M. Nagy 1 , M. Csanád 1 , T. Csörgő 2 1 Eötvös University, Budapest, Hungary

1. Analysis of the anomalous tail of pion production in Au+Au collisions as measured by the PHENIX experiment at RHIC M. Nagy1, M. Csanád1, T. Csörgő2 1Eötvös University, Budapest, Hungary 2MTA KFKI RMKI, Budapest, Hungary Zimányi 2006 Winter Schoolon Heavy Ion PhysicsBudapest, Hungary, 13/12/06

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 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: 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 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 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: 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; l,a,R) • - Calculate the Coulomb-correction from S(r; l,a,R) • - Divide the corrected C(q; l,a,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 (l,a,R) • The fix point of this iteration process is the final result. 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 < kT < 0.36 GeV • 2.) Centrality: 0%-20% • 0.48 GeV < kT < 0.6 GeV • 3.) Centrality: 50%-90% • 0.2 GeV < kT < 0.4 GeV Zimányi 2006 Winter School on Heavy Ion Physics, Budapest

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

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

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

12. Resulting correlation functions: 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 sNN=200 GeV Au+Au: • Interesting new topic: if l>1, then there were a hint at squeezed correlations. Zimányi 2006 Winter School on Heavy Ion Physics, Budapest

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