aa r X i v : . [ nu c l - e x ] N ov March 25, 2018 22:25 WSPC/INSTRUCTION FILE bes˙review
Modern Physics Letters Ac (cid:13)
World Scientific Publishing Company
REVIEW OF RECENT RESULTS FROM THE RHIC BEAMENERGY SCAN
LOKESH KUMAR
School of Physical Sciences, National Institute of Science Education and Research,Bhubaneswar, Odisha 751005, [email protected]; [email protected]
We review recent results from the RHIC beam energy scan (BES) program, aimed tostudy the Quantum Chromodynamics (QCD) phase diagram. The main goals are tosearch for the possible phase boundary, softening of equation of state or first order phasetransition, and possible critical point. Phase-I of the BES program has recently concludedwith data collection for Au+Au collisions at center-of-mass energies ( √ s NN ) of 7.7, 11.5,19.6, 27, and 39 GeV. Several interesting results are observed for these lower energieswhere the net-baryon density is high at the mid-rapidity. These results indicate that thematter formed at lower energies (7.7 and 11.5 GeV) is hadron dominated and might nothave undergone a phase transition. In addition, the centrality dependence of freeze-outparameters is observed for the first time at lower energies, slope of directed flow for(net)-protons measured versus rapidity shows an interesting behavior at lower energies,and higher moments of net-proton show deviation from Skellam expectations at lowerenergies. An outlook for the future BES Phase-II program is presented and efforts forthe detailed study of QCD phase diagram are discussed. Keywords : Quark Gluon Plasma; QCD phase diagram; QCD critical point; Phase tran-sition; Chemical and Kinetic freeze-out; Directed and elliptic flow, dynamical chargecorrelations, Eccentricity, Nuclear modification factor.PACS Nos.: 25.75.-q,25.75.Nq, 12.38.Mh,25.75.Dw,25.75.Gz,25.75.Ld
1. Introduction
The main goals of high-energy heavy-ion collision experiments are to search andstudy the hot and dense matter called Quark-Gluon Plasma (QGP) formed in thesecollisions 1. Moreover, there is a great interest in understanding the QCD phasediagram, a phase diagram for strong interactions, to the level of that for electro-magnetic interactions such as water. The results from top RHIC energies suggestthe formation of QGP 1. The focus has now shifted to study the QGP properties 2and establish the QCD phase diagram. In this review, we will concentrate on thelatter part which is establishing the QCD phase diagram through a dedicated pro-gram at RHIC called beam energy scan program 3 , ,
5. Figure 1 shows the schematicQCD phase diagram plotted as temperature T vs. baryonic chemical potential µ B arch 25, 2018 22:25 WSPC/INSTRUCTION FILE bes˙review Lokesh Kumar
Quark-Gluon Plasma
The Phases of QCD T e m pe r a t u r e Hadron Gas
Early Universe
Future FAIR Experiments
Future LHC Experiments
NuclearMatterVacuum
ColorSuperconductor
Critical Point
Current RHIC Experiments R H I C E n e r g y S c a n C r o ss o v e r Baryon Chemical Potential ~170 MeV 0 MeV 900 MeV0 MeV
Neutron Stars s t o r d e r p h a s e t r a n s i t i o n Fig. 1. (Color online) Schematic QCD phase diagram plotted as temperature T versus baryonchemical potential µ B . gas phase. Lattice QCD calculations predict that the transition between QGP andthe hadronic gas at baryonic chemical potential µ B = 0 is a crossover 7. At large µ B , the transition between QGP and hadron gas is expected to be a first orderphase transition 8 ,
9. Subsequently, the end-point of this first-order phase transitionline (while going towards the crossover) would be the position of a critical point 10.While there is a little guidance from the theory side about the QCD phase diagram,efforts are ongoing from the experimental side to establish some of its distinct struc-tures such as phase boundary between de-confined phase of quarks and gluons andhadron gas phase, first-order phase transition line, and the critical point.Experimentally, the two axes: T and µ B of the QCD phase diagram can beobtained from the momentum distributions and the ratios of the produced particlesin heavy-ion collisions. Each collision energy corresponds to one T - µ B point in thephase diagram. So, idea is to collect data at different center-of-mass energies bycolliding heavy-ions. Once, the T - µ B point is obtained, one can look at the varioussignatures for the phase boundary, first-order phase transition, and the critical point.One of the interesting aspect is to locate the energy where the established signaturesof the QGP (at top RHIC energy) disappear or “turn-off”. This is how the RHICbeam energy scan program was planned 3 , ,
