1Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 “A thinker sees his own actions as experiments and questions--as attempts to find out something. Success and failure are for him answers above all.” ― Friedrich Nietzsche

2 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Known unknowns  Location of the critical End point (CEP)? Order of the transition? Value of the critical exponents?  Location of phase coexistence regions?  Detailed properties of each phase? All are fundamental to charting the phase diagram Known knowns Spectacular achievement:  Validation of the crossover transition leading to the QGP  Initial estimates for the transport properties of the QGP 2 nd Order O(4) 2 nd Order Z(2) 1 st Order Crossover m s > m s3 Conjectured Phase Diagram 1 st Order cs- broken TCP CEP The QCD Phase Diagram

3 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 The QCD Phase Diagram What new insights do we have on: II. The CEP “landmark”? (T,μ B ) location? Critical exponents? Universality Class?  HBT excitation function measurements See A. Majumdar’s talk

(η/s) RHIC estimates – QM2009  Excellent Convergence on the magnitude of η/s at RHIC Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, πη/s ~ of 17 Reminder Status Quo A major uncertainty in the extraction of η/s stems from Incomplete knowledge of the Initial-state eccentricity model ε n – η/s interplay?  T dependence of η/s?  μ B dependence of η/s?  Possible signal for CEP? Subsequently

Song et al 5 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Status Quo Note The Initial-state eccentricity difference between MC-KLN and MC-Glauber is ~ 20% due to fluctuation differences in the models! ε n – η/s interplay? New methodology and constraints required Luzum et al. arXiv η/s is a property of the medium and should not depend on initial geometry! This is NOT an uncertainty; It is a failure of the method of extraction

6 Acoustic viscous modulation of v n Staig & Shuryak arXiv: Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Matter Flow Flow is acoustic Scaling expectations: v n is related to v 2 System size dependence n 2 dependence Each of these scaling expectations has been exquisitely validated Initial Geometry characterized by many shape harmonics (ε n )  drive v n

7 A B  Geometric fluctuations included  Geometric quantities constrained by multiplicity density. Phys. Rev. C 81, (R) (2010) arXiv: σ x & σ y  RMS widths of density distribution Geometric quantities for scaling Geometry Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015

8 Scaling properties of flow

9 A constraint for initial-state fluctuations Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 ALICE data q 2(Lo) q 2(Hi)  Viable models for initial-state fluctuations should still scale Shape fluctuations lead to a distribution of the Q vector at a fixed centrality Lacey et. al, arxiv:

10 Acoustic Scaling of shape-engineered events Scaling properties of flow Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Lacey et. al, arxiv:

11 Scaling properties of flow Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, Viscous Hydrodynamics

12 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Extraction of η/s Lacey et. al, arxiv:

13 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Viscous Hydro arXiv: arXiv: & CMS PAS HIN Slope sensitive to η/s Extraction of η/s

GeV 19.6 GeV39 GeV 62.4 GeV 200 GeV 2.76 TeV Scaling properties of flow Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Lacey et. al, Phys.Rev.Lett. 112 (2014)

15 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 What new insights do we have on: II. The CEP “landmark”? (T,μ B ) location? Critical exponents? Universality Class?

16 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 The critical end point is characterized by several (power law) divergences Anatomy of search strategy Approaching the critical point of a 2 nd order phase transitions  The correlation length diverges Renders microscopic details (largely) irrelevant  This leads to universal power laws and scaling functions for static and dynamic properties Ising model  Search for “critical fluctuations” in HIC Stephanov, Rajagopal, Shuryak PRL.81, 4816 (98)

17 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Anatomy of search strategy

18 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Source function (Distribution of pair separations) Encodes FSI Correlationfunction Inversion of this integral equation  Source Function 3D Koonin Pratt Eqn. Interferometry as a susceptibility probe Two-particle correlation function Alias (HBT) Hanbury Brown & Twist S. Afanasiev et al. (PHENIX) PRL 100 (2008) In the vicinity of a phase transition or the CEP, the divergence of the compressibility leads to anomalies in the expansion dynamics  Measurements of the space-time extent provides a good probe for the (T,μ B ) dependence of the susceptibility

