Search for the QCD Critical Point -

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Presentation transcript:

Search for the QCD Critical Point - Fluctuations of Conserved Quantities in High Energy Nuclear Collisions at RHIC Xiaofeng Luo (罗晓峰) Central China Normal University (CCNU) Oct. 8, 2015 Search for the QCD Critical Point -

QCD Phase Diagram (Conjectured) Very rich phase structure in the QCD phase diagram. K. Fukushima and T. Hatsuda, Rept. Prog. Phys. 74, 014001(2011); arXiv: 1005.4814 Large Uncertainties in determining phase structure by theory at finite μB.

I would rather fishing than thinking about the Critical Point….. Fishing Diagram: Theorist’s thinking I would rather fishing than thinking about the Critical Point….. Fish, fish, fish…..

The QCD Critical Point Need proper observables in HIC. Singularity of EOS: Diverges of the thermodynamics quantities, such as correlation length (ξ), Susceptibilities (χ), heat capacity (CV). Long wavelength fluctuations of order parameter. Critical Opalescence in liquid gas PT. Water: H2O T. Andrews. Phil. Trans. Royal Soc., 159:575, 1869 Need proper observables in HIC. 1. finite size/time. 2. Non-CP physics effects. 3. Need CFO closer enough to CP. 4. Signal didn’t wash out after evolution. ξ=2 ~ 3 fm Very Challenging !!! 武汉·汤逊湖，2015.10.7 工欲善其事，必先利其器 Sharp tools make good work

Location of QCD Critical Point: Theory Lattice QCD: DES: Lattice QCD： 1): Reweighting:Fodor&Katz,2004: μEB/TE ~ 2.2  √sNN ~ 9.5 GeV 2): Tylor Expansion: Gavai&Gupta 2013 μEB/TE ~ 1.7  √sNN ~ 14.5 GeV DSE: 1): Y. X. Liu, et al., PRD90, 076006 (2014). μEB/TE ~ 2.88  √sNN ~ 8 GeV 2): C. S. Fischer et al., PRD90, 034022 (2014). μEB/TE ~ 4.4  √sNN ~ 6 GeV In my talk, I will focus on how we search for the QCD critical point by using fluctuation observable in heavy-ion experiment. Due lattice QCD Proposed Colliding Energy Range for CP Search:√sNN = 6 ~ 14.5 GeV

Observables: Higher Moments (fluctuations) “Shape” of the fluctuations can be measured: non-Gaussian moments. C2,x~ ξ2 C3,x ~ ξ4.5 C4,x~ ξ7 M. A. Stephanov, PRL102, 032301 (2009); PRL107, 052301 (2011); M. Akasawa, et al., PRL103,262301 (2009). Lattice Cheng et al, PRD (2009) 074505. B. Friman et al., EPJC 71 (2011) 1694. H.T. Ding et al, Susceptibility ratios  Moments of Conserved Charges  Cumulant Ratios (q=B, Q, S)

Expectations from Skellam Distributions If proton and anti-proton are independent Poissonian distributions, the distributions of net-protons is Skellam distributions, which is the case in Hadron Resonance Gas Model. Npbar : Mean number of anti-protons Np : Mean number of protons Denote statistical/thermal fluctuations. Then we have the skellam expectations for various moments/cumulants :

RHIC Beam Energy Scan-Phase I √s (GeV) Statistics(Millions) (0-80%) Year μB (MeV) T (MeV) μB /T 7.7 ~4 2010 420 140 3.020 11.5 ~12 315 152 2.084 14.5 ~ 20 2014 266 156 1.705 19.6 ~36 2011 205 160 1.287 27 ~70 155 163 0.961 39 ~130 115 164 0.684 62.4 ~67 70 165 0.439 200 ~350 20 166 0.142 μB , T : J. Cleymans et al., Phys. Rev. C 73, 034905 (2006).