5. The proposal for the BES programwas made in the year 2008. This was followed by a successful data taking and physicsanalysis of a test run of Au+Au collisions below injection energies at √ s NN = 9.2GeV 11. The first phase of the BES program was started in the year 2010 with datataking in Au+Au collisions at three low energies of 7.7, 11.5, and 39 GeV. In 2011,two more energies at √ s NN = 19.6 and 27 GeV were included. Table 1 lists variousarch 25, 2018 22:25 WSPC/INSTRUCTION FILE bes˙review Review of Recent Results from the RHIC Beam Energy Scan energies and corresponding number of events collected by the STAR detector in2010–2011 for Phase-I of the BES program. Table 1. The data collected during thePhase-I of the BES program.Year √ s NN (GeV) N event (Million)2010 7.7 52010 11.5 122010 39 1302011 19.6 362011 27 70 This review is organized as follows. In Sec. 2, we discuss freeze-out parametersthat provide information about T - µ B points in the QCD phase diagram. In Sec.3, signatures of first-order phase transition and that for turn-off of QGP are dis-cussed. These include results on freeze-out eccentricity, directed flow, elliptic flow,dynamical charge correlations, and nuclear modification factor. The signatures forthe search of possible critical point are discussed in Sec. 4 that include energydependence of particle ratio fluctuations and higher moments of conserved quantitiessuch as net-proton. Section 5 provides the outlook for the BES Phase-II program.Finally, we conclude with a summary in Sec. 6.
2. Freeze-out Parameters
The QCD phase diagram is the variation of temperature T and baryon chemicalpotential µ B . These quantities can be extracted from the measured hadron yields.Transverse momentum spectra for the BES Phase-I energies are obtained for π , K , p , Λ, Ξ, K S , and φ ,
13. From these distributions, corresponding particle yields areobtained and various particle ratios are constructed. These particle ratios are usedto obtain the chemical freeze-out (a state after the collision when the yields of parti-cles get fixed) conditions using the statistical thermal model (THERMUS) 14 , , T ch and µ B . Figure 2 (left panel) shows the variation of the extracted chemical freeze-outparameters using the Grand-Canonical Ensemble (GCE) approach of THERMUSfor different energies and centralities 17 ,
18. The curves represent the parameteri-zations of T ch and µ B ,
20. We observe that at top RHIC energy, there is a littlevariation of chemical freeze-out parameters with centrality. While at lower energies, T ch shows a variation with µ B as a function of centrality. The centrality depen-dence of these parameters is observed for the first time in heavy-ion collisions atthese lower energies. One advantage of having such a dependence is that one canexplore larger portion of the QCD phase diagram.The particle spectra can be used to obtain the kinetic freeze-out (a state afterthe collision when the spectral shapes of particles get fixed) conditions using theBlast Wave (BW) model 21. The BW model is used to simultaneously fit the π , K , p arch 25, 2018 22:25 WSPC/INSTRUCTION FILE bes˙review Lokesh Kumar (GeV) B m ( G e V ) c h T Au+Au
200 GeV39 GeV 7.7 GeV11.5 GeV
STAR Preliminary
Grand Canonical Ensemble æ b Æ ( G e V ) k i n T
200 GeV62.4 GeV39 GeV11.5 GeV7.7 GeV
STAR PreliminaryAu+Au
Fig. 2. (Color online) Left panel: Variation of T ch with µ B for different energies and centralities.Right panel: Variation of T kin with h β i for different energies and centralities. Errors in both panelsrepresent the quadrature sum of systematic and statistical errors. spectra and the two main extracted parameters are kinetic freeze-out temperature T kin and average flow velocity h β i . Figure 2 (right panel) shows the variation ofkinetic freeze-out parameters for different energies and centralities 18. We observethat at a given collision energy, there is an anti-correlation between T kin and h β i .For a given collision centrality, the freeze-out temperature at high energy is lowerand the average collectivity velocity h β i is larger due to expansion.
