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Systematic studies of global observables by PHENIX

Systematic studies of global observables by PHENIX. Longitudinal density fluctuations Meson-meson and baryon-meson correlation Kensuke Homma for the PHENIX collaboration Hiroshima University. Feb 9, 2008 at QM2008 in Jaipur, India. Understanding of QCD phase structure.

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Systematic studies of global observables by PHENIX

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  1. Systematic studies of global observables by PHENIX Longitudinal density fluctuations Meson-meson and baryon-meson correlation Kensuke Homma for the PHENIX collaboration Hiroshima University Feb 9, 2008 at QM2008 in Jaipur, India Kensuke Homma / Hiroshima Univ.

  2. Understanding of QCD phase structure Quark number scaling of elliptic flow T What RHIC achieved • Dense medium • Deconfined phase with partonic d.o.f Tc Phys. Rev. Lett. 98, 162301 (2007) CEP ? Is accessible region by RHIC really crossover? Crossover for any kinds of order parameters? 1st order ? mB Kensuke Homma / Hiroshima Univ.

  3. Intuitive observable: blob intensity a x blob size x Order parameter f(h)=r(h)-<r(h)> f<<1 in T>>Tc, Ginzburg-Landau(GL) free energy up to 2nd order term Two point correlation <f(h1)f(h2)> in 1-D longitudinal space At RHIC Non monotonic increase ofaxindicates T~Tc w.r.t. monotonically decreasing baseline as mean density <r> increases. T=Tc T<Tc Many length scales appear (a typical fk disappears) GL with higher order terms Kensuke Homma / Hiroshima Univ.

  4. Centrality Density measurement: inclusive dNch/dh Cu+Cu@200GeV Cu+Cu@62.4GeV Negative Binomial Distribution (NBD) perfectly describes multiplicities in all collision systems and centralities at RHIC. P(Nch) Nch/< Nch > p+p@200GeV Cu+Cu@22.5GeV Au+Au@200GeV Au+Au@62.4GeV Kensuke Homma / Hiroshima Univ.

  5. Two point correlation via NBD Uncorrelated sources Correlated sources source 1 k=k1 k=k1 k=k1+k2 k=k2 k=k2 k!=k1+k2 source 2 source 1+2 k=1 Bose-Einstein k=∞ Poisson NBD 1/k corresponds to integral of two point correlation Kensuke Homma / Hiroshima Univ.

  6. Differential multiplicity measurements dh Δη<0.7 integrated over Δφ<π/2 PHENIX: Au+Au @√sNN=200GeV Probability (A.U.) Phys. Rev. C 76, 034903 (2007) small dh large dh Zero magnetic field to enhance low pt statistics per collision event. n/m NBD can well describe differential distribution too. Kensuke Homma / Hiroshima Univ.

  7. h h º r h h - r h r h C ( , ) ( , ) ( ) ( ) 2 1 2 2 1 2 1 1 1 2 h h C ( , ) - dh x = a + b / 2 1 2 e r 2 1 1 dh = x << dh k ( ) ( ) ax dh + b 2 / Extraction of ax product Fit with approximated functional form Parametrization of two particle correlation 10% 5% k(dh) • absorbs rapidity independent bias such as centrality bin width Exact relation with NBD k Look at slopes Phys. Rev. C 76, 034903 (2007) dh Approximated functional form Kensuke Homma / Hiroshima Univ.

  8. αξ, β vs. Npart Dominantly Npart fluctuations and possibly correlation in azimuth β is systematically shift to lower values as the centrality bin width becomes smaller from 10% to 5%. This is understood as fluctuations of Npart for given bin widths αξ product, which is monotonically related with χk=0 indicates the non-monotonic behavior around Npart ~ 90. Significance with Power + Gaussian: 3.98 σ (5%), 3.21 σ (10%) Significance with Line + Gaussian: 1.24 σ (5%), 1.69 σ (10%) ●5% ○10% β Au+Au@200GeV ●5% ○10% αξ Npart Phys. Rev. C 76, 034903 (2007) Kensuke Homma / Hiroshima Univ.

  9. Analysis in smaller system: Cu+Cu@200GeV Cu+Cu@200GeV 5% bin width Cu+Cu@200GeV 5% bin width Kensuke Homma / Hiroshima Univ.

  10. Analysis in lower energy: Au+Au@62.4GeV Au+Au@62.4GeV Au+Au@62.4GeV Kensuke Homma / Hiroshima Univ.

  11. Comparison of three collision systems Npart~90 in AuAu@200GeV eBJt~2.4GeV/fm2/c Au+Au@200GeV Phys. Rev. C 76, 034903 (2007) Cu+Cu@200GeV αξ <mc>/<mc>@AuAu200 Normalized mean multiplicity to that of top 5% in Au+Au@200GeV Au+Au@200GeV Phys. Rev. C 76, 034903 (2007) Au+Au@62.4GeV Kensuke Homma / Hiroshima Univ.

