Csanád Máté 1 Experimental and Theoretical Investigation of Heavy Ion Collisions at RHIC Máté Csanád (ELTE, Budapest, Hungary) Why heavy ion physics – Introduction Data taking – PHENIX Zero Degree Calorimeter Actuation Software development Data analysis – Correlation functions Methods of the calculation Status Model building – Buda-Lund hydro model Calculation of observables Comparing the results to the data

Csanád Máté 2 The Big Bang Early universum: hot, expanding system Quark matter, Quark Gluon Plasma Nucleon freeze-out

Csanád Máté 3 The Little Bang Heavy ion collisions: hot, expanding system Hot and dense enough? New- old matter? Melting the nucleons Quark deconfinement Image: water from ice This all is possible with high energy collisions (?)

Csanád Máté 4 RHIC and PHENIX

Csanád Máté 5 The Zero Degree Calorimeter The interaction region and the ZDCs ZDC from the front

Csanád Máté 6 Online monitoring

Csanád Máté 7 Three-particle correlation function Experimental definition:, where invariant triplet momentum actual triplet distribution (three particles from the same event) background triplet distribution (arbitrary particles)

Csanád Máté 8 Theoretical aspects Theoretical definition: Parts of the source core / halo partially coherent / incoherent The correlation function at zero relative momenta

Csanád Máté 9 Goals Measuring the correlation function Core-halo ratio Both C 3 and C 2 is needed Thermal models are acceptable? Ratio of partially coherent fraction Jets Bose-Einstein condensate Fireball

Csanád Máté 10 Event selection, applied cuts Start from AuAu run2_v03_burn1/CNT, only MinBias events ~17000 files every second is different Have to reproduce the two particle results  same cuts as ppg021 Needed variables

Csanád Máté 11 One track cuts Momentum cuts Other cuts Particle identification: Pions: Kaons: Protons:

Csanád Máté 12 One track cuts Mass versus charge over momentum:

Csanád Máté 13 Two track cuts EMC, radius: DCH, angle and zed ~5% of the pairs and triplets are cut this way

Csanád Máté 14 Correlation functions of pions Two-particle correlation functions: Three-particle correlation functions: (+,+)  (–,–)  (+,+,+)  (–,–, –) 

Csanád Máté 15 Correlation functions of kaons Two-particle correlation functions: Three-particle correlation functions: (+,+)  (–,–)  (+,+,+)  (–,–, –) 

Csanád Máté 16 Correlation functions of protons Two-particle correlation functions: Three-particle correlation functions: (+,+)  (–,–)  (+,+,+)  (–,–,–) 

Csanád Máté 17 Summary, plans Correlation function at high relative momenta ~ 1 Enhancement at small relative momenta Few entries at small momenta  low statistics Need of enhancement in statistics  to use more events To improve on cuts Make corrections Coulomb correction Solve the two-particle Schrödinger-equation Symmetrization  Three-particle wave-function Devide through plain-wave approximation (Alt, Csörgő, Lörstad, Schmidt-Sorensen, hep-ph/ )

Csanád Máté 18 Principles of Buda-Lund hydro Analytic expressions for all observables Symmetric, 3D expansion Local thermalization Known hydro solutions in the nonrelativistic limit Core-Halo picture Core: hydrodynamical evolution Halo: decay products of long lived resonances

Csanád Máté 19 Nonrelativistic hydrodynamics Equations of nonrel hydro Equation of state Scaling variable X, Y and Z: characteristic scales, depend on (proper)time

Csanád Máté 20 A nonrelativistic solution A group of nonrelativistic solutions (hep-ph/ ):  ( s ),  ( s ) : scaling functions This is a solution, if for the scales:  ( s ) arbitrary, eg.  constant, then  ( s ) exponential, or: Buda-Lund Zimányi-Bondorf-Garpman

Csanád Máté 21 Numeric results Propagate the hydro solution in time:

Csanád Máté 22 A relativistic solution Relativistic hydro: and A group of general solutions (nucl-th/ ): Overcomes two shortcomings of Bjorken’s solution: Rapidity distribution Transverse flow Hubble flow  lack of acceleration

Csanád Máté 23 The emission function The phase-space distribution looks like Maxwell-Boltzman, for sake of simplicity with the constant: Consider the collisionless Boltzmann-equation Calculates the source of a given phase-space distribution: Emission function in the simplest case (instant. source, at t=t 0 ):

Csanád Máté 24 Observables from Buda-Lund hydro Core-halo correction: One-particle spectrum with core-halo correction: Two-particle correlation function: Flow coefficients:

Csanád Máté 25 The generalized Buda-Lund model The original model was developed for axial symmetry only  central collisions In the most general hydrodynamical form: ‘Inspired by’ nonrelativistic solutions Have to assume special shapes: Generalized Cooper-Frye prefactor: and Four-velocity distribution: Temperature: Fugacity:

Csanád Máté 26 Az invariáns impulzus-eloszlás A nyeregpont-módszerrel a következőt kapjuk: Az átlagos energia és térfogat: és Koordináta-transzformáció szükséges: A táguló rendszer koordinátái  Mérés koordinátái Transzverz impulzus iránya Impulzusmomentum miatt kis forgás

Csanád Máté 27 The saddlepoint approximation A good approximation for the product of a narrow Gaussian-like function and a broad distribution: Exact for convolution of Gaussians, good for narrow distributions, where a parameter controls the width The saddlepoint can be computed from This method can be generalized for more dimensions

Csanád Máté 28 Correlation function and radii The correlation function: The radii are in the simplest case, and in the B-P system: Azimuthal depencence appears

Csanád Máté 29 Some analytic results Distribution widths with Slopes, effective temperatures Flow coefficients with