3. Search for First Order Phase Transition & Turn-off of QGPSignatures
Having discussed about accessing the QCD phase diagram by obtaining T − µ B points, we can now discuss various signatures for first order phase transition or soft-est point in equation of state and those showing “turn-off” of QGP. These includefreeze-out eccentricity, directed flow, elliptic flow, dynamical charge correlations,and nuclear modification factor. Freeze-out Eccentricity
Eccentricity at freeze-out can be extracted as: ǫ F = σ y − σ x σ y + σ x ≈ R s, /R s, , where σ x and σ y correspond to the widths of the participant zone at freeze-out in the in-planeand and out-of-plane directions, respectively 22. R s, and R s, are the 2 nd -order and0 th -order Fourier coefficients radius terms along the “side” direction (perpendicularto the direction of average transverse pair momentum or “out” and that along thebeam direction or “long”), respectively. The ratio R s, /R s, is less affected by flowso it carries mainly the geometric information. Freeze-out eccentricity may provideimportant information related to both the equation of state and dynamical pro-cesses involved in heavy-ion collisions as explained below. In non-central collisions,there is an initial anisotropy created (elliptic shape) that leads to more compres-arch 25, 2018 22:25 WSPC/INSTRUCTION FILE bes˙review Review of Recent Results from the RHIC Beam Energy Scan sion along the shorter axis and hence larger initial pressure gradients. This mightlead to expansion along the shorter axis thereby reducing the eccentricity. Ulti-mately, the system must evolve to a more round freeze-out shape. Increasing energywould lead to longer lifetimes and pressure gradients, and hence a monotonicallydecreasing excitation function for the freeze-out eccentricity would be expected. Ifthe system undergoes a first-order phase transition, a mixed phase is expected. Thesystem could spend more time in the mixed phase compared to that in other phases.This may lead to different expansions for different phases and hence non-monotonicfreeze-out shape. Figure 3 shows the energy dependence of freeze-out eccentricitycompared to several model calculations including UrQMD 23 and other 2D hydro-dynamical models 24. These results suggest a monotonic decrease in the freeze-outeccentricity with beam energy.
