Kensuke Homma / Hiroshima Univ. from PHENIX collaboration

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Kensuke Homma / Hiroshima Univ. from PHENIX collaboration

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Kensuke Homma / Hiroshima Univ. from PHENIX collaboration Search for critical temperature by measuring spatial correlation length via multiplicity density fluctuations Kensuke Homma / Hiroshima Univ. from PHENIX collaboration July 3, 2006 in Florence (Italy) at the Galileo Galilei Institute Outline What is the critical behavior ? Order parameter and phase transition Free energy coefficients and correlation function How can we define initial temperature ? PHENIX preliminary results Summary Kensuke Homma / Hiroshima Univ.

What is the critical behavior ? Ordered T=0.995Tc Critical T=Tc Disordered T=1.05Tc Spatial pattern of ordered state Scale transformation Black Black & White Various sizes from small to large Gray Spatial pattern of spin correlation. Black is the aligned state of spins. Large fluctuations of correlation sizes on order parameters: critical temperature (focus of this talk) 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.

Order parameter and phase transition In Ginzburg-Landau theory with Ornstein-Zernike picture, free energy density g is given as φ g-g0 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 Interpretation. In the vicinity of Tc, f must vanish, hence b>0 for 2nd order 1-D spatial multiplicity density fluctuation from the mean density is introduced as an order parameter in the following. Kensuke Homma / Hiroshima Univ.

Two point correlation function & Fourier transformation . Relative distance between two points Kensuke Homma / Hiroshima Univ.

Expectation value of |fk|2 from free energy deviation Fourier expression of order parameter Statistical weight can be obtained from free energy Kensuke Homma / Hiroshima Univ.

Function form of two point correlation function Fourier transformation of two point correlation of order parameter From Dg (up to 2nd order) due to spatial fluctuation A function form of correlation function is obtained by inverse Fourier transformation. Kensuke Homma / Hiroshima Univ.

From two point correlation to two particle correlation Two point correlation function in 1-D case at fixed T Two particle correlation function Summarize Rapidity independent term is added. Kensuke Homma / Hiroshima Univ.

Number of participants, Np and Centrality peripheral central 0-5% 15-20% 10-15% 5-10% b To ZDC To BBC Spectator Participant Np Multiplicity distribution

Can Np be related with initial temperature? Transverse energy ET Np scan may be a fine scan on the initial temperature T, while collision energy is a coarse scan (?). Tc should be rather investigated with fine scan. Let’s suppose that Np can be a monotonic function of T. Kensuke Homma / Hiroshima Univ.

Multiplicity density measurements in PHENIX Δη<0.7 integrated over Δφ<π/2 PHENIX: Au+Au √sNN=200GeV Probability (A.U.) PHENIX Preliminary small dh large dh Zero magnetic field to enhance low pt statistics per collision event n/<n> Negative Binomial Distribution can describe data very well. Kensuke Homma / Hiroshima Univ.

Relations between N.B.D k and integrated correlation function Negative Binomial Distribution (Distribution from k Bose-Einstein emission sources) Integrated correlation function can be related with 1/k Summarize Kensuke Homma / Hiroshima Univ.

Kensuke Homma / Hiroshima Univ. 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.

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.

What b parameter represents ? x PHENIX Preliminary 10% cent. bin width 5% cent. bin width Shift to smaller fluctuations can absorb all rapidity independent fluctuations caused by; 1. finite centrality bin width (initial temperature fluctuations) 2. azimuthal correlations (under investigation) 3. Whatever you want. Our parametrization can produce stable results on a and x. Np

Kensuke Homma / Hiroshima Univ. Summary Multiplicity density distribution in Au+Au collisions at √SNN=200 GeV can be well approximated by N.B.D.. Two point correlation lengths have been extracted based on the function form by relating pseudo rapidity density fluctuations to 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. Kensuke Homma / Hiroshima Univ.