1. Two- and three-particle Bose-Einstein correlations M. Csanád for the PHENIX Collaboration

2. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 2/17 PHENIX introduction Detectors involved: Detectors involved: BBC: start time BBC: start time DC, PC: tracking, p t DC, PC: tracking, p t TOF: time of flight  PID TOF: time of flight  PID EMC:  E  PID EMC:  E  PID Acceptance: Acceptance:  < 0.35  < 0.35  =   =  PID by TOF and EMC: PID by TOF and EMC: Identify pions Identify pions from 0.2 to 2.0 GeV/c High precision TOF High precision TOF  TOF = 100-130 ps  TOF = 100-130 ps  p/p= 0.7%  1.1%p  p/p= 0.7%  1.1%p The PHENIX detector system

3. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 3/17 Goals of the analysis Measure Bose-Einstein correlation functions Measure Bose-Einstein correlation functions Parts of the source Parts of the source Core + halo Core + halo Partially coherent + incoherent (part of the source) Partially coherent + incoherent (part of the source) N 1 (p) … Invariant mom. distr. N c (p) … Core fraction N c (p) … Core fraction N c p (p) … Part. coh. fraction C 2 and C 3 at zero relative momenta: C 2 and C 3 at zero relative momenta: Two regions on Two regions on the f c -p c plane T. Csörgő Heavy Ion Phys. 15, 1 (2002) hep-ph/0001233 =1+ NA44

4. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 4/17 Goals of the analysis (m t ) dependence at low momenta (m t ) dependence at low momenta Prediction: Prediction:  ’ mass reduction in hot and dense matter Kapusta, Kharzeev, McLerran Phys.Rev.D53:5028-5033,1996 Z. Huang, X-N. Wang Phys.Rev.D53(1996)5034 Vance, Csörgő Kharzeev Phys.Rev.Lett.81:2205-2208,1998 NA44, S+Pb

5. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 5/17 Coulomb-corrected correlations PHENIX PRELIMINARY C 2 (q inv ) PHENIX PRELIMINARY C 2 (q inv ) Gauss EdgeworthLévy C 3 (q 12 = q 23 = q 31 ) PHENIX PRELIMINARY C 3 (q 12 = q 23 = q 31 ) GaussEdgeworthLévy Conf. lev.: 10 -18 7  10 -7 0.18

6. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 6/17 f c versus p c of pions NA44 S+Pb PHENIX PRELIMINARY Lévy fit used

7. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 7/17 Pion C 2 at different m t bins Ten bins in the range 0.2-0.5 GeV Ten bins in the range 0.2-0.5 GeV Shape analysis carried out Shape analysis carried out A cut at q inv =20MeV was made A cut at q inv =20MeV was made Three shapes tested Three shapes tested PHENIX PRELIMINARY

8. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 8/17 Three shapes: Three shapes: Gauss:, R Gauss:, R Edgeworth:, R,  3 Edgeworth:, R,  3 Lévy:, R,  Lévy:, R,  Fit parameters PHENIX PRELIMINARY 1+ T. Csörgő, S. Hegyi and W. A. Zajc Eur. Phys. J. C 36, 67 (2004)

9. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 9/17 Pion C 2 at different m t bins Edgeworth PHENIX PRELIMINARY Three shapes: Three shapes: Gauss, R Gauss, R Edgeworth, R,  3 Edgeworth, R,  3 Lévy, R,  Lévy, R,  Gauss PHENIX PRELIMINARY Lévy

10. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 10/17 Quality of the fits PHENIX PRELIMINARYGauss Low CL Lévy High CL Edgeworth Uniformly distr. Edgeworth

11. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 11/17 (m t ) dependence (m t ) dependence Prediction: Hot and dense matter   ’ mass reduction enhanced  ’ content  ’  +  + +  -  (  0 +  + +  − )+  + +  − average p t = 138 MeV  More  ’s in the halo at 138 MeV  A hole in (m t ) Data points needed at very low m t ! PHENIX FINAL DATA Au+Au 200 GeV S. S. Adler et al., PRL93,152302(2004)

12. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 12/17 Gaussian fit PHENIX PRELIMINARY RUN4 Au+Au 200 GeV

13. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 13/17 Edgeworth fit PHENIX PRELIMINARY RUN4 Au+Au 200 GeV

14. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 14/17 Levy fit PHENIX PRELIMINARY RUN4 Au+Au 200 GeV Low   low Low   low Same physics: dominant tail Underconstrained problem

15. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 15/17 Renormalized data points PHENIX PRELIMINARY

16. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 16/17 Summary Two- and three-particle correlations Two- and three-particle correlations Fractional core and partial coherence Fractional core and partial coherence Two-particle correlation function in 10 m t bins Two-particle correlation function in 10 m t bins Gauss, Edgeworth, Lévy Gauss, Edgeworth, Lévy R and as a function of m t R and as a function of m t U A (1) restoration tested U A (1) restoration tested Results critically dependent on understanding of statistical and systematic errors Results critically dependent on understanding of statistical and systematic errors Additional analysis required for definitive statement Additional analysis required for definitive statement

17. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 17/17 Sweden Lund University, Lund USA Abilene Christian University, Abilene, TX Brookhaven National Laboratory, Upton, NY University of California - Riverside, Riverside, CA University of Colorado, Boulder, CO Columbia University, Nevis Laboratories, Irvington, NY Florida State University, Tallahassee, FL Florida Technical University, Melbourne, FL Georgia State University, Atlanta, GA University of Illinois, Urbana-Champaign, IL Iowa State University and Ames Laboratory, Ames, IA Los Alamos National Laboratory, Los Alamos, NM Lawrence Livermore National Laboratory, Livermore, CA University of New Mexico, Albuquerque, NM New Mexico State University, Las Cruces, NM Dept. of Chemistry, Stony Brook Univ., Stony Brook, NY Dept. Phys. and Astronomy, Stony Brook Univ., NY Oak Ridge National Laboratory, Oak Ridge, TN University of Tennessee, Knoxville, TN Vanderbilt University, Nashville, TN 12 Countries 58 Institutions 480 Participants* * as of January 2004 Brazil University of São Paulo, São Paulo China Academia Sinica, Taipei, Taiwan China Institute of Atomic Energy, Beijing Peking University, Beijing France LPC, University de Clermont-Ferrand, Clermont-Ferrand Dapnia, CEA Saclay, Gif-sur-Yvette IPN-Orsay, Universite Paris Sud, CNRS-IN2P3, Orsay LLR, Ecòle Polytechnique, CNRS-IN2P3, Palaiseau SUBATECH, Ecòle des Mines at Nantes, Nantes Germany University of Münster, Münster Hungary Central Research Institute for Physics (KFKI), Budapest Debrecen University, Debrecen Eötvös Loránd University (ELTE), Budapest India Banaras Hindu University, Banaras Bhabha Atomic Research Centre, Bombay Israel Weizmann Institute, Rehovot Japan Center for Nuclear Study, University of Tokyo, Tokyo Hiroshima University, Higashi-Hiroshima KEK, Institute for High Energy Physics, Tsukuba Kyoto University, Kyoto Nagasaki Institute of Applied Science, Nagasaki RIKEN, Institute for Physical and Chemical Research, Wako RIKEN-BNL Research Center, Upton, NY Rikkyo University, Tokyo, Japan Tokyo Institute of Technology, Tokyo University of Tsukuba, Tsukuba Waseda University, Tokyo S. Korea Cyclotron Application Laboratory, KAERI, Seoul Kangnung National University, Kangnung Korea University, Seoul Myong Ji University, Yongin City System Electronics Laboratory, Seoul Nat. University, Seoul Yonsei University, Seoul Russia Institute of High Energy Physics, Protovino Joint Institute for Nuclear Research, Dubna Kurchatov Institute, Moscow PNPI, St. Petersburg Nuclear Physics Institute, St. Petersburg St. Petersburg State Technical University, St. Petersburg PHENIX Collaboration

18. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 18/17 Thanks for your attention Spare slides coming…

19. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 19/17 Used data, PID 70M events 70M events 200M  + 's 200M  + 's 900M pairs >4G triplets 10M  + 's 10M  + 's 2M pairs 250k triplets One-track cuts: One-track cuts: DCH quality = 31 or 63 DCH quality = 31 or 63  PC3 <3,  EMC <3,  TOF <3  PC3 <3,  EMC <3,  TOF <3  TOF :  m (p) 2  TOF :  m (p) 2 K TOF :  m (K) 2 K TOF :  m (K) 2  EMC :  m (  ) 3.1  EMC :  m (  ) 3.1 K EMC :  m (K) 2.1 K EMC :  m (K) 2.1 TOF EMC

20. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 20/17 Two-track cuts  r PC1 > 8cm  r PC1 > 8cm  r TOF > 25cm  r TOF > 25cm  r EMC > 18cm  r EMC > 18cm ,  z: ,  z:  z < 1    z < 1    z < 5    z < 5    z > 5    z > 5   Now let’s take a closer look… Now let’s take a closer look… K

21. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 21/17 Pions

22. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 22/17 Additional check on  0<  z<0.6 0.06<  z<5

23. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 23/17 Additional check on  r EMC Same  r EMC p lot, just with ghosting cut

24. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 24/17 Kaons

25. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 25/17 Pair and triplet distributions  + A(q 3 ) B(q 3 )  + A(q inv ) B(q inv ) K + A(q inv ) B(q inv ) K + A(q 3 ) B(q 3 )

26. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 26/17 Raw correlation functions  + C 3 (q 3 )  + C 2 (q inv ) K + C 2 (q inv ) K + C 3 (q 3 )

27. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 27/17 Cut on q inv Below 20 MeV there is a non-BEC background Below 20 MeV there is a non-BEC background  production?  production? Anyhow, that has to be take out of the fit Anyhow, that has to be take out of the fit

28. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 28/17 Method of Coulomb-correction See E. O. Alt, T. Csörgő, B. Lörstad, J. Schmidt-Sørensen, Phys. Lett. B 458 (1999)407: See E. O. Alt, T. Csörgő, B. Lörstad, J. Schmidt-Sørensen, Phys. Lett. B 458 (1999)407: Solve the two-body Schrödinger-equation Solve the two-body Schrödinger-equation Simmetrize to get a two- or three- body solution Simmetrize to get a two- or three- body solution Coulomb-correction from this: Coulomb-correction from this: Depends on the assumed source-function  ( x ) Depends on the assumed source-function  ( x ) One has to iterate to do the correction One has to iterate to do the correction

29. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 29/17 Method of Coulomb-correction Iteration: Iteration: Fit the raw correlation function with a proper shape Fit the raw correlation function with a proper shape Extract the parameters (R, lambda) from it Extract the parameters (R, lambda) from it Calculate the Coulomb-correction with these Calculate the Coulomb-correction with these Multiply the raw correlation function with it Multiply the raw correlation function with it Fit this new correlation function again, extract new R and lambda Fit this new correlation function again, extract new R and lambda Calculate a new Coulomb-correction Calculate a new Coulomb-correction Until parameters do not change… Until parameters do not change… Raw C n Fit: R, Fit: R, K Coul C n ’ = K Coul ×C n

30. M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 30/17 Understanding the Lévy parameters  ’ lifetime: 1000 fm  ’ lifetime: 1000 fm Eg. mass reduction 958MeV  400MeV Eg. mass reduction 958MeV  400MeV Excess in the source at 1000fm: factor of 15 Excess in the source at 1000fm: factor of 15 Levy:  = 0.2 … 0.4 Levy:  = 0.2 … 0.4