STAR Detector System Large, Uniform Acceptance at Mid-y EEMC Magnet MTD BEMC TPC TOF BBC Large, Uniform Acceptance at Mid-y Excellent Particle Identification Full TOF became available in 2010

First Order Phase Transition ? Courtesy of Nu Xu Indication of a First Order Phase Transition. D.H. Rischke et al. HIP1, 309(1995) H. Stoecker, NPA750, 121(2005) J. Steinheimer et al., arXiv:1402.7236 P. Konchakovski et al., arXiv:1404.276

How to ? Raw net-p prob. distribution Moments/Cumulants 1. Finite particle detection efficiency. Need efficiency correction. It is not straight forward for higher moments. 2. Initial volume fluctuations. Improve centrality resolution and apply centrality bin width correction. 3. Remove auto-correlation. Particles used in the analysis are excluded in centrality definition. 4. Proper error calculations. STAR: PRL112, 32302(14) STAR: PRL113,092301(14) X. Luo, J. Phys.: Conf. Ser. 316 012003 (2011). X. Luo, JPG 39, 025008 (2012). X. Luo,et al., JPG 40, 105104 (2013). X. Luo, PRC 91, 043907 (2015). Delta theorem and Bootstrap

Higher Moments Results Net-proton results: All data show deviations below Poisson for κσ2 at all energies. Larger deviation at √sNN ~ 20 GeV Net-charge results: Need more statistics. Poisson: κσ2=1 STAR: PRL112, 32302(14) / arXiv: 1309.5681 STAR: PRL113,092301(14) / arXiv: 1402.1558

New Net-proton results: Larger pT Acceptance Published net-proton results: Only TPC used for proton/anti-proton PID. TOF PID extends the phase space coverage. Au+Au  protons STAR Preliminary TOF TOF TPC TPC Acceptance: |y| ≤ 0.5, 0.4 ≤ pT ≤ 2 GeV/c Efficiency corrections: TPC (0.4 ≤ pT ≤ 0.8 GeV/c): εTPC ~ 0.8 TPC+TOF (0.8 ≤ pT ≤ 2 GeV/c): εTPC*εTOF ~ 0.5

Efficiencies for Protons and Anti-protons TPC TPC+TOF STAR Preliminary Systematic errors: 1) Uncertainties on efficiency, 2) PID, 3) Track Cuts.

Efficiency Correlation and Error Estimation We provide a unified description of efficiency correction and error estimation for higher moments analysis in heavy-ion collisions. X. Luo, PRC91, 043907 (2015). Fitting formula: We can express the moments and cumulants in terms of the factorial moments, which can be easily efficiency corrected. One can also see: A. Bzdak and V. Koch, PRC91,027901(2015), PRC86，044904(2012).

Statistical Errors Comparison Between for Net-Q, Net-P and Net-K X. Luo, JPG 39, 025008 (2012). 14.5 GeV: 0-5% Net-Charge (Q) Net-proton (B) Net-Kaon (K) Typical Width (σ) 12.2 4.2 3.4 Aver. Efficiency (ε) 65% 75% 38% 355 32 82 With the same # of events: error(Net-Q) > error(Net-K) > error (Net-P)

Cumulants: C1~C4 In general, cumulants are increasing with <Npart>. Significant increase for C4 at most two central bin at 7.7 GeV after eff. corr. .

Centrality Dependence:Cumulants Ratios Large increase for Kσ2 are observed in the most central 7.7 GeV Oscillations are observed at 0-5% and 5-10% for 14.5 and 19.6 GeV.

Energy Dependence for Net-proton κσ2 Net-proton as proxy for net-baryon. Non-monotonic trend is observed for the 0-5% most central Au+Au collisions. Dip structure is observed around 19.6 GeV. Separation and flipping for the results of 0-5% and 5-10% centrality are observed at 14.5 and 19.6 GeV. ( Oscillation Pattern observed !) UrQMD (no CP) results show suppression at low energies. Consistent with the effects of baryon number conservation.

Sign of Kurtosis :Model and Theoretical Calculations M.A. Stephanov, PRL107, 052301 (2011). PQM Schaefer&Wanger, PRD 85, 034027 (2012) PQM V. Skokov, QM2012 NJL VDW Memory Effects JW Chen et al., arXiv:1509.04968 Vovchenko et al., arXiv:1506.05763 Swagato,et al, PRC92,034912 (2015).

Lattice Calculation μEB/TE~1.7. Large uncertainty will appear when approaching critical point. S. Gupta et al., Lattice 2013

Oscillation Pattern: Signature of Critical Region ? Blue: Positive Contribution Red: Negative Contribution Depending on relative position between reaction trajectories/freeze out position and critical region. 0-5% 5-10% 14.5 GeV 1+Pos. 1+Neg. 19.6 GeV “Oscillation pattern” around baseline for Kurtosis may indicate a signature of critical region. Propose to scan 16.5 GeV (μB =238 MeV) or even finer step between 14.5 and 19.6 GeV,expect to see bigger dip and no separation for the results of the 0-5% and 5-10%.