Directed Flow
The directed flow v is calculated as h cos( φ − Ψ ) i , where φ and Ψ are the azimuthalangle of the produced particles and orientation of the first-order event plane, respec-tively. The directed flow measurements near midrapidity for protons are proposedto be sensitive to the equation of state (EOS) 25 , ,
27. It has been predicted thatproton v slope show a non-monotonic behavior as a function of beam energy illus-trating change of sign from positive to negative at lower energies and again goingback to positive at higher energies 27. This is sometimes called collapse of protonflow. The minimum in proton v slope is proposed to correspond to a softest pointin equation of state. Figure 4 shows the results from the beam energy scan. Plottedhere is the v slope ( dv /dy ′ , where y ′ = y/y beam and y is rapidity), near midrapid-ity as a function of beam energy for the mid-central (10–40%) Au+Au collisions 28.arch 25, 2018 22:25 WSPC/INSTRUCTION FILE bes˙review Lokesh Kumar (GeV) NN s10 100 / d y ’ d v -0.06-0.04-0.0200.020.040.06 STAR Preliminary p p - p pp- Fig. 4. (Color online) Directed flow slope( dv /dy ′ , y ′ = y/y beam ) for π − , p , ¯ p , and net-protons ( p -¯ p ) near midrapidity as a functionof beam energy for mid-central (10–40%)Au+Au collisions. The shaded band refersto the systematic uncertainty on net-protonmeasurements. (GeV) NN s0 20 40 60 ) X ( ( X )- v v Au+Au, 0-80%-sub EP h + X - - X pp- L - L - -K + K - p - + p Fig. 5. (Color online) The difference in v between particles and their correspond-ing anti-particles as a function of beam en-ergy in 0–80% Au+Au collisions. The curvesrepresent fits to data points as discussed intext. Both statistical (vertical lines) and sys-tematic errors (caps) are shown. The pion and anti-proton v slopes show negative values for all the beam energiesstudied. The proton v slope changes sign while going from 7.7 GeV to 11.5 GeVand then stays negative up to 200 GeV. However, the net-protons v slope (obtainedusing v slopes of p , ¯ p and ratio of ¯ p/p ) changes sign from positive to negative andagain becomes positive as a function of beam energy. Both proton and net-proton v slopes show a dip (or minimum) around √ s NN = 10–20 GeV. In order to quantifythe minimum position, it will be interesting to add one more energy point around15 GeV. Also more theoretical as well as experimental studies are needed in orderto understand these interesting observations. Elliptic Flow
The elliptic flow v is calculated as h cos 2( φ − Ψ ) i , where Ψ is orientation of thesecond-order event plane. Elliptic flow mainly probes the early stages of heavy-ion collisions. At top RHIC energy of 200 GeV in Au+Au collisions, the ellipticflow scaled by the number of constituent quarks ( n q ) versus ( m T − m ) /n q (where m T = p p T + m ) shows a scaling behavior where mesons and baryons have sim-ilar values at intermediate p T . This is referred to as the number of constituentquark (NCQ) scaling 29. It is an established signature of partonic matter formedin Au+Au collisions at 200 GeV and deviations from such scaling would indicatethe dominance of hadronic interactions. Hence breaking of NCQ scaling at lowerenergies could be an indication of a “turn-off” of QGP signatures. Figure 5 showsthe difference in v of particles and corresponding anti-particles as a function ofbeam energy 30. The curves represent fits to data points with functional form: f ∆ v ( √ s NN ) = a √ s NN − b + c . The v difference between particles and anti-particlesis observed to increase when we go towards the lower energies. At low energies,arch 25, 2018 22:25 WSPC/INSTRUCTION FILE bes˙review Review of Recent Results from the RHIC Beam Energy Scan q / n v b) h p L + X + W - p - K s0 K f
27 GeV ) (GeV/c q )/n -m T (m0 0.5 1 1.5 200.050.1 0
39 GeV
