1. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 1 Search for a Possible QCD Critical Point in the RHIC Beam Energy Scan using the STAR Experiment W.J. Llope, for the STAR Collaboration Rice University Trajectories at low baryochemical potential,  B 2nd order in the Chiral Limit (m q = 0) Cross-over transition with m q ≠ 0 Trajectories at high baryochemical potential,  B Theory suggests a 1 st order transition… If so, does a Critical Point (CP) exist somewhere between these extremes? Finding the CP in the theory (lattice,  -model) is hard… finite lattice fermion sign problem quark masses, s-quark quenching So, find the CP experimentally! arXiv:1007.2613

2. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 2 A cartoon of the Phase Diagram (experimentalist’s view) Top beam energy at RHIC: crossover transition from QGP to HG. Decreasing the beam energy increases the baryochemical potential Systematic study of the data as a function of the beam energy allows a “scan” in streaks across the phase diagram... STAR BES data sets from RHIC Runs 10 and 11 (2010-2011)

3. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 3 An experimental avenue to finding a possible Critical Point So how could we find such a Critical Point if it exists? Assume that it’s going to have the same basic features of other CPs divergence of the susceptibilities,  … e.g. magnetism transitions 0801.4256v2 divergence of the correlation lengths,  e.g. critical opalescence CO 2 near the liquid-gas transition liquid SF 6 at 37atm heated to ~43.9 C and then cooled Brown University Undergraduate Physics Demonstration arXiv:0711.0336 Volume Pure SU(3) Gauge Theory, Polyakov Loop Susceptibilities Full QCD, Lattice T. Andrews. Phil. Trans. Royal Soc., 159:575, 1869 M. Smoluchowski, Annalen der Physik, 25 ( 1908) 205 - 226 A. Einstein, Annalen der Physik, 33 (1910) 1275-1298

4. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 4 Zooming in on the QCD Phase Diagram Unlike macroscopic systems, in HI collisions: finite system size finite system lifetime critical “slowing down” hep-ph/0912274v2 So,  cannot diverge to ∞  max ~ 2-3 fm  “natural” ~ 0.5 fm …How close is FO curve to CP? compression done… most of Entropy produced… hep-ph/0402115 arXiv:0809.3450v1 arXiv:0803.2449 So, concentrate on observables that are extremely sensitive to the value of  …...Statistical moments of identified particle multiplicities

5. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 5 Sensitivity of cumulants to the Critical Point from the theory Multiplicity cumulants related to conserved qty’s Q,B,S can be calculated on the lattice… m 1 ~  (3) T / [  (2) T 2 ]    Skewness * Standard Deviation m 2 ~  (4) / [  (2) T 2 ]    Kurtosis * Variance m 3 ~  (4) T / [  (2) /T]    Kurtosis * Standard Deviation / Skewness Stephanov arXiv:0809.3450v1 arXiv:0509051arXiv:610116PhysRevD.79.074505 In the Nonlinear Sigma Model, the cumulants of the occupation numbers (integral=multiplicity) are also related to  the higher the order of the moment, the higher the dependence on  m 0 = C 2 /C 1 = M m 1 = C 3 /C 2 = S  m 2 = C 4 /C 2 = K   m 3 = C 4 /C 3 = K  S Gavai&Gupta arXiv:1001.3796

6. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 6 Sensitivity of the cumulants in a Non-linear Sigma Model An ansatz reproducing the expected behavior or the correlation length vs  B : Athanasiou et al. arXiv:1006.4636v2 results in huge increases in the 4 th order cumulant for protons... this ansatz in experimental units convert  B into √s NN and T for  >1fm using (√s NN,  B,T) parameterizations hep-ph/0511094 perhaps  B (√s NN ) doesn’t have to be right on top of the CP to see the effects on the moments lattice suggests this value… Gavai&Gupta, PRD 78,114503 (2008) ×400!

7. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 7 Moments as an experimentalist can see them... Experimentally: The average values of powers of the deviates give cumulants, moments, and moments products.... STAR, Phys. Rev. Lett. 105 (2010) 022302 No. of particles in a single event... Average No. of particles in all “similar” events... Direct comparison of theoretical and experimental quantities!

8. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 8 The Solenoidal Tracker at RHIC (STAR) Time Projection Chamber (TPC)Time Of Flight (TOF) Solenoidal Magnet

9. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 9 STAR Particle Identification and Acceptance TPC “dE/dx” TOF M 2 High efficiency PID from TPC and TOF in a wide (|  |<1) and azimuthally complete acceptance

10. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 10 Selected Spectra and Ratios TPC & TOF π, K, p spectra √s NN =39 GeV Ratios of integrated yields model described on next slide...

11. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 11 Where are we on the Phase Diagram? Statistical-Thermal Model ( THERMUS ) Computer Physics Communications 180 (2009) 84–106 Free Parameters: T,   = 1/T -1 (fermions), +1 (bosons) Z = partition function V = volume m = mass K 2 = Bessel function g = degeneracy - Grand Canonical ensemble...(  B,T) values depend on √s NN and centrality (using only the π , K , p  ratios)

12. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 12 Getting to sensible experimental moments results... So, what we have to do is “simple.” Turn the “big knob” (√s NN ~  B ) and “fine knob” (centrality)… & then measure the multiplicity distributions of identified particles in ensembles of similar events... & then measure the various moments of these distributions… & then plot the moments values vs √s NN or  B … Golden signal is a “non-monotonic behavior” of the 3 rd and 4 th moments vs √s NN or  B......i.e. a significant & √s NN -localized deviation of the moments from “baselines” that are defined by Poisson statistics, the Hadron Resonance Gas model, etc... But life is not quite this simple, of course…. All “non-thermal” contributions to the moments values must be carefully controlled... physical: Volume fluctuations (try to control via centrality cuts) Jets, weak decays, etc. experimental: Time dependence in run (bad RDOs, missing sectors, etc.) Time dependence in fills (backgrounds) and, esp. at low √s NN, dependence on tuning Effects of event & track quality cuts, PID contamination… Autocorrelations between centrality cuts and moments values... Dependence of moments values on width of centrality bins… Getting these experimental aspects under control has taken a considerable amount of work... (see next slide)

13. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 13 Volume Normalization and Baselines Several approaches to define what the moments would be in the absence of any contributions from critical behavior... Poisson Statistics higher moments are simple functions of the mean values S  = (M + - M - )/(M + + M - ) K  2 = 1 Central Limit Theorem mean values vs centrality “predict” higher moments if particle production is from large number of independent sources Hadron Resonance Gas Model Karsch&Redlich, PLB 695, 136 (2011) Raw moments are not volume normalized. “CLT normalization”: look at moments products, S , K  2 “intensive normalized cumulants”: divide by mean multiplicity,  3 =  3 /M,  4 =  4 /M

14. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 14 Results: net-protons No statistically-significant non-monotonic behavior of 3 rd and 4 th moments values Values consistent with the baselines +10% -20% CLT & multiplicity normalization give similar results net-protons are a proxy of the Baryon number (conserved)

15. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 15 Results: Total protons Sigma field is “isospin blind” Athanasiou et al. arXiv:1006.4636v2 Net- and Total-Proton results are very similar....

16. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 16 Results: Net-Kaons net-Kaons are a possible proxy of the Strangeness number (conserved)

17. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 17 Results: Net-Charge Npos-Nneg is a proxy of the Charge number (conserved) HRG

18. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 18 Summary “moments” - cumulants, normalized cumulants, moments and moments products – have been suggested to be extremely sensitive to the proximity of a CP, if it exists... high(er) moments go like the correlation length, ξ, to high(er) powers The STAR Experiment has collected significant data sets over a wide range of energies from √s NN = 7.7 to 200 GeV We see no significant non-monotonic behavior of the moments values at the presently available beam energies....Insufficient statistics at lowest values? (these are event hungry observables!)...  B width of the critical enhancement region, , is much narrower than expected?...It’s hiding between available beam energies? wide gaps!

19. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 19 BACKUP

20. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 20

21. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 21

22. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 22

23. Search for a Possible QCD Critical Point using the STAR Experiment Click to edit Master subtitle style Heavy Ion Collisions in the LHC Era, Quy Nhon, Vietnam, July 15-21, 2012 23