1. A possible signature of QGP phase transition probed by density correlation and fluctuation Tomoaki Nakamura RIKEN 2007/1/12 Heavy Ion Cafe

2. 1/12/2008Tomoaki Nakamura - RIKEN2 QCD phase boundary and critical point [K. Rajagopal, Acta. Phys. Polon. B, 3021 (2000)] [M. A. Stephanov, Int. J. Mod. Phys. A20, 4387 (2005)] Critical phase boundary  No argument on the qualitative picture. Existence of critical point  Naturally expected. Where is critical point?  None of theories have reached an agreement. Experimental investigation is indispensable! μ

3. 1/12/2008Tomoaki Nakamura - RIKEN3 Experimental observables at RHIC energy High pT suppression  Parton level energy loss.  Even in the mid-central collision?  No indication on the critical phase boundary. Large V 2  Early thermalization. Quark number scaling  Final state hadrons keep the information of QGP phase. R AA central peripheral V2V2

4. 1/12/2008Tomoaki Nakamura - RIKEN4 Phase diagram of He 4 (Pressure vs. Temperature) Pressure [Atm] Temperature [K] Superfluidty phase Liquid phase Solid phase critical point [J. H. Vignos and H. A. Fairbank, Phys. Rev. Lett. 6, 265 (1961)]

5. 1/12/2008Tomoaki Nakamura - RIKEN5 Clear signature of phase boundary in He 4 Pressure [Atm] He 4 phase diagram Temperature [K] [K] [mK] [μK] Specific heat C s C s [J/gK] |TTS| phase boundary [W. M. Fairbank and M. J. Buckingam, Int. Conf. on Low Temp. Phys. (1957)]

6. 1/12/2008Tomoaki Nakamura - RIKEN6 Possible thermo-dynamic observables 1st order 2nd order Entropy Specific heat Order parameter Susceptibility Correlation function Function form Ginzbrug-Landau phenomenology

7. 1/12/2008Tomoaki Nakamura - RIKEN7 Correlation length a) T < T c b) T = T c c) T > T c Disordered phase  indicate short correlation length At critical temperature  coexistence of various correlation length  diverged measured value [H. Nishimura, 2D Ising model (2005)] Ordered phase  indicate long correlation length

8. 1/12/2008Tomoaki Nakamura - RIKEN8 The case in heavy-ion collisions Measuring density correlation by the final state particle density in proper time frame. Differential length dz among hydrodynamical sub elements (1), (2), (3) …, at a common proper time τ. Limiting the region of interest to the mid-rapidity. space time τｆτｆ nucleus hadron phase hadrons τcτc QGP phase nucleus (1) (2) (3)

9. 1/12/2008Tomoaki Nakamura - RIKEN9 Scanning the susceptibility / correlation length T, ε χ, ξ no phase transition hadron phase QGP phase critical phase boundary hadron-hadron interactionquark-gluon interaction

10. 1/12/2008Tomoaki Nakamura - RIKEN10 Charged track reconstruction in PHENIX Acceptance: Δη < 0.7, Δφ < π/2 Track identification: DC Track association: beam vertex (BBC), hit point in wire chamber (PC1, PC3), Cluster position in EMC. Measuring tracks at no magnetic field condition to optimize low momentum charged particles. Minimum pT threshold.  π: 0.1 GeV/c  K : 0.25 GeV/c  p : 0.35 GeV/c Particle composition.  π : K : p = 94 : 4 : 2 Mean pT for π = 0.57 GeV/c. For inclusive charged particle, maximum 3 % difference at η = 0.35 for the conversion of rapidity to pseudo rapidity.

11. 1/12/2008Tomoaki Nakamura - RIKEN11 Measurement of energy density Centrality is determined by the anti-correlation between the forward detectors. Centrality is converted to the N part based on the Gluaber model. Bjorken energy density is estimated by the E T measurement. [PHENIX, Phys. Rev. C76, 034903 (2007)] [PHENIX, Phys. Rev. C71, 34908 (2005)] Spectator Participant Energy density

12. 1/12/2008Tomoaki Nakamura - RIKEN12 Factorial moment and inclusive particle density

13. 1/12/2008Tomoaki Nakamura - RIKEN13 E802: 16 O+Cu 16.4AGeV/c at AGS most central events [DELPHI collaboration] Z. Phys. C56, 63 (1992)] [E802 collaboration] Phys. Rev. C52, 2663 (1995)] DELPHI: Z 0 hadronic Decay at LEP 2,3,4-jets events Charged particle multiplicity distributions

14. 1/12/2008Tomoaki Nakamura - RIKEN14 NBD and 2nd order NFM Negative binomial distribution Bose-Einstein distribution μ: average multiplicity σ: standard deviation NBD (k→∞) = Poisson distribution

