1. Analysis of the anomalous tail of pion production in Au+Au collisions as measured by the PHENIX experiment at RHIC M. Nagy 1, M. Csanád 1, T. Csörgő 2 1 Eötvös University, Budapest, Hungary 2 MTA KFKI RMKI, Budapest, Hungary Zimányi 2006 Winter School on Heavy Ion Physics Budapest, Hungary, 13/12/06

2. Zimányi 2006 Winter School on Heavy Ion Physics, Budapest 2 Outline Review of correlation functions Lévy stable distributions Methods for Coulomb-correction Results on PHENIX correlation data Concluding on the order of phase transition Outlook

3. Zimányi 2006 Winter School on Heavy Ion Physics, Budapest 3 Review of correlation functions Bose-Einstein Correlation (BEC): Important information about the space-time extent of the boson emitting source Experimentally: Theoretically: bosonic wavefunction of the particles has to be symmetrized Simple description in the case, when multi-particle correlations are negligible (Koonin-Pratt equation): In case, when final state interactions (FSI) are negligible:

4. Zimányi 2006 Winter School on Heavy Ion Physics, Budapest 4 Measurements at PHENIX The PHENIX experiment measured correlation functions of charged pions Imaging method: inverts the integral equation which calculates the correlation function (the Koonin-Pratt equation) nucl-ex/060532 : - The imaged source function has long, power-law like tail - Gaussian fit fails to describe this tail Aims of this analysis: check if the tail is consistent with a power-law. If yes, determine the power-law exponent and other parameters of the source function A problem with the imaging method: Correlated points & errors of S(r): cannot be fitted directly. Assumption of Lévy distribution of S(r): Based on Central Limit Theorem

5. Zimányi 2006 Winter School on Heavy Ion Physics, Budapest 5 Lévy stable distributions Central Limit Theorem: The (normalized) sum of many independent identical probability distributions will be Gaussian in the limiting case, if the elementary distributions have finite variance Generalization: the limiting distribution will be a Lévy-stable distribution Except of (Cauchy) and (Gaussian) distributions, there are no known simple analytic formulas. Important property: power-law tail with the exponent

6. Zimányi 2006 Winter School on Heavy Ion Physics, Budapest 6 Source function Core-halo picture: The emitting source has a core, which is described by hydrodynamics, and a halo, (consisting of the decay products of long-lived resonances) PCMS Coordinate-averaged source function: Intercept parameter: measures the ratio of the core So, the two-particle source function we assumed is:

7. Zimányi 2006 Winter School on Heavy Ion Physics, Budapest 7 Method of Coulomb-correction In order to fit to a dataset with independent (non-correlated) error bars: we must fit directly to the correlation function Re-write the Koonin-Pratt equation: Iterative method: - Assume a parameter set - Calculate the Fourier-transform and C(q;,,R) - Calculate the Coulomb-correction from S(r;,,R) - Divide the corrected C(q;,,R) by the Coulomb correction to get the raw correlation function - Fit the, uncorrected correlation function at a fixed Coulomb, to get a new value of (,,R) The fix point of this iteration process is the final result.

8. Zimányi 2006 Winter School on Heavy Ion Physics, Budapest 8 Fitted datasets Method applied to 3 different raw correlation functions of charged pions. Au+Au collisions at 200 GeV @ RHIC PHENIX rapidity domain: -0.5 < y < 0.5 1.) Centrality: 0%-20% 0.2 GeV < k T < 0.36 GeV 2.) Centrality: 0%-20% 0.48 GeV < k T < 0.6 GeV 3.) Centrality: 50%-90% 0.2 GeV < k T < 0.4 GeV

9. Zimányi 2006 Winter School on Heavy Ion Physics, Budapest 9 Resulting correlation functions:

10. Zimányi 2006 Winter School on Heavy Ion Physics, Budapest 10 Resulting correlation functions:

11. Zimányi 2006 Winter School on Heavy Ion Physics, Budapest 11 Resulting correlation functions:

12. Zimányi 2006 Winter School on Heavy Ion Physics, Budapest 12 Resulting correlation functions:

13. Zimányi 2006 Winter School on Heavy Ion Physics, Budapest 13 Summary and outlook Theoretical prediction for the case of second order phase transition: The universality class of QCD is the same as the 3D Ising model, so the Levy-stability exponent then will be 0.50  0.05 (random field 3d Ising) or even smaller. Our results: this is not the case for s NN =200 GeV Au+Au: Interesting new topic: if >1, then there were a hint at squeezed correlations. Dataset R  1.) 0.565±0,03410,6±0,591,14±0,049 2.) 0.356±0,0266,81±0,371,4±0,077 3.) 0.625±0,0765,59±0,631,1±0,011

14. Zimányi 2006 Winter School on Heavy Ion Physics, Budapest 14 Thank you for the attention!