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ゆらぎのはなし

ゆらぎのはなし. 本間謙輔 松本大学にて 内容 原始時代の紆余曲折。 こんな簡単なことで臨界現象が議論できるなんて！ 我田引水の解釈および現象論屋さんに考えて頂きたいこと。. Measure maximum deviation size in homogeneous flux in our method. Why fluctuation ?. Fluctuations carries information in early universe in cosmology despite of the only single Big-Bang event.

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ゆらぎのはなし

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  1. ゆらぎのはなし 本間謙輔 松本大学にて 内容 原始時代の紆余曲折。 こんな簡単なことで臨界現象が議論できるなんて！ 我田引水の解釈および現象論屋さんに考えて頂きたいこと。 Kensuke Homma / Hiroshima Univ.

  2. Measure maximum deviation size in homogeneous flux in our method Why fluctuation ? • Fluctuations carries information in early universe in cosmology despite of the only single Big-Bang event. • Why don’t we use the genuine event-by-event information by getting all phase space information to study evolution of dynamical system in Heavy Ion collisions ? • We can firmly search for interesting fluctuations with more than million times of mini Big-Bangs. The Microwave Sky image from the WMAP Mission http://map.gsfc.nasa.gov/m_mm.html Kensuke Homma / Hiroshima Univ.

  3. Au+Au √sNN = 200GeV at PHENIX • Using magnetic field-off • Charged Track Drift chamber, Pad chamber1 with BBC vertex • Photon ClusterElectro-magnetic calorimeter • Cluster shower shape • Time of flight • association cuts by tracks • Precisely data quality assurance was necessary to reject detector effect! Kensuke Homma / Hiroshima Univ.

  4. High resolution  extract this region Low resolution η Application of wavelet analysis Kensuke Homma / Hiroshima Univ.

  5. PHENIX 7.24 standard deviation ○: Photon + : Charged Particle • Charged track • Photon cluster J. J. Lord and J. Iwai. Int. Conference on High Energy Physics, TX, 1992 High energy cosmic ray experiment and PHENIX Can DCC scenario explain these events or something else? Kensuke Homma / Hiroshima Univ.

  6. Work in Progress δBmax [arbitrary unit] Maximum differential balance distributions • δBmax distribution (each centrality:10%) with base line fluctuation • black : binomial sample, 100 times larger statistics than real data obtained by hit map • red : data 明らかな離れ孤島は見つからず。 わざわざ大げさな探索しなくたって、 そもそも分布は、二項分布とは 明らかに異なる。 荷電πのみを使用して、熱・統計力学的に 分布を議論するほうが生産的。 Kensuke Homma / Hiroshima Univ.

  7. Measuring Multiplicity Fluctuations with Negative Binomial Distributions UA5 Multiplicity distributions in hadronic and nuclear collisions can be well described by the Negative Binomial Distribution. UA5: sqrt(s)=546 GeV p-pbar, Phys. Rep. 154 (1987) 247. E802: 14.6A GeV/c O+Cu, Phys. Rev. C52 (1995) 2663. E802 62 GeV Au+Au 5-10% Central 25-30% Central dN/Ntracks dN/Ntracks PHENIX Preliminary PHENIX Preliminary Central 62 GeV Au+Au Ntracks Ntracks Kensuke Homma / Hiroshima Univ.

  8. Current understanding of QCD phase diagram T QGP Experiments see partonic degree of freedom in collected flows at RHIC RHIC is accessible to this transition line 2nd order mq=0 tricritcal end-point mq=0 mq <qq> No quantitative agreement between theoretical predictions end-point line mq!=0 Surface of 1st order transitions mB Kensuke Homma / Hiroshima Univ.

  9. PHENIX on going analysis • Isothermal compressibility • Heat capacity • Near side azimuthal correlation function • Breaking of v2 scaling • Disappearance of baryon anomaly • Correlation length and susceptibility in longitudinal space Kensuke Homma / Hiroshima Univ.

  10. Ordered T=0.995Tc Critical T=Tc Disordered T=1.05Tc 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 (focus of this talk) • Universality (power law behavior) around Tc reflecting basic symmetries and dimensions of the underlying system: • critical exponent (future study after finding Tc) A simulation based on two dimensional Ising model from ISBN4-563-02435-X C3342l Kensuke Homma / Hiroshima Univ.

  11. g-g0 φ Order parameter and phase transition 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 b>0 for 2nd order Longitudinal multiplicity density fluctuation from the mean density is introduced as an order parameter in the following. Kensuke Homma / Hiroshima Univ.