Fig. 6. (Color online) v /n q as a function of ( m T − m ) /n q for different particles in Au+Aucollisions at √ s NN = 7.7, 11.5, 19.6, 27, 39 and 62.4 GeV. The errors shown are statistical only. v ( π − ) > v ( π + ), v ( K + ) > v ( K − ), and v (baryons) > v (anti-baryons). This dif-ference between particles and anti-particles suggests that the NCQ scaling amongparticles and anti-particles is broken. However, the observed difference between v of particles and anti-particles could be qualitatively explained by the models in-corporating baryon transport at midrapidity and hadronic interactions 31 ,
32. Wealso observe that the baryons-mesons splitting for v versus m T − m starts to dis-appear for anti-particles at 11.5 GeV and below. Figure 6 shows the v /n q versus( m T − m ) /n q for different particles for √ s NN = 7.7–62.4 GeV 30. We observe thatresults for all the particles are consistent among each other within ±
10% level, ex-cept for the φ -mesons at 7.7 and 11.5 GeV. At the largest m T − m the φ -mesondata points deviate by 1.8 σ and 2.3 σ for √ s NN = 7.7 and 11.5 GeV, respectively.Since φ -mesons have smaller hadronic interaction cross-section, their smaller v val-ues could indicate that the hadronic interactions start to dominate over partoniceffects for the systems formed at beam energies below √ s NN = 11.5 GeV 33 , m T − m range and significance of the deviation observed. Dynamical Charge Correlations
The dynamical charge correlations are studied through a three-particle mixed har-monics azimuthal correlator 35, γ = h cos ( φ α + φ β − RP ) i . This observable repre-sents the difference between azimuthal correlations projected onto the direction ofthe angular momentum vector and correlations projected onto the collision reactionplane. It is suggested that the difference in the correlations between same sign andopposite sign charges in heavy-ion collisions could be related to local parity violationif there is a deconfinement and a chiral phase transition 36. This is also referred toarch 25, 2018 22:25 WSPC/INSTRUCTION FILE bes˙review Lokesh Kumar
STAR preliminary b =- a Opposite Sign: b = a Same Sign: b =- a Opposite Sign: b = a Same Sign:
27 GeV Au+Au % Most Central · ] æ ) R P y - bf + af c o s ( Æ = g [ Fig. 7. (Color online) Dynamical charge correlations as a function of centrality for Au+Au colli-sions at √ s NN =7.7-200 GeV. For comparison, results for Pb+Pb collisions at 2.76 TeV are alsoshown. Errors are statistical only. as Chiral Magnetic Effect (CME). At top RHIC energies, we observed a separationbetween the correlations of same and opposite sign charges. If this difference canbe attributed to the QCD phase transitions, the absence of such observation couldbe an indication of the system which did not undergo the phase transition. Hence,the observable could be useful to locate the energy in the BES program where theQGP signature “turns off”. Figure 7 shows the results for the beam energies from7.7–200 GeV as a function of centrality 37. For comparison, Pb+Pb results fromALICE are also shown 38 which are observed to be consistent with the results fromtop RHIC energy. The separation between same and opposite sign charges decreaseswith decreasing energy and vanishes below √ s NN =11.5 GeV. Nuclear Modification Factor
Nuclear modification factor R CP is one of the established observable for the sig-nature of QGP at top RHIC energy 39. It is defined as ratio of yields at centralcollisions to those at peripheral collisions, scaled by the corresponding number of bi-nary collisions N bin . The number of binary collisions are calculated from the MonteCarlo model. It has been observed that at high p T , the R CP of various particles isless than unity 39, which is attributed to the energy loss of the partons in the densemedium. In the absence of dense medium, there may not be suppression of high p T particles, which can serve as an indication of “turn-off” of a QGP signature.Figure 8 (left panel) shows the R CP of K S in Au+Au collisions at √ s NN =7.7–39 GeV 40. We observe that for p T > c , the R CP ( K S ) is less than unity at39 GeV and then the value increases as the beam energy decreases. For √ s NN < R CP ( K S ) is above unity, indicating