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

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Outline:. Studying the QCD Phase diagram using Conserved Number distributions in high energy collisions. QCD Phase Diagram E xperimental M easurements Physics T opics Conclusion. Bedangadas Mohanty , VECC, Kolkata. CPOD 2011, Wuhan. QCD Phase Diagram. - PowerPoint PPT Presentation

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Studying the QCD Phase diagram using Conserved Number distributions in high energy collisionsBedangadas Mohanty, VECC, KolkataCPOD 2011, WuhanQCD Phase DiagramExperimental MeasurementsPhysics TopicsConclusionOutline:1QCD Phase Diagram

Physical systems undergo phase transitions when external parameters such as the temperature (T) or a chemical potential () is varied.Conserved Quantities: Baryon Number ~ Electric Charge ~ Q ~ small Strangeness ~ S ~ smallSignals for phase transition/phase boundarySearch for Critical PointBulk properties of QCD matter/Thermalization2Goals:2Experiment

Varying beam energy varies Temperature and Baryon Chemical Potential

TPCTOFTypical Experiment STAR @ RHIC

3Proton identificationUniform Acceptance P. Braun-Munzinger, J. StachelNature 448:302-309,20073Net-proton Number Distributions

Shape of distribution ~ higher ordercorrelations4Typical net-proton distributionsMoments relates to Susceptibility (c) : Study Bulk properties of QCD matterKurtosis x Variance ~ 4)/ [c T2]Skewness x Sigma ~ [3) T]/ [c T2]Product of moments cancel volume effectSTAR: Physical Review Letters 105 (2010) 022302< (N)2> ~ 2 < (N)3> ~ 4.5< (N)4> - 3 < (N)2>2 ~ 7Moments relates to Correlation length (): Study phase transition and Critical Point Negative Skewness: Signal of quark-hadron transition M. Asakawa et al., PRL 109 (2009) 2623014Moments of Net-proton Distribution

Moments:5Central Limit Theorem: Mi = CMx I

2i = C 2x I

Si = Sx/ [ C ]I

i = x/ [ C ]IBreakdown of CLT trends could indicate critical point like physics effect5Proton Detection Efficiency

6Cannot be corrected event-by-event in model independent wayEstimated to be small on distribution shape through realistic simulationsTypical efficiencyHIJING through STAR detector response6Statistical Errors7

Error formulaSub group methodBootstrap/Delta theorem methodOver estimatesLarge fluctuationsCorrect valueSimulations: Net proton distribution is Skellam, with average number of protons = 4and average number of anti-protons = 3 X. F. Luo: arXiv:1109.0593And Lizhu Chen7Other Baryons

8M. Kitazawa and M. Asakawa arXiv: 1107.2755Proton number modified in hadron phaseIsospin distribution of nucleons binomial

Individual Moments changeProducts of Moments similarUrQMDData

F. Karsch, CPOD 20118Net-Proton Distribution Baryon Sources

9C.B. Yang and in Wang - arXiv: 1107.4740Model based on: Baryon Stopping (initial state) Baryon pair production (final state)Single emission sourceMultiple emission sourceNo assumption of thermal equilibriumand critical fluctuationsHigher order correlations to study baryon production9Fluctuations and Hadron Resonance Gas ModelHigher order correlations a test of hadron resonance gas model

P. Braun-Munzinger et al., arXiv: 1107.4267,and Lizhu ChenSuccess of Thermal model

STAR: NPA 757, 102 (2005)

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F. Karsch, K. Redlich PLB 695 (2011) 16510

BNL-Bielefeld PreliminaryF. Karsch CPOD 2011Estimates of freeze-outtemperature

Fluctuations and test of QCDHigher order correlations to study thermodynamics of bulk strongly interacting matter

Perturbative regimeNon-perturbative regime11Science 322 (2008) 1224Science 332 (2011) 152511Fluctuations and Scale of Phase diagramTc sets the scale of the QCD phase diagram

12Science 332 (2011) 1525

Possible alternate approach12Fluctuations and Critical Point

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S. Gupta

Some results on Lattice, need more precise calculationsExpect susceptibilities to divergeKurtosis is negativeCritical point: Non-monotonic variations of fluctuations as a function of beam energyM. Stephanov, Physical Review Letters107 (2011) 052301S. Gupta, QM2011sKurtosisxVarianceCP13Fluctuations and Critical Point14

Experimental results:Effect of auto correlations (small at 200 GeV could be large at 7.7 GeV)Rapidity dependence to study effect of conservationMore accurate error estimatesImportant to have precise results in the energy range of 10 - 15 - 30 GeVSTAR: QM2011 + X. F. Luo CPOD 2011mB ~ 300 MeVmB ~ 200 MeVmB ~ 100 MeV14Fluctuations and Phase Transition15

Deviation from HRG if freeze-out curve close toPhase Boundary/Cross over line Cheng et al, Phys.Rev. D79 (2009) 074505; B. Friman et al., Eur. Phys. J. C 71 (2011) 1694

Lattice QCDPolyakov loop extendedQuark Meson ModelExperimental results feasibility study onlyNeed more studies to establish 6th order momentsSTAR DataSTAR PreliminaryChiral phase transitionL. Chen, BNL workshop, CPOD 201115Conclusions: Higher Moments Contribution to QCD phase diagram:Non-perturbative QCD testsScale of QCD phase diagramSearch for Critical PointSearch for Signals of Phase TransitionOther contributions:Test of Hadron Resonance Gas Model and other QCD based modelsThermalization and Freeze-out parameters (V, T, m) in heavy-ion collisionsBaryon production in heavy-ion collisions16Important realization/agreement:Comparison to QCD calculations and Heavy-Ion datapossible for studying bulk propertiesF. 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 searchM. 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

16OutlookTheory:More realistic Lattice QCD calculations Transverse momentum dependenceContribution from Quantum statistics (~ max 5% at 7.7 GeV M. Stephanov CPOD 2011)Baryon number conservation (Compare to models + study rapidity dependence)17Experiment: 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)

V. Koch CPOD 201117