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Experimental and Theoretical Investigation of Heavy Ion Collisions at RHIC

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

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Experimental and Theoretical Investigation of Heavy Ion Collisions at RHIC

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  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

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

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

  4. RHIC and PHENIX

  5. SMD ZDC PHENIX experiment The Zero Degree Calorimeter • The interaction region and the ZDCs • ZDC from the front

  6. Online monitoring

  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)

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

  9. Goals • Measuring the correlation function • Core-halo ratio • Both C3 and C2 is needed • Thermal models are acceptable? • Ratio of partially coherent fraction • Jets • Bose-Einstein condensate • Fireball

  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

  11. One track cuts • Momentum cuts • Other cuts • Particle identification: • Pions: • Kaons: • Protons:

  12. One track cuts • Mass versus charge over momentum:

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

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

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

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

  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/9812474)

  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

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

  20. A nonrelativistic solution • A group of nonrelativistic solutions (hep-ph/0111139): (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

  21. Numeric results • Propagate the hydro solution in time:

  22. A relativistic solution • Relativistic hydro: and • A group of general solutions (nucl-th/0306004): • Overcomes two shortcomings of Bjorken’s solution: • Rapidity distribution • Transverse flow • Hubble flow  lack of acceleration

  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=t0):

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

  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:

  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

  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

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

  29. Some analytic results • Distribution widths with • Slopes, effective temperatures • Flow coefficients with

  30. Buda-Lund fits to NA44/49 data A. Ster, T. Cs, B. Lörstad, hep-ph/9907338

  31. Buda-Lund fits toNA22 h + p data N. M. Agababyan et al, EHS/NA22 , PLB 422 (1998) 395 T. Csörgő, hep-ph/0001233, Heavy Ion Phys. 15 (2002) 1-80

  32. Buda-Lund fits to130 GeV RHIC data M. Csanád, T. Csörgő, B. Lörstad, A. Ster, nucl-th/0311102, ISMD03

  33. Buda-Lund fits to200 GeV RHIC data M. Csanád, T. Csörgő, B. Lörstad, A. Ster, nucl-th/0403074, QM04

  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/0310040 and nucl-th/0403074

  35. Fit results, comparing RHIC and SPS

  36. Discussion of fit results • RHIC: high central temperature • TRHIC 200MeV, Tcrit 160MeV, TSPS 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

  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: • H0= (71 ± 7) km/sec/Mpc • converted to SI units: • H0= (2.3 ± 0.2)x10-18 sec-1 • Hubble constant at Au+Au collisions with 200 GeV • HRHIC,1 = <ut>/RG (3.8 ± 0.5)x1022 sec-1 • HRHIC,2 = 1/0 (5.1 ± 0.1)x1022 sec-1 • Ratio of expansion rates: • HRHIC / H0 2 x 1040 • approx. the ratio of the ages of the objects • without correction for inflation...

  38. A useful analogy Fireball at RHIC  our Sun • Core  Sun • Halo  Solar wind • T0,RHIC  210 MeV  T0,SUN  16 million K • Tsurface,RHIC  100 MeV  Tsurface,SUN  6000 K

  39. Summary, plans • Succesful Buda-Lund hydro fits • RHIC Au+Au and also SPS h+p and Pb+Pb • Indication for deconfinement • T>Tc = 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

  40. Presentations • Elliptic flow and correlations from the Buda-Lund model 2nd Warsaw Meeting on Particle Correlations and Resonances in Heavy Ion Collisions October 15-18 2003, Warsaw, Poland http://hirg.if.pw.edu.pl/en/meeting/oct2003/talks/csanad/Csanad.ppt • Buda-Lund hydro modell and the rapidity dependence of the elliptic flow at RHIC 3rd Budapest Winter School on Heavy Ion Physics December 8-11 2003, Budapest, Hungary http://www.hef.kun.nl/~novakt/school03/agenda/csanad_bp03.ppt • Indication for quark deconfinement and evidence for a Hubble flow in Au+Au collisions at RHIC 17th International Conference on Quark Matter January 11-18 2004, Oakland, California, USA http://www-rnc.lbl.gov/qm2004/talks/parallel/Tuesday03/MCsanad_PPTWin.ppt • Indication for quark deconfinement and evidence for a Hubble flow in Au+Au collisions at RHIC PHENIX Global-Hadron Physics Working Group Meeting January 30 2004, Upton, New York, USA https://www.phenix.bnl.gov/WWW/p/draft/csanad/pwg/csanad_pwg_040130.ppt • Three pion correlation function analysis PHENIX Global-Hadron Physics Working Group Meeting April 2 2004, Upton, New York, USA https://www.phenix.bnl.gov/WWW/p/draft/csanad/pwg/csanad_pwg_040402.ppt • Buda-Lund hydro model Brookhaven National Laboratory Nuclear Physics Seminar April 6 2004, Upton, New York, USA https://www.phenix.bnl.gov/WWW/p/draft/csanad/seminar/csanad_nps_040406.ppt • Buda-Lund hydro in p+p collision at 200 GeV PHENIX Global-Hadron Physics Working Group Meeting May 21 2004, Upton, New York, USA and Budapest , Hungary https://www.phenix.bnl.gov/WWW/p/draft/csanad/pwg/csanad_pwg_040402.ppt

  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 http://arXiv.org/pdf/nucl-th/0403074 • A hint at quark deconfinement in 200 GeV Au+Au data at RHIC M. Csanád, T. Csörgő, B. Lörstad, A. Ster Accepted by Nukleonika http://arXiv.org/pdf/nucl-th/0402037 • Buda-Lund hydro model and the elliptic flow at RHIC M. Csanád, T. Csörgő, B. Lörstad Accepted by Nukleonika http://arXiv.org/pdf/nucl-th/0402036 • An indication for deconfinement in Au+Au collisions at RHIC M. Csanád, T. Csörgő, B. Lörstad, A. Ster Acta Phys. Polon. B35:191-196, 2004 http://arXiv.org/pdf/nucl-th/0311102 • 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 http://arXiv.org/pdf/nucl-th/0310040 • 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.91:072303,2003 http://arXiv.org/pdf/nucl-ex/0306021 • 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. http://arXiv.org/pdf/hep-ex/0404027 • 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 http://arXiv.org/pdf/hep-ph/0406042

  42. Thank you for your attention

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