decreasing partonic effects at lowerenergies. Figure 8 (right panel) shows the R CP results for charged hadrons in Au+Aucollisions at √ s NN =7.7–200 GeV 41. Again, we observe no suppression at lowerarch 25, 2018 22:25 WSPC/INSTRUCTION FILE bes˙review Review of Recent Results from the RHIC Beam Energy Scan R CP (cid:16) − − (cid:17) for K S in Au+Au collisions at √ s NN =7.7–39 GeV.Errors are statistical only. Right: R CP (cid:16) − − (cid:17) for charged hadrons in Au+Au collisions at √ s NN =7.7–200 GeV. Grey band corresponds to the systematic uncertainty. energies for p T > c , supporting the R CP ( K S ) results. Both results suggestthat partonic effects become less important at lower energies and the cold nuclearmatter effects (Cronin effect) start to dominate at these energies 42. (GeV/c) T p0 1 2 3 4 5 6 ) f N ( / ) + W + - W N (
200 GeV 0-12%Hwa&Yang (total)Hwa&Yang (thermal)39 GeV 0-10%27 GeV 0-10%19.6 GeV 0-10%11.5 GeV 0-10%
STAR Preliminaryb)
Fig. 9. (Color online) The baryon to me-son ratio N (Ω − + Ω + ) / (2 Nφ ) as a func-tion of p T in central Au+Au collisions at √ s NN =11.5–200 GeV. The curves repre-sent model calculations by Hwa and Yangfor √ s NN = 200 GeV. Both statistical er-rors (vertical lines) and systematic errors(shaded bands) are shown. Fig. 10. (Color online) ν dyn for K/π (along with K + /π + , K − /π − , K + /π − , and K − /π + ) ratio in 0–5% central Au+Au colli-sions are shown as a function of energy. Re-sults are compared with transport modelssuch as UrQMD and HSD. Errors are statis-tical. Figure 9 shows the baryon to meson ratio N (Ω − + Ω + ) / (2 N φ ) as a functionof p T in central Au+Au collisions at √ s NN =11.5–200 GeV. The curves representmodel calculations by Hwa and Yang in central collisions at √ s NN = 200 GeV 43 , φ yields to be generated from the recombination of ther-mal strange quarks having exponential p T distribution. The particle ratio results atarch 25, 2018 22:25 WSPC/INSTRUCTION FILE bes˙review Lokesh Kumar √ s NN = 19.6, 27, and 39 GeV seem to follow that of 200 GeV, indicating a maxi-mum around p T ≥ c and then turning down as the p T is increased. However,results at 11.5 GeV show different behavior i.e. show a maximum at somewhat lower p T of ∼ c before turning down for higher values of p T . This observation sug-gests that there might be a significant change in the underlying p T distributions ofstrange quarks recombining to form final Ω and φ for √ s NN =11.5 GeV and thosefor √ s NN ≥
4. Search for QCD Critical Point
In this section, we discuss the observables that could possibly be related to thecritical point search. First, we discuss the particle ratio fluctuations such as
K/π ratio fluctuations as a function of beam energy. After that, we discuss about theconserved number fluctuations that include net-proton higher moments results.
K/π
Ratio Fluctuations
If a system passes close to a critical point, large density variations or enhancedfluctuations are expected e.g. as seen in critical opalescence. From experimentalside, one expects a non-monotonic variation of a potential observable as a functionof beam energy. Dynamical particle ratio fluctuations such as
K/π , p/π , and K/p ,might be sensitive to the initial state fluctuations arising from the existence ofcritical point 45 ,
46. The observable used to quantify these (e.g.
K/π ) dynamicalfluctuations ν dyn is given by ν dyn,K/π = h N K ( N K − ih N K i + h N π ( N π − ih N π i − h N K N π ih N K ih N π i , (1)where N K and N π are the average number of kaons and pions in an event, respec-tively. For a pure Poisson distribution, ν dyn,K/π will be zero. Figure 10 shows the ν dyn results for K/π (along with K + /π + , K − /π − , K + /π − , and K − /π + ) ratio in0–5% central collisions as a function of beam energy47. The dynamical K/π ratiofluctuations show a smooth or monotonic behavior as a function of beam energy.The transport models such as HSD 48 and UrQMD 23 show a similar smoothdependence on beam energy as observed in data.
