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Search for a Possible QCD Critical Point in the RHIC Beam Energy Scan using the STAR Experiment

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, m B 2nd order in the Chiral Limit (m q = 0) Cross-over transition with m q ≠ 0.

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Search for a Possible QCD Critical Point in the RHIC Beam Energy Scan using the STAR Experiment

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  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, mB 2nd order in the Chiral Limit (mq = 0) Cross-over transition with mq ≠ 0 If so, does a Critical Point (CP) exist somewhere between these extremes? Trajectories at high baryochemical potential, mB Theory suggests a 1st order transition… Finding the CP in the theory (lattice, s-model) is hard… finite lattice fermion sign problem quark masses, s-quark quenching So, find the CP experimentally! arXiv:1007.2613

  2. A cartoon of the Phase Diagram (experimentalist’s view) Top beam energy at RHIC: crossover transition from QGP to HG. STAR BES data sets from RHIC Runs 10 and 11 (2010-2011) 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...

  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, c… e.g. magnetism transitions 0801.4256v2 • divergence of the correlation lengths, x… e.g. critical opalescence liquid SF6 at 37atm heated to ~43.9 C and then cooled CO2 near the liquid-gas transition 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 Brown University Undergraduate Physics Demonstration Susceptibilities arXiv:0711.0336 Full QCD, Lattice Pure SU(3) Gauge Theory, Polyakov Loop Volume

  4. Zooming in on the QCD Phase Diagram hep-ph/0402115 arXiv:0809.3450v1 compression done… most of Entropy produced… arXiv:0803.2449 Unlike macroscopic systems, in HI collisions: finite system size finite system lifetime critical “slowing down” hep-ph/0912274v2 So, x cannot diverge to ∞ xmax ~ 2-3 fm x“natural” ~ 0.5 fm …How close is FO curve to CP? So, concentrate on observables that are extremely sensitive to the value of x… ...Statistical moments of identified particle multiplicities

  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… m1 ~ c(3)T / [c(2)T2] ~x7/2 Skewness * Standard Deviation m2 ~ c(4) / [c(2)T2] ~x5Kurtosis * Variance m3 ~ c(4)T / [c(2)/T] ~x5/2 Kurtosis * Standard Deviation / Skewness Gavai&Gupta arXiv:1001.3796 m0 = C2/C1 = M m1 = C3/C2 = Ss m2 = C4/C2 = Ks2 m3 = C4/C3 = Ks/S arXiv:0509051 arXiv:610116 PhysRevD.79.074505 In the Nonlinear Sigma Model, the cumulants of the occupation numbers (integral=multiplicity) are also related to x…the higher the order of the moment, the higher the dependence on x…. Stephanov arXiv:0809.3450v1

  6. Sensitivity of the cumulants in a Non-linear Sigma Model An ansatz reproducing the expected behavior or the correlation length vsmB: Athanasiou et al. arXiv:1006.4636v2 lattice suggests this value… Gavai&Gupta, PRD 78,114503 (2008) this ansatz in experimental units convert mB into √sNN and T for x>1fm using (√sNN,mB,T) parameterizations hep-ph/0511094 results in huge increases in the 4th order cumulant for protons... ×400! perhaps mB (√sNN) doesn’t have to be right on top of the CP to see the effects on the moments

  7. Moments as an experimentalist can see them... Experimentally: The average values of powers of the deviates give cumulants, moments, and moments products.... No. of particles in a single event... Average No. of particles in all “similar” events... STAR, Phys. Rev. Lett. 105 (2010) 022302 Direct comparison of theoretical and experimental quantities!

  8. The Solenoidal Tracker at RHIC (STAR) Time Projection Chamber (TPC) Time Of Flight (TOF) Solenoidal Magnet

  9. STAR Particle Identification and Acceptance TPC “dE/dx” TOF M2 High efficiency PID from TPC and TOF in a wide (|h|<1) and azimuthally complete acceptance

  10. Selected Spectra and Ratios TPC & TOF π, K, p spectra √sNN =39 GeV Ratios of integrated yields model described on next slide...

  11. Where are we on the Phase Diagram? Statistical-Thermal Model (thermus) Computer Physics Communications 180 (2009) 84–106 Free Parameters: T, m b = 1/T -1 (fermions), +1 (bosons) Z = partition function V = volume m = mass K2 = Bessel function g = degeneracy - Grand Canonical ensemble (using only the π±, K±, p± ratios) ...(mB,T) values depend on √sNN and centrality

  12. Getting to sensible experimental moments results... So, what we have to do is “simple.” Turn the “big knob” (√sNN~mB) 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 √sNN or mB… Golden signal is a “non-monotonic behavior” of the 3rd and 4th moments vs √sNN or mB... ...i.e. a significant & √sNN-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 √sNN, 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. Volume Normalization and Baselines Hadron Resonance Gas Model 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 Ss = (M+ - M-)/(M+ + M-) Ks2 = 1 Central Limit Theorem mean values vs centrality “predict” higher moments if particle production is from large number of independent sources Karsch&Redlich, PLB 695, 136 (2011) Raw moments are not volume normalized. “CLT normalization”: look at moments products, Ss, Ks2 “intensive normalized cumulants”: divide by mean multiplicity, w3 = k3/M, w4 = k4/M

  14. Results: net-protons No statistically-significant non-monotonic behavior of 3rd and 4th 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. Results: Total protons Sigma field is “isospin blind” Athanasiou et al. arXiv:1006.4636v2 Net- and Total-Proton results are very similar....

  16. Results: Net-Kaons net-Kaons are a possible proxy of the Strangeness number (conserved)

  17. Results: Net-Charge Npos-Nneg is a proxy of the Charge number (conserved) HRG

  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 √sNN = 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!) ...mB width of the critical enhancement region, D, is much narrower than expected? ...It’s hiding between available beam energies? wide gaps!

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