Energy Dependence for Net-proton Sσ Non-monotonic trend is observed for the 0-5% most central Au+Au collisions. Peak structure is observed around 14.5 GeV for both Sσ and Sσ/Skellam UrQMD (no CP) results show suppression for (Sσ)/Skellam at low energies. STAR Preliminary

Κσ2 Vs. Sσ Taylor expansion in Lattice : THERMO-meter : BARYO-meter : A structure is observed for 0-5% most central data while it is flat for peripheral collisions. Can be directly compared with theoretical calculations.

Eff. Corrected and Eff. Uncorrected Efficiency corrections are important not only for the values in the higher moments analysis, but also the statistical errors.

Acceptance Study: pT and Rapidity Bjorken rapidity Δηcorr=ξ/τf~0.1-0.3 << Kinematic rapidity Δycorr~ 2 (Misha) Significant pT and rapidity dependence are observed at low energies. Large acceptance is crucial for the fluctuation measurement.

STAR: Moments of Net-Charge and Net-Kaon Distributions STAR Preliminary Within current errors, Net-Kaon and Net-Charge κσ2 are consistent with unity. More statistics are needed to make a conclusion. UrQMD (no CP), show no energy dependent. σ： Measured width of distributions. ε: Efficiency. STAT, QM 2015. In STAR, with the same # of events: error(Net-Q) > error(Net-K) > error (Net-P)

STAR Upgrades and BES Phase-II (2019-2020) Larger rapidity acceptance crucial for further critical point search with net-protons iTPC proposal: http://drupal.star.bnl.gov/STAR/starnotes/public/sn0619 BES-II whitepaper: http://drupal.star.bnl.gov/STAR/starnotes/public/sn0598 Electron cooling upgrade will provide increased luminosity ~ 3-10 times. Inner TPC(iTPC) upgrade : |η| < 1 to | η |< 1.5. Better dE/dx resolution. Forward Event Plane Detector (EPD): Centrality and Event Plane Determination. 1.8 < |η| < 4.5

Summary Dip Discovery Potential at High Baryon Density: Intriguing structures are observed at low energies. Dip Peak Oscillation Discovery Potential at High Baryon Density: First order phase transition and QCD Critical Point etc. The Race is on…..

It is time to discover the QCD Critical Point ! Thank you for your attention !

Exploring QCD Phase Structure 3 RHIC, NICA, FAIR 1 LHC, RHIC 2 RHIC RHIC BES-II QCD phase structure and critical point √sNN ≤ 20 GeV RHIC Quarkyonic matter? For region μB > 500 MeV, √sNN ≤ 5 GeV, fixed-target experiments are much more efficient RHIC sQGP properties √sNN = 200GeV 39 11.5 8

Observables: Higher Moments Citation: 251 Cumulant Ratios: (q=B, Q, S) Volume cancel.

Baryon Stopping Phys. Rev. Lett. 93, 102301(2004) Phys.Rev. C74, 047901(2006) Phys. Rev. Lett. 93, 102301(2004) Baryon stopping strongly depends on the collision energy and become more important at low energies. Maximum freeze out baryon density is reached at √sNN ~ 8 GeV. (higher when consider the finite size of the nucleon.)

Verification of the Eff. Correction with Model AMPT model: Au+Au 39 GeV. Set different efficiency for two pT range. (0.4，0.8): 80%, (0.8, 2): 50% for p and pbar. X. Luo, PRC91, 043907 (2015). Random Sampling The eff. corrected results match the model inputs very well, which indicate the efficiency correction method works well. 2. The error estimation for eff. corrected results are based on the Delta theorem.

Centrality Determination Defined by charged Kaon and Pion within |eta|<1, DCA<3, Nfits>10. 1. Avoid auto-correlation, 2. Suppress volume fluctuations.

Event-by-Event Net-proton Multiplicity Distributions

Transport Model Calculations

Resonance Decay Effect Net-baryon arXiv: 1304.7133 Resonance Decay Effect Study by Hadron Resonance Gas Model Net-charge Net-proton is a good approximation of Net-baryon. Net-baryon has less resonance decay effect compare to net-charge and net-strangeness. Net-strangeness

Trends change significantly from peripheral to central. Collision Energy and Centrality Dependence Trends change significantly from peripheral to central.