two- and three-particle bose-einstein correlations m. csanád for the phenix collaboration

Two- and three-particle Two- and three-particle Bose-Einstein correlationsBose-Einstein correlations

M. Csanád for the M. Csanád for the PHENIX CollaborationPHENIX Collaboration

22/17/17M. Csanád for the PHENIX Collaboration, Quark Matter 2005, BudapestM. Csanád for the PHENIX Collaboration, Quark Matter 2005, Budapest

PHENIX introductionPHENIX introduction• Detectors involved:Detectors involved:

• BBC: start timeBBC: start time• DC, PC: tracking,DC, PC: tracking, p ptt

• TOF: TOF: time of flight time of flight PID PID • EMCEMC: : E E PID PID

• Acceptance:Acceptance:• < 0.35< 0.35• = =

• PID by TOFPID by TOF and EMCand EMC::• Identify pionsIdentify pions

from 0.2 tofrom 0.2 to 2.02.0 GeV/c GeV/c • High precision TOFHigh precision TOF

• TOFTOF = 100-130 ps = 100-130 ps• p/p= 0.7% p/p= 0.7% 1.1%p 1.1%p

The The PHENIX detector PHENIX detector systemsystem


Goals of the analysisGoals of the analysis• Measure Bose-Einstein correlation functionsMeasure Bose-Einstein correlation functions• Parts of the sourceParts of the source

• Core + haloCore + halo• Partially coherent + incoherent (part of the source)Partially coherent + incoherent (part of the source)

NN11(p) … Invariant (p) … Invariant mom. distr.mom. distr. NNcc(p) … Core fraction(p) … Core fraction

NNccpp(p) … Part. coh. (p) … Part. coh.

fractionfraction

• CC22 and C and C33 at zero relative momenta: at zero relative momenta:

• Two regions onTwo regions on

the fthe fcc-p-pcc plane plane

T. CsT. CsöörgrgőőHeavy Ion Phys. 15, 1 (2002)Heavy Ion Phys. 15, 1 (2002)hep-ph/00012hep-ph/000123333

=1+=1+

NA44


Goals of the analysisGoals of the analysis• (m(mtt)) dependence at low momenta dependence at low momenta

• Prediction:Prediction:

’’ mass reduction in hotmass reduction in hot

and dense matterand dense matter

Kapusta, Kharzeev, McLerranKapusta, Kharzeev, McLerran

Phys.Rev.D53:5028-5033,1996Phys.Rev.D53:5028-5033,1996

Z. Huang, X-N. WangZ. Huang, X-N. Wang

Phys.Rev.D53(1996)5034Phys.Rev.D53(1996)5034

Vance, Csörgő Kharzeev Vance, Csörgő Kharzeev

Phys.Rev.Lett.81:2205-2208,1998Phys.Rev.Lett.81:2205-2208,1998

NA44, NA44, S+PbS+Pb


Coulomb-corrected correlationsCoulomb-corrected correlationsPHENIX PRELIMINARY

C2

(qinv)

PHENIX PRELIMINARY PHENIX PRELIMINARY

C2

(qinv)C2

(qinv)

Gauss Edgeworth

Lévy

C3 (q12= q23=

q31)

PHENIX PRELIMINARY PHENIX PRELIMINARYPHENIX PRELIMINARY

C3 (q12= q23=

q31) C3 (q12= q23=

q31)

Gauss Edgeworth

Lévy

Conf. lev.: 10Conf. lev.: 10-18-18 7 71010-7-7 0.180.18


ffcc versus p versus pcc of pions of pions

NA44 S+Pb

PHENIX PRELIMINARY

Lévy fit Lévy fit usedused


Pion CPion C22 at different m at different mtt bins bins

• Ten bins in Ten bins in the range 0.2-the range 0.2-0.5 GeV0.5 GeV

• Shape Shape analysis analysis carried outcarried out

• A cut at A cut at qqinvinv=20MeV =20MeV was madewas made

• Three shapes Three shapes testedtested

PHENIX PRELIMINARY


• Three shapes:Three shapes:• Gauss: Gauss: , R, R

• Edgeworth: Edgeworth: , R, , R, 33

• Lévy: Lévy: , R, , R,

Fit parametersFit parameters

PHENIX PRELIMINARY

1+

1+

1+

T. CsT. Csöörrgőgő, S. Hegyi and W. A. , S. Hegyi and W. A. ZajcZajc Eur. Phys. J. C 36, 67 Eur. Phys. J. C 36, 67 (2004)(2004)


Pion CPion C22 at different m at different mtt bins bins

EdgewortEdgeworthh

PHENIX PRELIMINARY

• Three shapes:Three shapes:• GaussGauss , ,

RR• EdgeworthEdgeworth , ,

R, R, 33

• LévyLévy , R, , R,

GaussGauss

PHENIX PRELIMINARY

LévyLévy

PHENIX PRELIMINARY


Quality of the fitsQuality of the fitsPHENIX PRELIMINARY

GaussGaussLow CLLow CL

LévyLévyHigh CLHigh CL

EdgeworthEdgeworthUniformly Uniformly distr.distr.

EdgeworthEdgeworthUniformly Uniformly distr.distr.


(m(mtt) dependence) dependence

Prediction:Prediction:Hot and dense matterHot and dense matter

’’ mass reductionmass reduction

enhanced enhanced ’’ content content

’’+++ + ++-- ((00++++++−−)+)+++

++−−

average paverage ptt = 138 MeV = 138 MeV

More More ’s in the halo at 138 ’s in the halo at 138

MeVMeV

A hole in A hole in (m(mtt) )

Data points Data points needed at very needed at very

low mlow mtt!!

