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Two- and three-particle Bose-Einstein correlations

Two- and three-particle Bose-Einstein correlations. M. Csanád for the PHENIX Collaboration. PHENIX introduction. Detectors involved: BBC: start time DC, PC: tracking, p t TOF: time of flight  PID EMC : D E  PID Acceptance: || < 0.35  =  PID by TOF and EMC :

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Two- and three-particle Bose-Einstein correlations

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

  2. PHENIX introduction • Detectors involved: • BBC: start time • DC, PC: tracking, pt • TOF: time of flight  PID • EMC: DE  PID • Acceptance: • || < 0.35 •  =  • PID by TOFand EMC: • Identify pions from 0.2 to2.0 GeV/c • High precision TOF • sTOF = 100-130 ps • dp/p= 0.7%  1.1%p The PHENIX detector system

  3. =1+ =1+ NA44 Goals of the analysis • Measure Bose-Einstein correlation functions • Parts of the source • Core + halo • Partially coherent + incoherent (part of the source) N1(p) … Invariant mom. distr. Nc(p) … Core fraction Ncp(p) … Part. coh. fraction • C2 and C3 at zero relative momenta: • Two regions on the fc-pc plane T. Csörgő Heavy Ion Phys. 15, 1 (2002) hep-ph/0001233

  4. NA44, S+Pb Goals of the analysis • l(mt) dependence at low momenta • Prediction: h’ 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

  5. PHENIX PRELIMINARY PHENIX PRELIMINARY PHENIX PRELIMINARY Edgeworth Lévy Gauss C2 (qinv) C2 (qinv) C2 (qinv) PHENIX PRELIMINARY PHENIX PRELIMINARY PHENIX PRELIMINARY Gauss Edgeworth Lévy C3 (q12= q23=q31) C3 (q12= q23=q31) C3 (q12= q23=q31) Coulomb-corrected correlations Conf. lev.: 10-18 710-70.18

  6. fc versus pc of pions NA44 S+Pb Lévy fit used PHENIX PRELIMINARY

  7. PHENIX PRELIMINARY Pion C2 at different mt bins • Ten bins in the range 0.2-0.5 GeV • Shape analysis carried out • A cut at qinv=20MeV was made • Three shapes tested

  8. 1+ 1+ 1+ PHENIX PRELIMINARY Fit parameters • Three shapes: • Gauss: l, R • Edgeworth: l, R, k3 • Lévy: l, R, a T. Csörgő, S. Hegyi and W. A. ZajcEur. Phys. J. C 36, 67 (2004)

  9. PHENIX PRELIMINARY PHENIX PRELIMINARY Gauss Edgeworth PHENIX PRELIMINARY Lévy Pion C2 at different mt bins • Three shapes: • Gauss l, R • Edgeworth l, R, k3 • Lévy l, R, a

  10. Lévy High CL Edgeworth Uniformly distr. Gauss Low CL Quality of the fits PHENIX PRELIMINARY

  11. l(mt) dependence Prediction: Hot and dense matter  h’ mass reduction enhanced h’ content h’h+p+ +p-(p0+p++p−)+p++p− average pt = 138 MeV  More p’s in the halo at 138 MeV  A hole in l(mt) Data points needed at very low mt! PHENIX FINAL DATA Au+Au 200 GeV S. S. Adler et al., PRL93,152302(2004)

  12. Gaussian fit RUN4 Au+Au 200 GeV PHENIX PRELIMINARY

  13. Edgeworth fit RUN4 Au+Au 200 GeV PHENIX PRELIMINARY

  14. Levy fit RUN4 Au+Au 200 GeV PHENIX PRELIMINARY Low a low l Same physics: dominant tail Underconstrained problem

  15. Renormalized data points PHENIX PRELIMINARY

  16. Summary • Two- and three-particle correlations • Fractional core and partial coherence • Two-particle correlation function in 10 mt bins • Gauss, Edgeworth, Lévy • R and l as a function of mt • UA(1) restoration tested • Results critically dependent on understanding of statistical and systematic errors • Additional analysis required for definitive statement

  17. PHENIX Collaboration 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 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

  18. Thanks for your attention Spare slides coming…

  19. Used data, PID TOF EMC • 70M events • 200M p+'s 900M pairs >4G triplets • 10M K+'s 2M pairs 250k triplets • One-track cuts: • DCH quality = 31 or 63 • sPC3<3, sEMC<3, sTOF<3 • pTOF: sm(p)<2, sm(K)>2 • KTOF: sm(K)<2, sm(p)>2 • pEMC: sm(p)<1.9, sm(K)>3.1 • KEMC: sm(K)<2.5, sm(p)>2.1

  20. Two-track cuts • DrPC1 > 8cm • DrTOF > 25cm • DrEMC > 18cm • Df, Dz: • Dz < 1  Df > 0.05 • Dz < 5  Df > 0.03 • Dz > 5  Df > 0.02 • Now let’s take a closer look… K p

  21. Pions

  22. Additional check on Df 0<Dz<0.6 0.06<Dz<5

  23. Additional check on DrEMC Same DrEMCplot, just with ghosting cut

  24. Kaons

  25. Pair and triplet distributions K+ A(qinv) B(qinv) p+ A(qinv) B(qinv) p+ A(q3) B(q3) K+ A(q3) B(q3)

  26. Raw correlation functions K+ C2(qinv) p+ C2(qinv) K+ C3(q3) p+ C3(q3)

  27. Cut on qinv • Below 20 MeV there is a non-BEC background • h production? • Anyhow, that has to be take out of the fit

  28. Method of Coulomb-correction • See E. O. Alt, T. Csörgő, B. Lörstad, J. Schmidt-Sørensen, Phys. Lett. B 458 (1999)407: • Solve the two-body Schrödinger-equation • Simmetrize to get a two- or three- body solution • Coulomb-correction from this: • Depends on the assumed source-function r(x) • One has to iterate to do the correction

  29. Method of Coulomb-correction • Iteration: • Fit the raw correlation function with a proper shape • Extract the parameters (R, lambda) from it • Calculate the Coulomb-correction with these • Multiply the raw correlation function with it • Fit this new correlation function again, extract new R and lambda • Calculate a new Coulomb-correction • Until parameters do not change… Raw Cn Fit: R, l KCoul Cn’ = KCoul×Cn

  30. Understanding the Lévy parameters • h’ lifetime: 1000 fm • Eg. mass reduction 958MeV 400MeV • Excess in the source at 1000fm: factor of 15 • Levy: Da = 0.2 … 0.4

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