  12. Are there symptoms in other observables at around the same Npart? Kensuke Homma / Hiroshima Univ.

  13. Meson-meson and baryon-meson fluctuations Au+Au@200GeV Au+Au@200GeV Npart ~90 Kensuke Homma / Hiroshima Univ.

  14. Deviation from scaling at low KET region ? Npart ~90 In lower KET, there seems to be different behaviors between baryon and mesons. The transition is at Npart~90. Kensuke Homma / Hiroshima Univ.

  15. Conclusion • Correlation function derived from GL free energy density up to 2nd order term in the high temperature limit is consistent with what was observed in NBD k vs dh in three collision systems. This provides a way to directly determine transition points without tunable model parameters with relatively fewer event statistics. • The product of susceptibility and temperature, ax as a function of Npart indicates a possible non monotonic increase at Npart~90. The corresponding Bjorken energy density is 2.4GeV/fm3 with t=1.0 fm/c and the transverse area=60fm2 • The trends of ax in smaller system in the same collision energy (Cu+Cu 200GeV) and in the same system size in lower collision energy (Au+Au 62.4) as a function of mean multiplicity are similar to that of Au+Au at 200GeV except the region where the possible non monotonicity is seen. We need careful error estimates and increase of statistics for smaller size and lower energy systems to obtain the conclusive result. • Combining other symptoms in the same multiplicity region, we hope to understand possibly interesting behaviors. Kensuke Homma / Hiroshima Univ.

  16. Backup Kensuke Homma / Hiroshima Univ.

  17. 102 Npart arXiv:0801.0220v1 [nucl-ex] How about <cc> suppression? Au+Au@200GeV Npart~90 in AuAu@200GeV eBJt~2.4GeV/fm2/c Cu+Cu@200GeV If we put a biased line … Kensuke Homma / Hiroshima Univ.

  18. Other symptoms?: baryon-meson correlation Npart ~90 KET/nq Npart ~90 Kensuke Homma / Hiroshima Univ.

  19. KET + Number of constituent Quarks (NCQ) scaling • Scaling holds well for different centralities • Deviations at low KET may be due to radial flow Kensuke Homma / Hiroshima Univ.

  20. Future prospect • It would be important to see coherent behaviors on other observables like; J/y suppression pattern, breaking point of quark number scaling of V2, fluctuation on baryon-meson production, low pt photon yield and so on to investigate what kind of phase transition is associated with ax measurement, if ax is really the indication of a phase transition. • Quick finer energy and species scan with 100M events for each system would provide enough information on the structure of the possible non monotonicity. This would reveal the relation between initial temperature and speed of blob evolution and speed of medium expansion. Kensuke Homma / Hiroshima Univ.

  21. What is the energy density at Npart~90? Measurement of transverse energy ET Preliminary Npart~90 corresponds to etBJ~2.4GeV/fm2/c Kensuke Homma / Hiroshima Univ.

  22. Density correlation in longitudinal space Longitudinal space coordinate z can be transformed into rapidity coordinate in each proper frame of sub element characterized by a formation time t where dominant density fluctuations are embedded. Due to relatively rapid expansion in y, analysis in y would have an advantage to extract initial fluctuations compared to analysis in transverse plane. In narrow midrapidity region like PHENIX, cosh(y)~1 and y~h. Longitudinal multiplicity density fluctuation from the mean density can be an order parameter: Kensuke Homma / Hiroshima Univ.

  23. Direct observable for Tc determination GL free energy density g with f ~ 0 from high temperature side is insensitive to transition order, but it can be sensitive to Tc spatial correlation f disappears at Tc → Fourier analysis Susceptibility Susceptibility in long wavelength limit 1-D two point correlation function Product between correlation length and amplitude can also be a good indicator for T~Tc Correlation length Kensuke Homma / Hiroshima Univ.

  24. NBD fitsin CuCu@200 L=0 16 fit examples in most left edge in top 10% events out of 28/2*(1+28) times NBD fits Level (window size) L=28(1-dh/DhPHENIX) L=240 Kensuke Homma / Hiroshima Univ.

  25. Hit and dead map of East arm Hit map Dead map 256 f bins 256 h bins 3-sigma cut as the central cut to define dead map. Today only 3-sigma result will be shown. Number of bins Number of hits (counts*events per minimum bin size) Kensuke Homma / Hiroshima Univ.

  26. Example of 5% most central sample Position dependent NBD corrections L=72 L=0 dh=0.7 • Require geometrical correction factor on NBD k below 2.0 • h-window size dh is defined as: L=28(1-dh/DhPHENIX) Corrected NBD k L=79 L=7 Correction factor on NBD k L=152 L=224 L=159 L=231 dh>0.06 Kensuke Homma / Hiroshima Univ.

  27. Cu+Cu@200GeV with only statistical errors Confirmation of absorption of bin width bias 5% bin width with 2.5% shift 10% bin width Fit with only statistical errors in k vs. dh Kensuke Homma / Hiroshima Univ.

  28. Corrected mean multiplicity <mc> Cu+Cu@200GeV 10% bin width Cu+Cu@200GeV 5% bin width Au+Au@62.4GeV 10% bin width Kensuke Homma / Hiroshima Univ.

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