitative answers about the structure of the QCDphase diagram at high µ B have proven elusive. In many cases marginal statistics limits theaccuracy of existing measurements and their corresponding ability to constrain the possiblephysics at play. For this reason, collecting significantly higher statistics is an essential part ofany next generation experiment that hopes to provide clarification about the open questions thatstill remain about the QCD phase diagram. The ongoing RHIC beam energy scan II programis precisely aimed at this goal, of re-measuring the range of energies covered in the BES I, butwith higher statistics and with a significantly upgraded STAR detector. The BES II programwill also feature a STAR fixed target program that extends the energy reach of the energy scandown to √ s NN ≈
5. Acknowledgements
This work was funded in part by the U.S. DOE Office of Science under the contract numberde-sc0012704, the Brookhaven National Laboratory LDRD 18-037, and by Shandong University.
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