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

PHENIX introduction • Detectors involved: BBC: start time • DC, PC: tracking, pt • PHENIX introduction • Detectors involved: BBC: start time • DC, PC: tracking, pt • TOF: time of flight PID • EMC: E PID • The PHENIX detector system • Acceptance: • • | | < 0. 35 = • PID by TOF and EMC: Identify pions from 0. 2 to 2. 0 Ge. V/c • High precision TOF • • • s. TOF = 100 -130 ps dp/p= 0. 7% 1. 1%p M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 2

Goals of the analysis • Measure Bose-Einstein correlation functions • Parts of the source Goals of the analysis • Measure Bose-Einstein correlation functions • Parts of the source Core + halo • Partially coherent + incoherent (part of the source) • N 1(p) … Invariant mom. distr. Nc(p) … Core fraction Ncp(p) … Part. coh. fraction • C 2 and C 3 at zero relative momenta: =1+ • Two regions on the fc-pc plane NA 44 T. Csörgő Heavy Ion Phys. 15, 1 (2002) hep-ph/0001233 M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 3

Goals of the analysis • l(mt) dependence at low momenta • Prediction: ’ mass Goals of the analysis • l(mt) dependence at low momenta • Prediction: ’ mass reduction in hot and dense matter Kapusta, Kharzeev, Mc. Lerran Phys. Rev. D 53: 5028 -5033, 1996 NA 44, S+Pb Z. Huang, X-N. Wang Phys. Rev. D 53(1996)5034 Vance, Csörgő Kharzeev Phys. Rev. Lett. 81: 2205 -2208, 1998 M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 4

Coulomb-corrected correlations PHENIX PRELIMINARY Gauss C 2 (qinv) Conf. lev. : 10 -18 PHENIX Coulomb-corrected correlations PHENIX PRELIMINARY Gauss C 2 (qinv) Conf. lev. : 10 -18 PHENIX PRELIMINARY Edgeworth C 2 (qinv) 7 10 -7 PHENIX PRELIMINARY Gauss Edgeworth C 3 (q 12= q 23= q 31) PHENIX PRELIMINARY Lévy C 2 (qinv) 0. 18 PHENIX PRELIMINARY Lévy C 3 (q 12= q 23= q 31) M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 5

fc versus pc of pions Lévy fit used NA 44 S+Pb PHENIX PRELIMINARY M. fc versus pc of pions Lévy fit used NA 44 S+Pb PHENIX PRELIMINARY M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 6

Pion C 2 at different mt bins PHENIX PRELIMINARY • Ten bins in the Pion C 2 at different mt bins PHENIX PRELIMINARY • Ten bins in the range 0. 2 -0. 5 Ge. V • Shape analysis carried out • A cut at qinv=20 Me. V was made • Three shapes tested M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 7

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

Pion C 2 at different mt bins PHENIX PRELIMINARY Gauss Edgeworth PHENIX PRELIMINARY Lévy Pion C 2 at different mt bins PHENIX PRELIMINARY Gauss Edgeworth PHENIX PRELIMINARY Lévy • Three shapes: Gauss • Edgeworth • Lévy • M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest l, R, k 3 l, R, a 9

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

l(mt) dependence Prediction: Hot and dense matter ’ mass reduction enhanced ’ content ’ l(mt) dependence Prediction: Hot and dense matter ’ mass reduction enhanced ’ content ’ + + + - ( 0+ ++ −)+ ++ − average pt = 138 Me. V More ’s in the halo at 138 Me. V A hole in l(mt) Data points needed at very low mt! PHENIX FINAL DATA Au+Au 200 Ge. V S. S. Adler et al. , PRL 93, 152302(2004) M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 11

Gaussian fit RUN 4 Au+Au 200 Ge. V PHENIX PRELIMINARY M. Csanád for the Gaussian fit RUN 4 Au+Au 200 Ge. V PHENIX PRELIMINARY M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 12

Edgeworth fit RUN 4 Au+Au 200 Ge. V PHENIX PRELIMINARY M. Csanád for the Edgeworth fit RUN 4 Au+Au 200 Ge. V PHENIX PRELIMINARY M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 13

Levy fit RUN 4 Au+Au 200 Ge. V PHENIX PRELIMINARY Low a low l Levy fit RUN 4 Au+Au 200 Ge. V PHENIX PRELIMINARY Low a low l Same physics: dominant tail Underconstrained problem M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 14

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

Summary • Two- and three-particle correlations • Fractional core and partial coherence • Two-particle 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 • M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 16

PHENIX Collaboration Brazil China University of São Paulo, São Paulo Academia Sinica, Taipei, Taiwan PHENIX Collaboration Brazil China University of São Paulo, São Paulo 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-IN 2 P 3, Orsay LLR, Ecòle Polytechnique, CNRS-IN 2 P 3, 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 * as of January 2004 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 State Technical University, St. Petersburg 12 Countries Sweden Lund University, Lund USA Abilene Christian University, Abilene, TX Brookhaven National Laboratory, Upton, NY University of California - 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 58 Institutions 480 Participants* M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 17

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

 • 70 M events Used data, PID 200 M +'s 900 M pairs • 70 M events Used data, PID 200 M +'s 900 M pairs >4 G triplets • 10 M K+'s 2 M pairs 250 k triplets • TOF EMC • One-track cuts: • • • DCH quality = 31 or 63 s. PC 3<3, s. EMC<3, s. TOF<3 TOF: sm(p)<2, sm(K)>2 KTOF: sm(K)<2, sm( )>2 EMC: sm( )<1. 9, sm(K)>3. 1 KEMC: sm(K)<2. 5, sm( )>2. 1 M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 19

Two-track cuts • • Dr. PC 1 > 8 cm Dr. TOF > 25 Two-track cuts • • Dr. PC 1 > 8 cm Dr. TOF > 25 cm Dr. EMC > 18 cm Df, Dz: K z < 1 > 0. 05 • z < 5 > 0. 03 • z > 5 > 0. 02 • • Now let’s take a closer look… p M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 20

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

Additional check on 0<Dz<0. 6 0. 06<Dz<5 M. Csanád for the PHENIX Collaboration, Quark Additional check on 0

Additional check on r. EMC Same Dr. EMC plot, just with ghosting cut M. Additional check on r. EMC Same Dr. EMC plot, just with ghosting cut M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 23

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

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

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

Cut on qinv • Below 20 Me. V there is a non-BEC background production? Cut on qinv • Below 20 Me. V there is a non-BEC background production? • Anyhow, that has to be take out of the fit • M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 27

Method of Coulomb-correction • See E. O. Alt, T. Csörgő, B. Lörstad, J. Schmidt. 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 M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 28

Method of Coulomb-correction • Iteration: Fit the raw correlation function with a proper shape 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 M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 29

Understanding the Lévy parameters • • h’ lifetime: 1000 fm Eg. mass reduction 958 Understanding the Lévy parameters • • h’ lifetime: 1000 fm Eg. mass reduction 958 Me. V 400 Me. V Excess in the source at 1000 fm: factor of 15 Levy: Da = 0. 2 … 0. 4 M. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest 30