PHENIX Capabilities for Studying the QCD Critical Point

1. PHENIX Capabilities for Studying the QCD Critical Point Kensuke Homma / Hiroshima Univ. 9 Jun, 2006 @ RHIC&AGS ANNUAL USERS’ MEETING Outline What is the critical behavior ? Search for critical temperature via correlation length Universality in compressibility Summary Future prospects Kensuke Homma / Hiroshima Univ.

2. Ordered T<Tc Critical T=Tc Disordered T>Tc What is the critical behavior ? Spatial pattern of ordered state Scale transformation Black Black & White Gray Various sizes from small to large • Large fluctuations of correlation sizes on order parameters: • critical temperature • Universality (power law behavior) around Tc caused by basic symmetries and dimensions of an underlying system: • critical exponent A simulation based on two dimensional Ising model from ISBN4-563-02435-X C3342l Kensuke Homma / Hiroshima Univ.

3. g-g0 φ Search for critical temperature In Ginzburg-Landau theory with Ornstein-Zernike picture, free energy density g is given as spatial correlation disappears at Tc external field h causes deviation of free energy from the equilibrium value g0. Accordingly an order parameter f fluctuates spatially. a>0 a=0 a<0 In the vicinity of Tc, f must vanish, hence 1-D spatial multiplicity density fluctuation from the mean density is introduced as an order parameter in the following. Kensuke Homma / Hiroshima Univ.

4. Multiplicity density measurements in PHENIX PHENIX: Au+Au √sNN=200GeV Zero magnetic field to enhance low pt Δη<0.7 integrated over Δφ<π/2 PHENIX Preliminary Negative Binomial Distribution (Bose-Einstein distribution from k emission sources) Kensuke Homma / Hiroshima Univ.

5. Participant Np To ZDC b To BBC Spectator 15-20% 10-15% 5-10% peripheral central 0-5% 0-5% Number of participants, Np and Centrality Multiplicity distribution Np can be related with initial temperature.

6. Relations to the observable N.B.D k Two point correlation function in one dimensional case in a fixed T Two particle correlation function Fluctuation caused by centrality bin width Relation to N.B.D. k Kensuke Homma / Hiroshima Univ.

7. N.B.D. k vs. dh PHENIX Preliminary k(dh) 10 % centrality bin width Function can fit the data remarkably well ! dh PHENIX Preliminary 5% centrality bin width Kensuke Homma / Hiroshima Univ.

8. Correlation length x and static susceptibility c Divergence of correlation length is the indication of a critical temperature. PHENIX Preliminary Au+Au √sNN=200GeV Correlation length x(h) Divergence of susceptibility is the indication of 2nd order phase transition. T~Tc? Np PHENIX Preliminary Au+Au √sNN=200GeV c k=0 * T Np Kensuke Homma / Hiroshima Univ.

9. PHENIX Preliminary 10% cent. bin width 5% cent. bin width a PHENIX Preliminary Shift to smaller fluctuations b PHENIX Preliminary x Stability of the parametrization • can absorb finite centrality bin width effects, namely, • finite initial temperature • fluctuations, while physically • important parameters are • stable. Our parametrization is well controlled. Np

10. What about universality? On going analysis to extract critical exponents are: • Compressibility via scaled variance of multiplicity • Correlation lengths via multiplicity density fluctuations • Heat capacity via pt fluctuations Kensuke Homma / Hiroshima Univ.

11. Isothermal Compressibility Definition of isothermal compressibility In grand canonical ensemble, KT can be related to scaled variance This can be related with N.B.D. k Given a proper estimate on T and measured Tc, we can investigate universality among various collision systems. Kensuke Homma / Hiroshima Univ.

12. Np dependence of compressibility All species are scaled to match 200 GeV Au+Au points 1/m+1/k 1/m+1/k 0.2 < pT < 0.75 GeV/c 0.2 < pT < 3.0 GeV/c Np Np • All systems appear to obey a universal curve • by using Glauber T_AB as a volume V. • This behavior is dominated by low pt charged particles !!! Kensuke Homma / Hiroshima Univ.