Conserved Number Fluctuations
Higher moments of conserved number fluctuations are proposed to be potential ob-servables for the search of the critical point 49 , ,
51. For a static, infinite medium,the correlation length ξ diverges at critical point. The various moments of event-by-event conserved numbers (such as net-baryons, net-charge, and net-strangeness) dis-tributions are related to different powers of the correlation length. Higher momentssuch as skewness S and kurtosis κ are related to higher power of the correlationlength 52 ,
53. Thus, these higher moments have a better sensitivity for the search ofarch 25, 2018 22:25 WSPC/INSTRUCTION FILE bes˙review
Review of Recent Results from the RHIC Beam Energy Scan the critical point. It has been proposed that the appropriate products of these mo-ments such as κσ and Sσ can be related to the ratios of order susceptibilities calcu-lated in lattice QCD and HRG model as κσ = χ (4) B /χ (2) B and Sσ = χ (3) B /χ (2) B , Au+Au Collisions at RHIC
Net-proton <0.8 (GeV/c),|y|<0.5 T Skellam Distribution p+p dataAu+Au 70-80%Au+Au 0-5%Au+Au 0-5% (UrQMD) s S s k ) / S k e ll a m s ( S (GeV) NN sColliding Energy Fig. 11. (Color online) κσ , Sσ and Sσ values normal-ized by the Skellam expectations as a function of collisionenergy and two different centralities. Results from p + pcollisions are also shown. All the results presented arecorrected for detector efficiency. Results from UrQMDmodel calculations are also shown. The widths of bandsrepresent statistical uncertainties. The error bars on datapoints are statistical while caps represent the systematicerrors. Figure 11 shows the κσ and Sσ for net-protons as a function ofbeam energy for different colli-sion centralities 56 ,
57. For com-parison, the results are shownfor Skellam expectations andUrQMD model calculations thatdo not include critical point 23.The results from p + p colli-sions at 200 GeV are also shown.The bottom panel shows the Sσ values normalized by the corre-sponding Skellam expectations.We observe that the momentproducts κσ and Sσ show sim-ilar values for central for cen-tral 0–5% and peripheral colli-sions (70–80%) for √ s NN = 39–200 GeV. For beam energies be-low 39 GeV, they have differ-ent values for central and pe-ripheral collisions. These valuesare below Skellam expectationsfor √ s NN > √ s NN =19.6 and 27 GeV. TheUrQMD model calculations showa smooth monotonic behavior as a function of collision energy. There are large un-certainties for data points below 19.6 GeV that call for higher statistics data atthese energies. In addition, a direct comparison to QCD calculations with criticalpoint obtained using similar dynamics at that of heavy-ion collisions can providedefinite answer about the existence of critical point.arch 25, 2018 22:25 WSPC/INSTRUCTION FILE bes˙review Lokesh Kumar
5. BES Phase-II
The first phase of the BES program has yielded several promising results for the un-derstanding of QCD phase diagram. Some of the observables require high statisticsdata to make definite statements. These include φ -meson v to test the NCQ scal-ing hypothesis at lower energies and higher moments of net-protons to see whetherthere is a non-monotonic variation towards lower energies that could suggest apossible critical point. In addition, energy dependence of some observables suggest Table 2. Proposed energies, µ B values, and required number of events for the BESPhase-II. Also listed are the corresponding fixed target √ s NN , centre of mass rapidity,and µ B reach. BES Phase - II Fixed Target Collisions √ s NN (GeV) µ B (MeV) N event (Million) √ s NN (GeV) y CM µ B (MeV)19.6 205 400 4.5 1.52 58515 250 100 4.0 1.39 62011.5 315 120 3.5 1.25 6707.7 420 80 3.0 1.05 720 to have a need of one more energy point around 15 GeV. For example, protonand net-proton v slopes suggest a minimum around 11.5–19.6 GeV as a func-tion of energy which could be related to the softest point in equation of state. Fig. 12. (Color online) Improvement in RHIC luminos-ity for the lower energies with electron cooling and longbunches (with space charge tune spread ∆ Q SC = 0.05 and σ s = 3 m.) Having one more energy pointin between would indicate theexact location of the mini-mum. Similar reason (althoughthere is a monotonic variationas a function of beam energyat the moment) might be ar-gued for the freeze-out eccen-tricity. For net-proton highermoments, adding 15 GeV