The Study of the Critical Point of QCD using Fluctuations. Gary Westfall Terry Tarnowsky Hui Wang Michigan State University

Transcription

1 The Study of the Critical Point of QCD using Fluctuations Gary Westfall Terry Tarnowsky Hui Wang Michigan State University 1

2 Search for QCD Transitions If we pass through a QCD phase transition, we expect a change in the number of degrees of freedom and a corresponding change in particle number fluctuations Hadronic matter to quark gluon matter If we pass near a QCD critical point, we expect an increase in susceptibilities and a corresponding increase in particle number fluctuations Look for changes in fluctuations as a function of incident energy 2

3 Lattice QCD Calculations Cheng et al., PRD, (2009), quadratic and quartic fluctuations of baryon number, electric charge and strangeness, all quantities normalized to hadron gas 3

4 QCD Phase Diagram 4

5 Statistical Model T ch = 163 ± 4 MeV µ B = 24 ± 4 MeV γ s = 0.99 ± 0.07 n i = N i V = g i 2π 2 p 2 dp 3, µ 0 n γ s ( s e E i (p) µ i )/T i = µ B B i µ s S i µ I3 I i ch ± 1 5

6 Focusing Calculations for 40 AGeV Pb+Pb Asakawa, Bass, Müller, Nonaka PRL 101, (2008) 6

7 Onset of Deconfinement Gazdzicki, Gorenstein, Seyboth v1 [hep-ph] 7

8 K/π Ratios from STAR Gazdzicki, Gorenstein, Seyboth v1 [hep-ph] 8

9 RHIC Beam Energy Scan ( ) 2 K cm is the kinetic energy of each beam s = 2K cm + 2m p c 2 s NN = 2 K cm nucleon + 2m p c2 Study Au+Au collisions through the T / µ B region of interest using the following energies s NN = 6, 7.7, 11.5, 17 Below RHIC injection energy, 29, 39, 62.4, 200 GeV STAR has the advantage over previous NA49 measurements because of the collider geometry 9

10 Fluctuations Measure the number of pions, kaons, and protons event-by-event Study K/π and p/π fluctuations to help remove event-by-event volume fluctuations Relate K/π fluctuations to strangeness fluctuations Relate p/π fluctuations to baryon number fluctuations 10

11 Fluctuation Observables σ dyn = sgn ( σ data σ mixed ) σ data σ is the relative width of the K / π or p / π distributions 2 σ mixed Measure deviation from Poisson behavior ( ) ν dyn,iπ = N i N i 1 N i 2 ( ) + N π N π 1 N π 2 2 N i N π N i N π, i = K, p It turns out that 2 σ dyn = ν dyn for K/π and p/π 11

12 Fluctuations Data STAR Collaboration Au+Au at 20, 62.4, 130, and 200 GeV at BNL RHIC Phys. Rev. Lett. 103, (2009) for K/π Brand new results (not for attribution) from Run 10 NA49 Collaboration Pb+Pb central collisions (0-3.5%) for K/π and p/π 6.3, 7.6, 8.8, 12.3, and 17.3 GeV at CERN SPS (20, 40, 60, 80, 160 AGeV Pb+Pb) Phys. Rev. C79, (2009) 12

13 Models SH, Statistical Hadronization Model Torrieri, arxiv: v1 [nucl-th] (2007) Torrieri et al., arxiv:1001:0087v1 [nucl-th] (2009) HIJING Phys. Rev. D44, 3501 (1991). UrQMD, Ultrarelativistic Quantum Molecular Dynamics, HSD, Hadron String Dynamics, Phys. Rev. C79, (2009) 13

14 K/π Fluctuations Gary Westfall 14

15 K/π Fluctuations in Central Collisions 15

16 Another Explanation for K/π Koch and Schuster, PRC 81, (2010) 16

17 Scaling for K/π Fluctuations Poisson: σ dyn ( s ) = σ dyn Particle Number: σ dyn N K : σ dyn ( s ) = σ dyn Geometric: σ dyn ( 200 GeV) ( s ) = σ dyn ( 200 GeV) ( s ) = σ dyn 1 K + 1 π 1 K + 1 π K ( 200 GeV) K ( 200 GeV) 200 GeV K s ( ) 1/4 K K s 200 GeV K + π + π 200 GeV s N π in a similar way π π ( ) 1/4 200 GeV s 17

18 Centrality Dependence a + b / ( dn ch / dη) 18

19 Separate Signs 200 GeV Au+Au ν dyn,k + π = N K N + ( K 1 + ) 2 + N π N ( π 1 ) 2 2 N K +N π N K + N π N K + N π Summed signs Same signs Opposite signs 19

20 Scale with dn ch /dη HIJING 20

21 Same Sign ν dyn Au+Au central collisions ν dyn,k + π = N K N + ( K 1 + ) 2 + N π N + ( π 1 + ) 2 2 N K +N π + N K + N π + N K + N π + 21

22 p/π Fluctuations Gary Westfall 22

23 p/π Fluctuations 23

24 Plot ν dyn 24

25 Compare ν dyn and σ dyn 25

26 Same Signs Λ p + π 26

27 Conclusions - K/π Current data for the incident energy dependence of K/π fluctuations in central collisions are insufficient to state whether there are any deviations from monotonic behavior Centrality-selected K/π fluctuations seem to scale with dn ch /dη for 62.4 and 200 GeV Au+Au collisions Same-sign K/π fluctuations are close to zero Opposite-sign K/π fluctuations are negative Sign-selected K/π fluctuations can be related to various observables such resonance production, K * /K - 27

28 Conclusions - p/π Low energy data seem to be dominated by resonances Λ p + π Δ ++ p + π + Current data for p/π fluctuations in central collisions show a smooth dependence on incident energy UrQMD calculations for p/π fluctuations reproduce the trend observed in central collisions Sign selected p/π fluctuations are always negative 28

29 Future Complete the analysis of Run 10 data Complete the beam energy scan in Run 11 (next year) Other observables are promising forward/backward fluctuations balance functions 29

30 STAR Time of Flight Array m 2 = p 2 1 β 2 β 2 30

31 The End 31

32 Extra Slides 32

33 Comparison Between UrQMD and HSD 33

34 K/π Distribution Au+Au 0-5% Ratio of Data to Mixed Real is wider than Mixed Gary Westfall 34

35 Compare STAR K/π Data with UrQMD and HSD STAR acceptance used for all energies 35

36 Relation of K/π Fluctuations to Resonance Re-interaction Predict K/π fluctuations and resonance production using the statistical hadronization model Torrieri et al., SQM, arxiv:1001:0087v1 [nucl-th] (2009) Relate ν dyn,k-π- and ν dyn,k+π- to K *0 (892)/K - ratio (3/4)<N π- >(ν dyn,k-π- - ν dyn,k+π- ) K *0 /K - 36

37 SH Predictions 37

38 SH Predictions 38

39 Compare STAR Data with UrQMD and HSD STAR acceptance used for all energies 39