  12. More exact free potential form In narrow midrapidity region, cosh(y)~1 and y~h. Although theorists want to define U(f) as a power term by assuming the system is just on Tc and/or on critical end-point, most of experimentally accessible phase spaces are relatively far from the critical temperature or end-point. It is more natural to use the polynomial expansion for the potential term. Kensuke Homma / Hiroshima Univ.

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

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

  15. 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. In 1-D case Kensuke Homma / Hiroshima Univ.

  16. From two point correlation to two particle correlation Two point correlation function in 1-D case at fixed T Two particle correlation function Rapidity independent term must be added, since T has a finite range in experiments. Kensuke Homma / Hiroshima Univ.

  17. 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. p pt down to 100MeV/c in B-OFF 200MeV/c in B-ON Kensuke Homma / Hiroshima Univ.

  18. Relations between N.B.D andintegrated correlation function Negative Binomial Distribution k →∞ corresponds to Poisson distribution. k = 1 corresponds to Bose-Einstein distribution. Intuitively k is the number of Bose-Einstein emission sources. Integrated correlation function can be related with 1/k x can be obtained from fit to k vs. dh Kensuke Homma / Hiroshima Univ.

  19. Intuitive summary of advocated observation exponential damping of the number of waves with a typical correlation length GL applicable GL not applicable Absence of typical correlation length causes fractal nature (power law behavior) Compare many systems by changing resolutions and find the increase of correlation length in the very vicinity of Tc but not at Tc ! Kensuke Homma / Hiroshima Univ.

  20. How to define initial temperature? Transverse energy ET Np can be a fine scan on initial temperature T, while collision energy can be a coarse scan. Tc can be investigated with the fine scan. It is a natural assumption that Np is a monotonic function of initial T. Kensuke Homma / Hiroshima Univ.

  21. 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 dNp depends on centrality bin width

  22. N.B.D. k vs. dh PHENIX Preliminary Au+Au @√sNN=200GeV k(dh) 10 % centrality bin width One correlation length assumption is reasonable. dh PHENIX Preliminary Au+Au @√sNN=200GeV 5% centrality bin width Kensuke Homma / Hiroshima Univ.

  23. PHENIX preliminary results • can absorb all rapidity independent fluctuations or offset contributions like; 1. finite centrality bin width ( Np or initial temperature fluctuations ) • 2. reaction plain rotations and • elliptic flows due to partial • sampling in azimuth by PHENIX PHENIX Preliminary 10% cent. bin width 5% cent. bin width a PHENIX Preliminary Shift to smaller fluctuations b Divergence of correlation length can be a signature of critical temperature. PHENIX Preliminary Au+Au @√sNN=200GeV x Np

  24. 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.

  25. What about relation with <qq> NA50, Eur. Phys. J. C39 (2005):355 PHENIX eBJ (t=1fm/c) corresponding to Np~90 PRC 71, 034908 (2005) PHENIX dNch/dh corresponding to Np~90 PRC 71, 034908 (2005) Accidental coincidence ?Need more simultaneous observations! Kensuke Homma / Hiroshima Univ.

  26. 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. One correlation length assumption is enough accurate. • Absolute scale of correlation length is 0.001~0.01. • The static susceptibility as a function of Np indicate a non monotonic increase at Np~90. The corresponding Bjorken energy density is 2.4GeV/fm3 with t=1.0 fm and transverse area=60fm2 • It is interesting to note the coincidence with the energy density at which J/y suppression begins at SPS. Need more simultaneous observations by independent methods in order to conclude whether the non monotonic behavior is related with critical temperature or not. Kensuke Homma / Hiroshima Univ.

  27. Questions • What can be an external field to the longitudinal density correlation? • Why the correlation length can be so small ? Is it possible to cause temperature like correlations by using particles each of which occupies 1/1000 of unit rapidity (dNch/dEta ~ 1000 at RHIC)? Is there another type of thermalizaion before hadron formation? • Why the non monotonic behavior of correlation length looks like a peak rather than a step?Why is the behavior so sensitive to initial energy densities rather than the density at the critical temperature. • How rapid is the longitudinal expansion? • Are there plural formation times? Is there a time for fluctuations are embed before hadron formation time? • How fluctuations in very early stage survive in the final state, while the collision system is rapidly expanding in longitudinal space? Kensuke Homma / Hiroshima Univ.

  28. The answer might be Hawking-Unruh effect in background condensed color electric field Hawing Unruh (QED) (QCD) Kensuke Homma / Hiroshima Univ.

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