1. Máté Csanád, Imre Májer Eötvös University Budapest WPCF 2011, Tokyo

2. Photon spectrum: information on the time development of the sQGP Thermalization time Equation of state Initial temperature Freeze-out time Freeze-out temperature Expansion at freeze-out Hadronic spectrum information on the final state thermalization 2 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

3. Jet suppression in Au+Au: new phenomenon Phys. Rev. Lett. 88, 022301 (2002) No jet suppression in d+Au: new form of matter Phys. Rev. Lett. 91, 072303 (2003) Summary of the results: matter is a liquid Nucl. Phys. A 757, 184-283 (2005) Elliptic flow scaling: quark degrees of freedom Phys. Rev. Lett. 98, 162301 (2007) Heavy quark flow: nearly perfect fluid Phys. Rev. Lett. 98, 172301 (2007) Direct photon spectrum: high initial temperature Phys. Rev. Lett. 104, 132301 (2010) 3 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

4. 4 Background from h  Idea: thermal & virtual photons and dielectrons X → e + e − X →  and X →   → e + e − e + e - and  related Direct and inclusive also Direct photons calculable Thermal below 3 GeV! Initial temperature? EoS? Hydrodynamics! Phys. Rev. Lett. 104, 132301 (2010) from same process

5. 1. Hydrodynamics gives u  (x), T(x), p(x) etc. Famous: Landau, Hwa-Bjorken (1D); few 3D known 2. Source function S(x,p) based on flow, temperature etc. E.g. a Bose-Einstein or a simple thermal distribution 3. Calculate observables N 1 (p t ), v 2 (p t ) etc. come from integrals of S(x,p) 4. Compare to data: determine model parameters Final state: hadrons; Initial state, EoS: photons 5 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

6. By Csörgő, Csernai, Hama, Kodama, 2004 Only available 3D relativistic and realistic solution Hubble-flow: u  =x  /  In the Universe: v=Hr, Hubble constant ~ (time) -1 Ellipsoidal symmetry: Thermodynamic quantities const. on the s=const. ellipsoid X, Y, Z describe the expanding ellipsoid here Gaussian temperature profile, expanding and shrinking over time: 6 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011 TIME

7. 0-30% centrality, Au+Au, PHENIX data [PRC69 & PRL91] T 0 199 ± 3 MeVcentral freeze-out temp.  0.80 ± 0.02momentum space ecc. u t 2 /b-0.84± 0.1 (b<0)transv. flow/temp. grad  0 7.7 ± 0.1freeze-out proper time Eur. Phys. J. A 44, 473–478 (2010) Eur. Phys. J. A 44, 473–478 (2010) 7 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

8. 0-92% centrality, Au+Au, PHENIX data [PRL93] T 0 204 ± 7 MeVf.o. temperature  0.34 ± 0.01eccentricity u t 2 /b-0.34 ± 0.07 (b<0)transv. flow/temp. grad. Eur. Phys. J. A 44, 473–478 (2010) 8 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

9. From hadronic observables: Hadronic observables cannot decide! EoS & T ini from penetrating probes! Eur. Phys. J. A 44, 473 (2010) 9 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011 Fixed from hadronic observables

10. Fits to 0-92% centrality PHENIX data [PRL104] Parameters from hadronic fit Important new parameter:  =7.7±0.8  c s =0.36±0.02 Average EoS, compare Lacey et al., nucl-ex/0610029 arXiv: 1101.1279, 1101.1280(2010) 10 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

11. From hadronic observables: EoS from photon spectra:  =7.7±0.8 or c s =0.36 ± 0.02 Initial temperature (at  =1 fm/c) T i > 519 ± 12 MeV Eur. Phys. J. A 44, 473 (2010) 11 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011 Fixed from hadronic observables Determined from photon spectra

12. 12 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011 Elliptic flow from PHENIX data [arXiv:1105.4126] Early times more important Many models fail to describe Non-hydro effects kick in >2 GeV Sign change possible here!

13. 13 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011 Bose-Einstein correlations R out /R side = 1 for hadrons R out » R side here! Large  ! Evolution time

14. Revival of interest in perfect hydro Our model: 3+1d relativistic model w/o acceleration Calculated hadronic source → N 1, v 2, HBT Calculated photon source → N 1, v 2, HBT Compared successfully to data, c s =0.36±0.02 T i ≈520 MeV Compared to fresh photon v 2 data Prediction on Bose-Einstein correlations 14 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

16. No data point even near the kinematic viscosity of 4 He (10/4  ) Close to AdS/CFT minimum, (1/4  ) 16 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