PHENIX FINAL DATAAu+Au 200 GeV

S. S. Adler et al., PRL93,152302(2004)


Gaussian fitGaussian fit

PHENIX PRELIMINARYRUN4 Au+Au 200 GeV


Edgeworth fitEdgeworth fit



Levy fitLevy fit


Low Low low low Same physics: dominant tailSame physics: dominant tail

Underconstrained problemUnderconstrained problem


Renormalized data pointsRenormalized data points

PHENIX PRELIMINARY


SummarySummary• Two- and three-particle correlationsTwo- and three-particle correlations• Fractional core and partial Fractional core and partial

coherencecoherence• Two-particle correlation function in Two-particle correlation function in

10 m10 mtt bins bins• Gauss, Edgeworth, LévyGauss, Edgeworth, Lévy• R and R and as a function of m as a function of mtt

• UUAA(1) restoration tested(1) restoration tested• Results critically dependent on understanding Results critically dependent on understanding

of statistical and systematic errorsof statistical and systematic errors• Additional analysis required for definitive Additional analysis required for definitive

statementstatement


Sweden Lund University, LundUSA 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 PauloChina Academia Sinica, Taipei, Taiwan China Institute of Atomic Energy, Beijing Peking University, BeijingFrance 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, NantesGermany University of Münster, MünsterHungary Central Research Institute for Physics (KFKI), Budapest Debrecen University, Debrecen Eötvös Loránd University (ELTE), Budapest India Banaras Hindu University, Banaras Bhabha Atomic Research Centre, BombayIsrael Weizmann Institute, RehovotJapan 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, SeoulRussia 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 CollaborationPHENIX Collaboration


Thanks for your attentionThanks for your attention

Spare slides coming…Spare slides coming…


Used data, PIDUsed data, PID• 70M events70M events

• 200M 200M ++'s's900M pairs900M pairs>4G triplets>4G triplets

• 1010M M ++'s's2M pairs2M pairs250k triplets250k triplets

• One-track cuts:One-track cuts:• DCH quality = 31 or 63DCH quality = 31 or 63• PC3PC3<3, <3, EMCEMC<3, <3, TOFTOF<3<3

• TOFTOF: : mm(p)<2, (p)<2, mm(K)>2(K)>2

• KKTOFTOF: : mm(K)<2, (K)<2, mm(()>2)>2

• EMCEMC: : mm(()<1.9, )<1.9, mm(K)>3.1(K)>3.1

• KKEMCEMC: : mm(K)<2.5, (K)<2.5, mm(()>2.1)>2.1

TOF TOF EMCEMC


Two-track cutsTwo-track cuts• rrPC1 PC1 > 8cm> 8cm• rrTOF TOF > 25cm> 25cm• rrEMC EMC > 18cm> 18cm• , , z:z:

• z < 1 z < 1 • z < 5 z < 5 • z > 5 z > 5

• Now let’s take a Now let’s take a closer look…closer look…

KK


PionsPions


Additional check on Additional check on

0<0<z<0.6 z<0.6 0.06<0.06<z<5 z<5


Additional check on Additional check on rrEMCEMC

Same Same rrEMCEMC pplot, just with lot, just with ghosting cutghosting cut


KaonsKaons


Pair and triplet distributionsPair and triplet distributions

++ A(q3)

B(q3)

++

A(qinv)

B(qinv)

KK++

A(qinv)

B(qinv)

KK++

A(q3)

B(q3)


Raw correlation functionsRaw correlation functions

++ C3(q3)

++

C2(qinv)

KK++

C2(qinv)

KK++

C3(q3)


Cut on qCut on qinvinv

• Below 20 MeV there is a non-BEC backgroundBelow 20 MeV there is a non-BEC background• production?production?• Anyhow, that has to be take out of the fitAnyhow, that has to be take out of the fit


Method of Coulomb-correctionMethod of Coulomb-correction• See E. O. Alt, T. Csörgő, B. Lörstad, J. See E. O. Alt, T. Csörgő, B. Lörstad, J.

Schmidt-Sørensen, Phys. Lett. B 458 Schmidt-Sørensen, Phys. Lett. B 458 (1999)407:(1999)407:• Solve the two-body Schrödinger-equationSolve the two-body Schrödinger-equation

• Simmetrize to get a two- or three- body solutionSimmetrize to get a two- or three- body solution• Coulomb-correction from this:Coulomb-correction from this:

• Depends on the assumed source-function Depends on the assumed source-function ((xx))

• One has to iterate to do the correctionOne has to iterate to do the correction


Method of Coulomb-correctionMethod of Coulomb-correction• Iteration:Iteration:

• Fit the raw correlation function with a proper Fit the raw correlation function with a proper shapeshape

• Extract the parameters (R, lambda) from itExtract the parameters (R, lambda) from it• Calculate the Coulomb-correction with theseCalculate the Coulomb-correction with these• Multiply the raw correlation function with itMultiply the raw correlation function with it• Fit this new correlation function again, extract Fit this new correlation function again, extract

new R and lambdanew R and lambda• Calculate a new Coulomb-correctionCalculate a new Coulomb-correction• Until parameters do not change…Until parameters do not change…

Raw Raw CCnn

Fit: R, Fit: R,

KKCoulCoul CCnn’ = ’ = KKCoulCoul××CCnn


Understanding the Lévy Understanding the Lévy parametersparameters• ’ ’ lifetime: 1000 fmlifetime: 1000 fm

• Eg. mass reduction 958MeVEg. mass reduction 958MeV 400MeV 400MeV• Excess in the source at 1000fm: factor Excess in the source at 1000fm: factor

of 15of 15• Levy: Levy: = 0.2 … 0.4 = 0.2 … 0.4

two- and three-particle bose-einstein correlations m. csanád for the phenix collaboration

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