alongwith high-statistics data atlower energies might providethe clear energy dependencetrend with high significance.One more energy point at 15GeV is also important in viewof the fact that the gap be-tween 11.5 and 19.6 GeV interms of µ B is more than 100 MeV.For the reasons mentioned above, RHIC has decided to continue the explorationof QCD phase diagram and hence proposed a second phase of the BES program. Theproposal for BES Phase-II includes high statistics data below 20 GeV as listed inarch 25, 2018 22:25 WSPC/INSTRUCTION FILE bes˙review Review of Recent Results from the RHIC Beam Energy Scan the Table 2. To achieve the high statistics data at lower energies, an electron coolingdevice is requested to be installed at RHIC for increasing the beam luminosity 58.Simulation results (see Fig. 12) indicate that with electron cooling, a significantimprovement can be made to increase luminosity (as shown by red solid curve inthe figure). An additional improvement in luminosity (as shown by blue dashedcurve) may be possible by operating with longer bunches at the space-charge limitin the collider 59. Electron cooling may increase the luminosity by a factor of 3–10 and with longer bunches the luminosity may be increased by another factor of2-5. The high statistics data from BES Phase-II will not only allow the precisionmeasurements of the important observables discussed here but will also be helpfulin the measurements of rare probes such as dilepton production and hypertritonmeasurements at lower energies 60 , µ B values for a given BES Phase-II energy. The beam energies and the µ B values forthe fixed target collisions are listed in the Table 2 corresponding to the proposedBES Phase-II energies. The µ B values are obtained from the parameterizations inRef. 20. Clearly, it provides an opportunity to reach the large values of µ B and henceto explore the larger portion of the QCD phase diagram. One of the advantages forsuch a proposal is that the data taking for these fixed target collisions can bedone concurrently during the normal RHIC running and hence it will not affect thenormal RHIC operations.These programs will also benefit from the proposed inner sector upgrade of STARTPC called the iTPC upgrade 62. At the moment, inner sector of the TPC has thefollowing issues: the inner sector wires are showing the signs of ageing and unlike theouter TPC sectors, it does not have the hermetic coverage at all radii. The spacingbetween the rows is greater than 5 cm which results in missing rows. To overcomethese issues, it has been proposed to increase the segmentation on the inner padplane and renew the inner sector wires. Simulation studies suggest that with iTPCupgrade it is possible obtain better momentum resolution, better dE/dx resolutionfor particle identification, and improved acceptance at higher pseudorapidity η andlow p T . At the moment, TPC η coverage is about | η | < | η | < p T achieved can be as low as 60MeV/ c compared to the present value of 125 MeV/ c . The above listed improvementswill definitely strengthen the technical aspects in the Physics analyses proposed forthe BES Phase-II. The BES Phase-II is expected to start around 2018-2019.
6. Summary
The BES Phase-I enables RHIC to cover large range of µ B (20–400 MeV) in thephase diagram. At lower energies, a centrality dependence of freeze-out parametersarch 25, 2018 22:25 WSPC/INSTRUCTION FILE bes˙review Lokesh Kumar is observed. The observables such elliptic flow v , nuclear modification factor R CP ,baryon to meson ratio Ω /φ , dynamical charge correlations, suggest that hadronicinteractions dominate for √ s NN ≤ v slope show interesting behavior for the energy range √ s NN <
20 GeV. The proton v slope changes sign between 7.7 and 11.5 GeV. The net-proton v slope changessign twice as a function of beam energy. Both proton and net- proton v slopesshow a minimum around 11.5–19.6 GeV. The κσ and Sσ for net-protons showmost significant deviations from Skellam expectations at √ s NN = 19.6 and 27GeV. BES Phase-II along with electron cooling, fixed target proposal, and iTPCupgrade provides optimistic future for the exploration of the QCD phase diagram,and hence for critical point and phase boundary search.We thank Prof. D. Keane, Prof. B. Mohanty, and Prof. Nu Xu for reading themanuscript and providing helpful comments and suggestions. References
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