15. 1/12/2008Tomoaki Nakamura - RIKEN15 Advantage of using NBD Uncorrected charged particle multiplicity distribution and NBD fits for most central (10%) events in Au+Au √s NN =200GeV (Accuracy of fits : 80% C.L.) Average multiplicity can be easily corrected but fluctuations are not. If the distribution is known, the fluctuation can be corrected. δη=0.09 δη=0.7 [PHENIX, Phys. Rev. C76, 034903 (2007)] Detector condition

16. 1/12/2008Tomoaki Nakamura - RIKEN16 2nd order normalized factorial moment

17. 1/12/2008Tomoaki Nakamura - RIKEN17 NBD vs. correlation length Using Ornstein-Zernike formula, 1D two particle correlation function is α: correlation strength ξ: correlation length β: constant Relation with NBD

18. 1/12/2008Tomoaki Nakamura - RIKEN18 Extraction of the correlation 99% C. L. [PHENIX, Phys. Rev. C76, 034903 (2007)] 10% 5% δη Large parameter correlation between α and ξ. But small correlation lengths are indicated. Good agreement with data. Can not separate α and ξ.

19. 1/12/2008Tomoaki Nakamura - RIKEN19 αξ, β vs. N part β αξ ● 5% ○ 10% ● 5% ○ 10% 5% binning 10% binning β absorb effects on the finite resolution of centrality binning i.e. the fluctuation of Npart. αξ product, which is monotonically related with χ k=0 indicates the non-monotonic behavior around Npart ~ 90. [PHENIX, Phys. Rev. C76, 034903 (2007)]

20. 1/12/2008Tomoaki Nakamura - RIKEN20 Evaluation of the non-monotonicity Power law + Gaussian Power law + Gaussian:3.98 σ (5%), 3.21 σ (10%) Linear + Gaussian:1.24 σ (5%), 1.69 σ (10%) 5% 10% Power lawLinear + Gaussian χ 2 /NDF = 2.76 : 0.60χ 2 /NDF = 1.23 : 0.79 χ 2 /NDF = 2.10 : 0.38χ 2 /NDF = 1.09 : 0.43 [PHENIX, Phys. Rev. C76, 034903 (2007)] 5%

21. 1/12/2008Tomoaki Nakamura - RIKEN21 On the relation with HBT effect If all correlations are originated in HBT effect,  α corresponds to the chaoticity parameter λ  ξ corresponds to the radius parameter R used in HBT analysis. However, λ is constant as a function of Npart, and R monotonically increases with increasing Npart. Therefore, known HBT effects cannot explain the non-monotonic behavior of αξ. One dimensional radius parameters. [A. Enokizono, Ph. D. thesis, Hiroshima Univ.] Au+Au √s NN =200GeV

22. 1/12/2008Tomoaki Nakamura - RIKEN22 Other correlation sources Pseudorapidity independent correlations are all absorbed by the constant term β. e.g. elliptic flow etc. Npart fluctuations (residual effect) are also absorbed owing to the β. Trivial particle correlations originating from charged track reconstructions in tracking detectors have been suppressed a priory. Effects from weak decay particles (Λ, Ks) were estimated for the NBD k by the MC calculation. It is less than 1% for each. Effects from photon conversion electrons is about 10 -3 %, which was obtained by GEANT MC simulation. Effects from knock on electron in detector material is about 10 -5 %. Above contribution is negligible as compared to total error on k.

23. 1/12/2008Tomoaki Nakamura - RIKEN23 Accidental coincidence? PHENIX ε BJ (t=1fm/c) corresponding to Np~90 [NA50, Eur. Phys. J. C39, 355 (2005)] Np~90

24. 1/12/2008Tomoaki Nakamura - RIKEN24 Conclusion I The charged particle multiplicity distributions for the various pseudorapidity gap, δη < 0.7, in Au+Au collisions at √s NN = 200 GeV are found to be well described by NBD as well as the other collision system. We found the constant β parameter is necessary to avoid the residual effects in the measurement for the extraction of correlations from the integrated correlation function. Upper limit of correlation length over all centrality bins is less than 0.035, which is obtained by the free parameter fits.

25. 1/12/2008Tomoaki Nakamura - RIKEN25 Conclusion II αξ product, which monotonically related to susceptibility in the long wavelength limit, χ k =0, show a non-monotonic behavior as a function of the number of participant nucleons, Npart. A possible indication of a local maximum or critical behavior is seen at Npart ~ 90 and the corresponding energy density is εBjτ ~ 2.4GeV/(fm 2 c). Furthermore systematic study is on going using the different collision system and energy. It will be presented at the next QM.