1Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 This is the first *significant and quantitative* indication (from the experimental point of view) of the CEP’s existence. Anonymous PRL reviewer Essential message Roy A. Lacey Phys.Rev.Lett. 114 (2015) 14, Outline  Introduction Phase Diagrams & HIC  Search strategy for the CEP Theoretical guidance Guiding principles for search  The probe Femtoscopic “susceptibility”  Analysis Finite-Size-Scaling Dynamic Finite-Size-Scaling  Summary Epilogue

2 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 A central goal of the worldwide program in relativistic heavy ion collisions, is to chart the QCD phase diagram 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- explicitly broken TCP CEP The QCD Phase Diagram

3 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 Essential Question What new insights do we have on: The QCD Phase Diagram All are required to fully characterize the CEP

4 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 Theoretical Guidance Experimental verification and characterization of the CEP is a crucial ingredient Dynamic Universality class for the CEP less clear  One slow mode (L) z ~ 3 - Model H Son & Stephanov Phys.Rev. D70 (2004) Moore & Saremi, JHEP 0809, 015 (2008)  Three slow modes (NL) z T ~ 3 z v ~ 2 z s ~ -0.8 Y. Minami - Phys.Rev. D83 (2011) M. A. Stephanov Int. J. Mod. Phys. A 20, 4387 (2005)

5 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 J. Cleymans et al. Phys. Rev. C73,

6 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 Anatomy of search strategy

7 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 Interferometry as a susceptibility probe

8 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 Source function (Distribution of pair separations) Encodes FSI Correlationfunction 3D Koonin Pratt Eqn. Measuring HBT Radii S. Afanasiev et al. PRL 100 (2008) Hanbury Brown & Twist (HBT) radii obtained from two-particle correlation functions q = p 2 – p 1

9 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 Interferometry signal A. Adare et. al. (PHENIX) arXiv: Two pion correlation functions

10 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 STAR ALICE -PoSWPCF2011 HBT Measurements This comprehensive Set of two-pion HBT measurements is used for our search

11 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 Chapman, Scotto, Heinz, PRL (95) 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 initial )/R long Interferometry Probe Hung, Shuryak, PRL. 75,4003 (95) Makhlin, Sinyukov, ZPC (88) The measured HBT radii encode space-time information for the reaction dynamics (R side - R init )/ R long sensitive to c s emission duration emission lifetime T. Csörgő. and B. Lörstad, PRC54 (1996)

12 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 The measurements validate the expected non-monotonic patterns!  Reaction trajectories spend a fair amount of time near a “soft point’’ in the EOS that coincides with the CEP! Finite-Size Scaling (FSS) is used for further validation of the CEP, as well as to characterize its static and dynamic properties Lacey QM2014. Adare et. al. (PHENIX) arXiv:

13 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 Basis of Finite-Size Effects  Only a pseudo-critical point is observed  shifted from the genuine CEP note change in peak heights, positions & widths  A curse of Finite-Size Effects (FSE) T > T c T close to T c L characterizes the system size Illustration large L small L

14 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 Finite-size shifts both the pseudo-critical point and the transition line  A flawless measurement, sensitive to FSE, can not give the precise location of the CEP directly 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

15 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 The Blessings of Finite-Size Finite-size effects have specific identifiable dependencies on size (L) The scaling of these dependencies give access to the CEP’s location, it’s critical exponents and scaling function. M. Suzuki, Prog. Theor. Phys. 58, 1142, 1977 Finite-size effects have a specific L dependence L scales the volume

16 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 Finite size scaling played an essential role for identification of the crossover transition! Finite size scaling and the Crossover Transition Y. Aoki, et. Al.,Nature, 443, 675(2006). Reminder. Crossover: size independent. 1 st -order: finite-size scaling function, and scaling exponent is determined by spatial dimension (integer). 2 nd -order: finite-size scaling function

17 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 The data validate the expected patterns for Finite-Size Effects Max values decrease with decreasing system size Peak positions shift with decreasing system size Widths increase with decreasing system size Data from L. Adamczyk et al. (STAR) Phys.Rev. C92 (2015) 1, Roy A. Lacey Phys.Rev.Lett. 114 (2015) 14, Large L small L

18 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 characteristic patterns signal the effects of finite-size III.Perform Finite-Size Scaling analysis with length scale t h

19 Length Scale for Finite Size Scaling Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 σ x & σ y  RMS widths of density distribution  scales the full RHIC and LHC data sets is a characteristic length scale of the initial-state transverse size,

20 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 (only two exponents are independent ) Note that is not strongly dependent on size

21 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015  The critical exponents validate the 3D Ising model (static) universality class 2 nd order phase transition for CEP From slope From intercept

22 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015  2 nd order phase transition  3D Ising Model (static) universality class for CEP ** A further validation of the location of the CEP and the (static) critical exponents** M. Suzuki, Prog. Theor. Phys. 58, 1142, 1977

23 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 What about Finite-Time Effects (FTE)? Non-linear dynamics  Multiple slow modes z T ~ 3, z v ~ 2, z s ~ -0.8 z s < 0 - Critical speeding up Y. Minami - Phys.Rev. D83 (2011) Significant signal attenuation for short-lived processes with z T ~ 3 or z v ~ 2 Dynamic Finite-Size Scaling (DFSS) is used to estimate the dynamic critical exponent z dynamic critical exponent An important consequence The value of the dynamic critical exponent/s is crucial for HIC z > 0 - Critical slowing down

24 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 DFSS ansatz  2 nd order phase transition For T = T c The magnitude of z is similar to the predicted value for z s but the sign is opposite **Experimental estimate of the dynamic critical exponent** M. Suzuki, Prog. Theor. Phys. 58, 1142, 1977

25 Epilogue Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 Strong experimental indication for the CEP and its location New Data from RHIC (BES-II) together with theoretical modeling, can provide crucial validation tests for the coexistence regions, as well as to firm-up characterization of the CEP!  3D Ising Model (static) universality class for CEP  2 nd order phase transition (Dynamic) Finite-Size Scalig analysis Landmark validated Crossover validated Deconfinement validated (Static) Universality class validated Model H dynamic Universality class invalidated? Other implications! Much additional work required to get to “the end of the line”

End 26 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015

27 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 Phys.Rev.Lett.100:232301,2008) Phys.Lett. B685 (2010) Space-time correlation parameter

28 Roy A. Lacey, Stony Brook University; Zimanyi School'15, Dec , 2015 Dirk Rischke and Miklos Gyulassy Nucl.Phys.A608: ,1996 In the vicinity of a phase transition or the CEP, the sound speed is expected to soften considerably. Interferometry as a susceptibility probe