13. Comparison of scaled variance to NA49 (17 GeV Pb+Pb) The NA49 scaled variance was corrected for impact parameter fluctuations from their 10% wide centrality bins and scaled up by 15% to lie on the 200 GeV Au+Au curve. 0.2 < pT < 3.0 GeV/c Np Given a reasonable temperature estimate with collision energies as well as Np, we would be able to study the universality by determining the critical exponent around Tc. Kensuke Homma / Hiroshima Univ.

14. Summary • Two point correlation lengths have been extracted based on the function form by relating pseudo rapidity density fluctuations and the GL theory up to the second order term in the free energy. The lengths as a function of Np indicates non monotonic increase at Np~100. • The product of the static susceptibility and the corresponding temperature shows no obvious discontinuity within the large systematic errors at the same Np where the correlation length is increased. • Isothermal compressibility via scaled variance of multiplicity shows a universal curve in various collision systems as a function of Np. Kensuke Homma / Hiroshima Univ.

15. Future prospects • If non monotonic increase of x is a good measure to define Tc and one can discuss critical exponents on thermodynamic quantities around Tc … • Preferable conditions to investigate critical • points along a phase boundary are: • High multiplicity per collision event • reasonably high initial temperature • capability to enhance lower pt particles • larger acceptance • Scan higher baryon density region • lower colliding energies • asymmetric colliding energy helps? • device with high position resolution in the forward region. T QGP Tricritical point Hadronic mB K. Rajagopal and F. Wilczek, hep-ph/0011333 Kensuke Homma / Hiroshima Univ.

16. Back up slides Kensuke Homma / Hiroshima Univ.

17. Fourier expression of order parameter Statistical weight can be obtained from free energy coefficient of spatial fluctuation Average of wave number dependentdensity fluctuations from free energy Kensuke Homma / Hiroshima Univ.

18. Fourier transformation oftwo point correlation function Kensuke Homma / Hiroshima Univ.

19. A function form of correlation function is obtained by inverse Fourier transformation. Function form of correlation function Kensuke Homma / Hiroshima Univ.

20. σinel is total inelastic cross section From field picture to particle picture Kensuke Homma / Hiroshima Univ.

21. Total rapidity interval ΔY is divided into M equal bins Normalized factorial moment Kensuke Homma / Hiroshima Univ.

22. Second order NFM and correlation function Kensuke Homma / Hiroshima Univ.

23. Bose-Einstein distribution Negative binomial distribution σ: standard deviation μ: average multiplicity NBD (k→∞) = Poisson distribution NBD (k<0) = Binomial distribution NBD and NFM Kensuke Homma / Hiroshima Univ.

24. NBD k and integrated correlation function Kensuke Homma / Hiroshima Univ.

25. Susceptibility is defined by the response of phase for the external field. In the static limit of k = 0, χ cannot be extracted separately without temperature control, but χT value can be obtained by the mean multiplicity μ and α and ξ. Susceptibility Kensuke Homma / Hiroshima Univ.

26. Geometrical acceptance (Δη<0.7, Δφ<π/2) Multiplicity measurement at PHENIX • Data was collected at the no magnetic filed condition to enhance charged particles with low momenta. • Charged tracks were reconstructed based on drift chamber by requiring association with two wire chamber (PC1, PC3) and EM calorimeter and collision vertex position measured by BBC. • All detector stability is carefully confirmed. • Dead areas of detectors are corrected by the MC simulation. Kensuke Homma / Hiroshima Univ.

27. 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 (1992) 63 [E802 collaboration] Phys. Rev. C52 (1995) 2663 Universally, hadron multiplicity distributions agree with NBD in high energy collisions. Charged particle multiplicity distributions and negative binomial distribution (NBD) Kensuke Homma / Hiroshima Univ.