Studying the QCD Phase diagram using Conserved Number distributions in high energy collisions

1. Outline: Studying the QCD Phase diagram using Conserved Number distributions in high energy collisions QCD Phase Diagram Experimental Measurements Physics Topics Conclusion BedangadasMohanty, VECC, Kolkata CPOD 2011, Wuhan

2. QCD Phase Diagram Physical systems undergo phase transitions when externalparameters such as the temperature (T) or a chemical potential (μ) isvaried. Conserved Quantities: Baryon Number ~  Electric Charge ~ Q ~ small Strangeness ~ S ~ small Goals: • Signals for phase transition/phase boundary • Search for Critical Point • Bulk properties of QCD matter/Thermalization

3. Experiment Typical Experiment – STAR @ RHIC TOF TPC P. Braun-Munzinger, J. Stachel Nature 448:302-309,2007 Proton identification Uniform Acceptance Varying beam energyvaries Temperature and Baryon Chemical Potential

4. Moments relates to Correlation length (): Study phase transition and Critical Point < (N)3> ~ 4.5 < (N)2> ~ 2 < (N)4> - 3 < (N)2>2 ~ 7 Net-proton Number Distributions Typical net-proton distributions Shape of distribution ~ higher order correlations Negative Skewness: Signal of quark-hadron transition M. Asakawa et al., PRL 109 (2009) 262301 Moments relates to Susceptibility (c) : Study Bulk properties of QCD matter Kurtosis x Variance ~ 4)/ [c T2] Skewness x Sigma ~ [3) T]/ [c T2] Product of moments cancel volume effect STAR: Physical Review Letters 105 (2010) 022302

5. Moments of Net-proton Distribution Moments: Central Limit Theorem: Mi = CMx <Npart>I  2i = C 2x <Npart>I Si= Sx/√[C <Npart>]I  i = x/[C <Npart>]I Breakdown of CLT trends could indicate critical point like physics effect

6. Proton Detection Efficiency HIJING through STAR detector response Typical efficiency Cannot be corrected event-by-event in model independent way Estimated to be small on distribution shape through realistic simulations

7. Statistical Errors Error formula Sub group method Bootstrap/Delta theorem method Over estimates Large fluctuations Correct value Simulations: Net proton distribution is Skellam, with average number of protons = 4 and average number of anti-protons = 3 X. F. Luo: arXiv:1109.0593 And Lizhu Chen

8. Other Baryons M. Kitazawa and M. Asakawa – arXiv: 1107.2755 UrQMD Proton number modified in hadron phase Isospin distribution of nucleons binomial Individual Moments change Data Products of Moments similar F. Karsch, CPOD 2011

9. Net-Proton Distribution – Baryon Sources C.B. Yang and in Wang - arXiv: 1107.4740 Multiple emission source Model based on: Baryon Stopping (initial state) Baryon pair production (final state) Single emission source No assumption of thermal equilibrium and critical fluctuations Higher order correlations to study baryon production

10. Fluctuations and Hadron Resonance Gas Model Success of Thermal model Higher order correlations a test of hadron resonance gas model STAR: NPA 757, 102 (2005) F. Karsch, K. Redlich PLB 695 (2011) 165 P. Braun-Munzinger et al., arXiv: 1107.4267, and Lizhu Chen

11. Fluctuations and test of QCD Perturbativeregime BNL-Bielefeld Preliminary F. Karsch – CPOD 2011 Higher order correlations to study thermodynamics of bulk strongly interacting matter Science 332 (2011) 1525 Science 322 (2008) 1224 Estimates of freeze-out temperature Non-perturbativeregime

12. Fluctuations and Scale of Phase diagram Possible alternate approach Tc sets the scale of the QCD phase diagram Science 332 (2011) 1525

13. S. Gupta Fluctuations and Critical Point Kurtosis is negative Some results on Lattice, need more precise calculations Expect susceptibilities to diverge S. Gupta, QM2011 M. Stephanov, Physical Review Letters 107 (2011) 052301 KurtosisxVariance Critical point: Non-monotonic variations of fluctuations as a function of beam energy CP √s

14. Fluctuations and Critical Point STAR: QM2011 + X. F. Luo CPOD 2011 • Experimental results: • Effect of auto correlations (small at • 200 GeV could be large at 7.7 GeV) • Rapidity dependence to study effect • of conservation • More accurate error estimates mB ~ 100 MeV mB ~ 300 MeV Important to have precise results in the energy range of 10 -15 - 30 GeV mB ~ 200 MeV

15. Fluctuations and Phase Transition Deviation from HRG if freeze-out curve close to Phase Boundary/Cross over line L. Chen, BNL workshop, CPOD 2011 STAR Data Polyakov loop extended Quark Meson Model Lattice QCD Chiral phase transition STAR Preliminary Experimental results – feasibility study only Need more studies to establish 6th order moments Cheng et al, Phys.Rev. D79 (2009) 074505; B. Friman et al., Eur. Phys. J. C 71 (2011) 1694

16. Conclusions: Higher Moments Important realization/agreement: Comparison to QCD calculations and Heavy-Ion data possible for studying bulk properties F. Karsch: “comparing this analysis with calculations of the QCD transition temperature allows to quantify the relation between freeze out and transition temperatures” (Conclusions, CPOD 2011) V. Koch: “Higher moments can tell us a lot! (Slide#8, CPOD 2011) M. Stephanov: “Higher moments more sensitive to CP search” M. Asakawa: The combination of the third moments of different channels, and their comparison with the numerical results in lattice QCD will bring various information on the phase structure • Other contributions: • Test of Hadron Resonance Gas Model • and other QCD based models • Thermalization and Freeze-out • parameters (V, T, m) in heavy-ion collisions • Baryon production in heavy-ion collisions • Contribution to QCD phase diagram: • Non-perturbative QCD tests • Scale of QCD phase diagram • Search for Critical Point • Search for Signals of Phase Transition

17. Outlook • Theory: • More realistic Lattice QCD calculations • Transverse momentum dependence • Contribution from Quantum statistics (~ max 5% at 7.7 GeV – M. Stephanov CPOD 2011) • Baryon number conservation (Compare to models + study rapidity dependence) V. Koch CPOD 2011 • Experiment: • Net-charge studies (also needed for baryon fluctuations) • Complete study on net-protons in BES program • with proper centrality selection and error estimates • Do we need data at 15 GeV ? – Yes! • LHC results (Complimentary to RHIC top energy)