Csanád Máté 30 Buda-Lund fits to NA44/49 data A. Ster, T. Cs, B. Lörstad, hep-ph/

Csanád Máté 31 Buda-Lund fits to NA22 h + p data N. M. Agababyan et al, EHS/NA22, PLB 422 (1998) 395 T. Csörgő, hep-ph/ , Heavy Ion Phys. 15 (2002) 1-80

Csanád Máté 32 Buda-Lund fits to 130 GeV RHIC data M. Csanád, T. Csörgő, B. Lörstad, A. Ster, nucl-th/ , ISMD03

Csanád Máté 33 Buda-Lund fits to 200 GeV RHIC data M. Csanád, T. Csörgő, B. Lörstad, A. Ster, nucl-th/ , QM04

Csanád Máté 34 Investigation of new data Description of the rapidity dependence of the elliptic flow, little underestimated Transverse momentum dependence OK Modification of parameters, new fits needed see nucl-th/ and nucl-th/

Csanád Máté 35 Fit results, comparing RHIC and SPS

Csanád Máté 36 Discussion of fit results RHIC: high central temperature T RHIC  200MeV, T crit  160MeV, T SPS  140 MeV Significantly higher (5  ), than the critical High temperature inhomogeneity Temperature of the center much higher, than that of the surface This gives a solution for the RHIC ‘‘HBT puzzle”. Almost sudden freeze-out Short freeze-out time: good approximation Hubble-constant is the same in all directions 3D Hubble-flow Ratio of temperature and chemical potential constant Explanation, why thermal models work at RHIC

Csanád Máté 37 RHIC and the Universe Developed Hubble-flow at RHIC and in the Universe Universality of the Hubble expansion: u = H r Hubble constant of the Universe: H 0 = (71 ± 7) km/sec/Mpc converted to SI units: H 0 = (2.3 ± 0.2)x sec -1 Hubble constant at Au+Au collisions with 200 GeV H RHIC,1 = /R G  (3.8 ± 0.5)x10 22 sec -1 H RHIC,2 = 1/ 0  (5.1 ± 0.1)x10 22 sec -1 Ratio of expansion rates: H RHIC / H 0  2 x approx. the ratio of the ages of the objects without correction for inflation...

Csanád Máté 38 A useful analogy Core Sun Halo Solar wind T 0,RHIC  210 MeV T 0,SUN  16 million K T surface,RHIC  100 MeV T surface,SUN  6000 K Fireball at RHIC  our Sun

Csanád Máté 39 Succesful Buda-Lund hydro fits RHIC Au+Au and also SPS h+p and Pb+Pb Indication for deconfinement T>T c = 164 MeV by 5 at RHIC, but not at SPS 3D Hubble-flow Complete the fitting package for the relativistic calculations Fitting the new data Anisotropic flow, higher order flows at STAR Centrality and rapidity dependent elliptic flow Make prediction J/ yield HBT for kaons Find the relat. hydro solution that leads to our source function Summary, plans

Csanád Máté 40 Presentations Elliptic flow and correlations from the Buda-Lund model 2nd Warsaw Meeting on Particle Correlations and Resonances in Heavy Ion Collisions October , Warsaw, Poland Buda-Lund hydro modell and the rapidity dependence of the elliptic flow at RHIC 3rd Budapest Winter School on Heavy Ion Physics December , Budapest, Hungary Indication for quark deconfinement and evidence for a Hubble flow in Au+Au collisions at RHIC 17th International Conference on Quark Matter January , Oakland, California, USA Indication for quark deconfinement and evidence for a Hubble flow in Au+Au collisions at RHIC PHENIX Global-Hadron Physics Working Group Meeting January , Upton, New York, USA Three pion correlation function analysis PHENIX Global-Hadron Physics Working Group Meeting April , Upton, New York, USA Buda-Lund hydro model Brookhaven National Laboratory Nuclear Physics Seminar April , Upton, New York, USA Buda-Lund hydro in p+p collision at 200 GeV PHENIX Global-Hadron Physics Working Group Meeting May , Upton, New York, USA and Budapest, Hungary

Csanád Máté 41 Publications Indication of quark deconfinement and evidence for a Hubble flow in 130 and 200 GeV Au+Au collisions M. Csanád, T. Csörgő B. Lörstad, A. Ster Accepted by Journal of Physics G A hint at quark deconfinement in 200 GeV Au+Au data at RHIC M. Csanád, T. Csörgő, B. Lörstad, A. Ster Accepted by Nukleonika Buda-Lund hydro model and the elliptic flow at RHIC M. Csanád, T. Csörgő, B. Lörstad Accepted by Nukleonika An indication for deconfinement in Au+Au collisions at RHIC M. Csanád, T. Csörgő, B. Lörstad, A. Ster Acta Phys. Polon. B35: , Buda-Lund hydro model for ellipsoidally symmetric fireballs and the elliptic flow at RHIC M. Csanád, T. Csörgő, B. Lörstad Accepted by Nucl. Phys. A Absence of suppression in particle production at large transverse momentum in 200-GeV d+Au collisions PHENIX Collaboration (S.S. Adler,..., M. Csanád,... et al.) Phys.Rev.Lett.91:072303, Double helicity asymmetry in inclusive mid-rapidity  0 production for polarized p+p collisions at ps =200 GeV PHENIX Collaboration (S.S. Adler,..., M. Csanád,... et al.) Submitted to Phys.Rev.Lett. Analysis of identified particle yields and Bose-Einstein (HBT) correlations in p+p collisions at RHIC T. Csörgő, M. Csanád, B. Lörstad, A. Ster. To appear in Heavy Ion Physics

Csanád Máté 42 Thank you for your attention