19 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Chapman, Scotto, Heinz, PRL (95) (R 2 out -R 2 side ) sensitive to the susceptibility Specific non-monotonic patterns expected as a function of √s NN  A maximum for (R 2 out -R 2 side )  A minimum for ~R side /R long Interferometry Probe Hung, Shuryak, PRL. 75,4003 (95) Makhlin, Sinyukov, ZPC (88)

20 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 These characteristic non-monotonic patterns signal a suggestive change in the reaction dynamics  Deconfinement Phase transition? CEP? How to pinpoint the onset of the Deconfinement Phase transition? and the CEP?  Study explicit finite-size effects A. Adare et. al. (PHENIX) arXiv:

21 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 The critical end point can be probed via measurements of critical fluctuations and proxies for the susceptibility, heat capacity, etc.  Divergences are modulated by the effects of finite-size Pinpointing the location of the CEP! from partition function

22 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 The curse of Finite-Size effects (note change in peak heights, positions & widths) The precise location of the critical end point is influenced by Finite-size effects  Only a pseudocritical point is observed – shifted from the genuine CEP

23 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Finite-size shifts both the pseudocritical endpoint and the transition line  Even flawless measurements Can Not give the precise location of the CEP in finite-size systems The curse of Finite-Size effects E. Fraga et. al. J. Phys.G 38:085101, 2011 Displacement of pseudo-first-order transition lines and CEP due to finite-size

24 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 The Blessings of Finite-Size (note change in peak heights, positions & widths) Finite-size effects are specific  allow access to CEP location and the critical exponents  L scales the volume

25 Acoustic Scaling of HBT Radii Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015

26 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 I.Max values decreases with decrease in system size II.Peaks shift with decreasing system size III.Widths increase with decreasing system size These characteristic patterns signal the effects of finite-size

27 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 characteristic patterns signal the effects of finite-size  Perform Finite-Size Scaling analysis

28 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 (only two exponents are independent ) Note that is not strongly dependent on V

29 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015  Critical exponents compatible with 3D Ising model universality class  2 nd order phase transition for CEP Finite-Size Scaling gives (Chemical freeze-out systematics)

30 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Finite-Size Scaling validated  2 nd order phase transition  3D Ising Model Universality class for CEP Finite-Size Scaling validation **A Clear initial indication for the CEP**

31 Epilogue Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Lots of work still to be done to fully chart the QCD phase diagram!!  Experimental constraints provide new insights on the QCD phase Diagram Additional Data from RHIC (BES-II) together with mature and sophisticated theoretical modeling now required!  2 nd order phase transition  3D Ising Model Universality class for CEP

Thank you for your attention 32 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015

33 Exploit the RHIC-LHC beam energy lever arm Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Energy scan Search Strategy M. Malek, CIPANP (2012) J. Cleymans et al. Phys. Rev. C73, Challenge  identification of robust signals

34 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 The blessings of Finite-Size Scaling Cross Check Extracted critical exponents and CEP values should lead to data collapse onto a single curve Essential Message Search for & utilize finite-size scaling!

35 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 exquisitely demonstrated via HBT measurement for several systems Femtoscopic measurementsarXiv:  Larger expansion rate at the LHC Acoustic Scaling of HBT Radii

36 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 The blessings of Finite-Size Scaling Finite-Size Scaling can be used to extract the location of the deconfinement transition and the critical exponents

37 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 The blessings of Finite-Size Scaling Finite-Size Scaling can be used to extract the location of the deconfinement transition and the critical exponents Critical exponents reflect the universality class and the order of the phase transition

38 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Freeze-out transverse size proportional to initial transverse size Freeze-out time varies with initial size Scaling properties of HBT Viscous Hydrodynamics – B. Schenke Freezeout size reflects;  Initial size + expanded size Characteristic acoustic Scaling validated in Viscous hydrodynamics E. Shuryak, I. Zahed Phys.Rev. D89 (2014)

39 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 Interferometry signal A. Adare et. al. (PHENIX) arXiv:

40 Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015 STAR ALICE -PoSWPCF2011 Exquisite data set for combined RHIC-LHC results? HBT Measurements

41 Acoustic Scaling of HBT Radii - LHC Roy A. Lacey, Stony Brook University, ICPAQGP, Kolkata, India, Feb. 1-6, 2015

42 m T Scaling of HBT Radii  PHENIX and STAR consistent arxiv: arxiv:  all radii linear ◦ R i =a+b/√m T  Useful to interpolate to common m T