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A possible signature of QGP phase transition probed by density correlation and fluctuation

A possible signature of QGP phase transition probed by density correlation and fluctuation. Tomoaki Nakamura RIKEN 2007/1/12 Heavy Ion Cafe. QCD phase boundary and critical point. Critical phase boundary No argument on the qualitative picture. Existence of critical point

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A possible signature of QGP phase transition probed by density correlation and fluctuation

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

  2. QCD phase boundary and critical point • 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! [K. Rajagopal, Acta. Phys. Polon. B, 3021 (2000)] μ [M. A. Stephanov, Int. J. Mod. Phys. A20, 4387 (2005)] Tomoaki Nakamura - RIKEN

  3. Experimental observables at RHIC energy RAA • High pT suppression • Parton level energy loss. • Even in the mid-central collision? • No indication on the critical phase boundary. • Large V2 • Early thermalization. • Quark number scaling • Final state hadrons keep the information of QGP phase. peripheral central V2 Tomoaki Nakamura - RIKEN

  4. Phase diagram of He4 (Pressure vs. Temperature) Solid phase critical point Liquid phase Pressure [Atm] Superfluidty phase Temperature [K] [J. H. Vignos and H. A. Fairbank, Phys. Rev. Lett. 6, 265 (1961)] Tomoaki Nakamura - RIKEN

  5. Clear signature of phase boundary in He4 Specific heat Cs He4 phase diagram phase boundary Pressure [Atm] Cs [J/gK] [K] [mK] [μK] Temperature [K] |TTS| [W. M. Fairbank and M. J. Buckingam, Int. Conf. on Low Temp. Phys. (1957)] Tomoaki Nakamura - RIKEN

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

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

  8. 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. time hadrons hadron phase (1) (2) (3) QGP phase τc τｆ space nucleus nucleus Tomoaki Nakamura - RIKEN

  9. Scanning the susceptibility / correlation length hadron-hadron interaction quark-gluon interaction hadron phase χ, ξ QGP phase no phase transition critical phase boundary T, ε Tomoaki Nakamura - RIKEN

  10. Charged track reconstruction in PHENIX • 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. 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. Tomoaki Nakamura - RIKEN

  11. Measurement of energy density [PHENIX, Phys. Rev. C76, 034903 (2007)] Centrality is determined by the anti-correlation between the forward detectors. Centrality is converted to the Npart based on the Gluaber model. Bjorken energy density is estimated by the ET measurement. Spectator Participant Energy density [PHENIX, Phys. Rev. C71, 34908 (2005)] Tomoaki Nakamura - RIKEN

  12. Factorial moment and inclusive particle density Tomoaki Nakamura - RIKEN

  13. Charged particle multiplicity distributions DELPHI: Z0 hadronic Decay at LEP 2,3,4-jets events E802: 16O+Cu 16.4AGeV/c at AGS most central events [DELPHI collaboration] Z. Phys. C56, 63 (1992)] [E802 collaboration] Phys. Rev. C52, 2663 (1995)] Tomoaki Nakamura - RIKEN

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

  15. Advantage of using NBD [PHENIX, Phys. Rev. C76, 034903 (2007)] Uncorrected charged particle multiplicity distribution and NBD fits for most central (10%) events in Au+Au √sNN=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 Detector condition Tomoaki Nakamura - RIKEN

  16. 2nd order normalized factorial moment Tomoaki Nakamura - RIKEN

  17. 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 Tomoaki Nakamura - RIKEN

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

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

  20. Evaluation of the non-monotonicity [PHENIX, Phys. Rev. C76, 034903 (2007)] χ2/NDF = 2.76 : 0.60 χ2/NDF = 1.23 : 0.79 5% 5% Power law Linear Power law + Gaussian Linear + Gaussian 10% 10% χ2/NDF = 2.10 : 0.38 χ2/NDF = 1.09 : 0.43 Power law + Gaussian: 3.98 σ (5%), 3.21 σ (10%) Linear + Gaussian: 1.24 σ (5%), 1.69 σ (10%) Tomoaki Nakamura - RIKEN

  21. On the relation with HBT effect Au+Au √sNN=200GeV • 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.] Tomoaki Nakamura - RIKEN

  22. 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. Tomoaki Nakamura - RIKEN

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

  24. Conclusion I The charged particle multiplicity distributions for the various pseudorapidity gap, δη < 0.7, in Au+Au collisions at √sNN = 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. Tomoaki Nakamura - RIKEN

  25. Conclusion II αξ product, which monotonically related to susceptibility in the long wavelength limit, χk=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/(fm2c). Furthermore systematic study is on going using the different collision system and energy. It will be presented at the next QM. Tomoaki Nakamura - RIKEN

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