17. 17 PHENIX measurement done: PRL 104, 132301 (2010) Problem: huge background from h →  Idea: thermal + virtual photon production parralel X → e + e −, X →  and X →   → e + e − from the same process Dielectron and real photon production related as: S process dependent, dn  /dn , for  0 and  e.g.: For p t » m ee » m e : L, S → 1

18. Phys. Rev. Lett. 104, 132301 (2010) VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011 18 Measured electron pairs with p t of 1-5 GeV Easy via electron ID capabilities Compare to dielectrons from hadronic cocktail Excess seen above pion mass due to virtual 

19. VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011 19 Excess: virtual direct photons (decaying into e + e − pairs) Inclusive e + e − : hadronic + dir. virtual photon components Hadronic electron pairs (f c ), calculated from cocktail: , , ,  ’,  Electron pairs from direct virtual photons ( f dir ) calculated from f c via previous formula Determine ratio r by fit for separate p t bins Use r to scale inclusive photon spectra

20. VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011 20 Landau’s solution (1D, developed for p+p): Accelerating, implicit, complicated, 1D L.D. Landau, Izv. Acad. Nauk SSSR 81 (1953) 51 I.M. Khalatnikov, Zhur. Eksp.Teor.Fiz. 27 (1954) 529 L.D.Landau and S.Z.Belenkij, Usp. Fiz. Nauk 56 (1955) 309 Hwa-Bjorken solution: Non-accelerating, explicit, simple, 1D, boost-invariant R.C. Hwa, Phys. Rev. D10, 2260 (1974) J.D. Bjorken, Phys. Rev. D27, 40(1983) Others Chiu, Sudarshan and Wang Baym, Friman, Blaizot, Soyeur and Czyz Srivastava, Alam, Chakrabarty, Raha and Sinha

21. SolutionBasic prop’sEoSObservables Csörgő, Nagy, Csanád Phys.Lett.B 663:306-311, 2008 Phys.Rev.C77:024908,2008 Ellipsoidal, 1D accelerating  -B=  (p+B) dn/dy,  Landau Izv. Acad. Nauk SSSR 81 (1953) 51 Cylindr., 1D, accelerating =p=p none Hwa-Björken R.C. Hwa, PRD10, 2260,1974 J.D. Bjorken, PRD27, 40(1983) Cylindr., 1D, non-accelerating =p=p dn/dy,  Bialas et al. Phys. Rev. C76, 054901 (2007). 1D, betweend Landau and Hwa-Björken =p=p dn/dy Csörgő et al. Heavy Ion Phys. A 21, 73 (2004)) Ellipsoidal, 3D, non-accelerating  -B=  (p+B) p t spectra, flow, correlations 21 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

22. Density, temperature, pressure (s) arbitrary, but realistic to choose Gaussian b<0 is realistic Ellipsoidal symmetry (thermodynamic quantities const. on the s=const. ellipsoid) Directional Hubble-flow v=Hr or H=v/r, the Hubble-constants: (T. Csörgő, L. P. Csernai, Y. Hama és T. Kodama, Heavy Ion Phys. A 21, 73 (2004)) 22 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

23. From hadronic observables: EoS from photon spectra:  =7.7±0.8 Initial temperature (at  =1 fm/c) T i > 519 ± 12 MeV Eur. Phys. J. A 44, 473 (2010) 23 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

24. 24 Initial time period: small contribution

25. VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011 25 Sensitive to  with these level of errors

26. VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011 26 Eccentricity dependence EoS dependence Initial time dependence

27. Source function: probability particle creation For hadrons: Maxwell-Boltzmann type H(  )d  freeze-out distribution (e.g. Dirac-  ) p  d 3   (x) Cooper-Fry prefactor (flux term) Photons are continously created, but not thermalized Thermal emission determins source functions 27 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

28. Single particle transverse momentum spectrum Elliptic flow (asymmetry in the transverse plane) with, I: Bessel func. Width of two-particle correlation functions: 28 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

29. Integration can be done analytically A and B are: 29 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

30. Revival of interest, new solutions Sinyukov, Karpenko, nucl-th/0505041 Pratt, nucl-th/0612010 Bialas et al.: Phys.Rev.C76:054901,2007 Borsch, Zhdanov: SIGMA 3:116,2007 Nagy et al.: J.Phys.G35:104128,2008 and arXiv/0909.4285 Liao et al.: arXiv/09092284 and Phys.Rev.C80:034904,2009 Mizoguchi et al.: Eur.Phys.J.A40:99-108,2009 Beuf et al.:Phys.Rev.C78:064909,2008 (dS/dy as well!) Need for solutions that are: accelerating + relativistic+ 3 dimensional explicit + simple + compatible with the data Need to calculate observables! 30 VII Workshop on Particle Correlations and Femtoscopy, Tokyo, 2011

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