Two pion correlations at SPS energies Dariusz Antończyk Institut fuer Kernphysik Frankfurt 11-14.09.2008 Workshop on Particle Correlations and Femtoscopy

Two pion correlations at SPS energies

Dariusz AntoDariusz AntońńczykczykInstitut fuer Kernphysik FrankfurtInstitut fuer Kernphysik Frankfurt

11-14.09.2008 Workshop on Particle Correlations and Femtoscopy 2008 Krakow, Poland

11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland

OutlineOutline

• Overview of SPS runsOverview of SPS runs• Experimental setups Experimental setups • Two particle analysis approachTwo particle analysis approach• Energy dependence of HBT radii Energy dependence of HBT radii • Reaction plane dependency analysis of HBT Reaction plane dependency analysis of HBT

radiiradii• Discussion and CommentsDiscussion and Comments


Historic overview of SPS Historic overview of SPS runs runs

• First beam more then 20 years agoFirst beam more then 20 years ago• In 1986, In 1986, 16O accelerated to 60 AGeVO accelerated to 60 AGeV

• Many experiments, covering broad spectrum of physics Many experiments, covering broad spectrum of physics topics, including HBT.topics, including HBT.• Recently, HBT analysis performed by CERES/NA45, NA49, NA57.Recently, HBT analysis performed by CERES/NA45, NA49, NA57.

1996 1998 2000 2002 2004 2006 2008199419921990

60/200A GeV

158A GeV

80A GeV

40A GeV

30A GeV

20A GeV

158A GeV114In207Pb

12O / 32S

NA45/CERES

NA49/SHINE

NA57


Experimental SetupsExperimental Setups

DetectorDetector SysteSystemm

Energy Energy AGeVAGeV

Acceptance Acceptance yy

Particle IDParticle ID

NA45/NA45/CERESCERES

Pb+Au 8.7, 12.3, 17.2 1.5-2.5 via dE/dx (TPC)

NA45/NA45/CERESCERES

Pb+Au 12.3, 17.2 1.5-2.5 via dE/dx (TPC)

NA49NA49 Pb+Pb 6.3, 7.6, 8.7, 12.5, 17.3

1.0-6.0 h-h-

NA57NA57 Pb+Pb 8.8 2.4-3.2 h-h-

s

Re-analysis of CERES HBT results for total available statistic and improved Re-analysis of CERES HBT results for total available statistic and improved momentum, centrality and reaction plane resolution. momentum, centrality and reaction plane resolution.

NA49 – PRC 77, 064908 (2008)NA49 – PRC 77, 064908 (2008)

NA57 – J. Phys. G: 34 (2007) 403-429NA57 – J. Phys. G: 34 (2007) 403-429

CERES – Nucl. Phys. A714 (2003) 124CERES – Nucl. Phys. A714 (2003) 124


Two particle analysis approach Two particle analysis approach (1)(1)

t pairsmixed even

pairsreal event

))n(pn(p

),pn(p),p(pC

21

21212

Correlation function

Analysis frame Bertsch-Pratt (qlong-qside-qout ) coordinate system in LCMS

mean transverse

pair momentum Pppk ,,

2

1

2

121


• Standard Gaussian fit used by all experiments

• Fitting algorithm• CERES and NA57 maximum likelihood assuming Poison

distribution

• NA49 minimization of 2

• No common method for removing Coulomb impact on HBT radii

Two particle analysis Two particle analysis approach (2)approach (2)

with i,j = out, side, long

ji

jiji qqR)qG(,

2,exp


Projection of correlation Projection of correlation functions CERES 158 AGeVfunctions CERES 158 AGeV

w. Coulomb

w/o Coulomb


HBT radii vs. kHBT radii vs. k┴┴

Centrality: CERES 0-5 % NA49 0-7.5%

Analysis of 80 GeV byAnalysis of 80 GeV byS.Schichmann (IKF)S.Schichmann (IKF)


HBT radii vs. kHBT radii vs. k┴┴

Centrality: CERES 0-5 % NA49 0-7.5%


HBT radii HBT radii @ @

40AGev40AGev

Centrality: CERES 0-5 % 5-10 % NA49 0-7.5 % NA57 0-11 %

J. Phys. G: 34 (2007) 403-429J. Phys. G: 34 (2007) 403-429


Beam energy systematics Beam energy systematics

PRL 90 (2003) 022301

Freeze-out volume

has a minimum at a beam energy of 10-40 AGeV

Nσ, particle multiplicity times mean hadron-hadron cross-section, has a similar beam energy

dependence

Vf / Nσ = λ f = 1 fmindependent of beam energy

Freeze-out when mean free path 1 fm

2232 sidelongf RRV


Mean free pathMean free path

• Extended with Extended with recentrecent• data from RHICdata from RHIC• data by NA49, NA35data by NA49, NA35

Including heavy and light systems Including heavy and light systems

Compilation by S.Schuchmann (IKF)Compilation by S.Schuchmann (IKF)

Agreement with Agreement with ffyy1fm for all 1fm for all energies and systemsenergies and systems

Universal pion freeze-out Universal pion freeze-out

conditioncondition

1


HBT vs. Reaction Plane HBT vs. Reaction Plane

• Reaction plane orientation from second Fourier harmonic

2

2

2

1

XY

arctanRP

i

it cospX 22

i

it sinpY 22

• recentering (Step 1)• dividing by width of

X, Y distribution, respectively (Step 2)


Resolution of the reaction Resolution of the reaction plane angleplane angle

Obtained reaction plane resolution 31-38 (centrality dependence) Ollitrault, arXiv:nucl-ex/9711003 (Met. 1)

Poskanzer , Voloshin, Phys. Rev. C58(1998)1671 (Met. 2)


HBT vs. RP - analysis strategyHBT vs. RP - analysis strategy

• HBT radii vs. reaction plane orientation probe spatial anisotropy at freeze-out U.A.Wiedemann, PRC 57 (1998) 266

• 3-dimensional correlation functions calculated separately in 8 bins

of pair - RPRside

Rout

Rlong

Reaction plane determined via elliptic flow,

range between -/2 and /2

• Assuming pure geometric effect one should expect such dependence of HBT radii

• RP resolution influence on HBT vs. RP results corrected based on MC study


HBT vs. RP – CERES 158 AGev DataHBT vs. RP – CERES 158 AGev Datauncorrected for RP resolutionuncorrected for RP resolution

• Centrality 15-25%• HBT vs. RP parameterized

by


Azimuthal pion source Azimuthal pion source eccentricity vs. event eccentricity vs. event

centralitycentrality

From geometrical From geometrical expectationexpectation

• RRout,2out,222 suggest out-of-plane suggest out-of-plane

elongationelongation• RRside,2side,2

22 and R and Rlong,2long,222 unexpected unexpected

• RRout-side,2out-side,222 consistent with R consistent with Rout,2out,2

22


Excitation function of source Excitation function of source anisotropyanisotropy

• Common centralityCommon centrality• 15-25%15-25%

• Source eccentricitySource eccentricity ≈≈ RR22

side,2 side,2 / R/ R22side,0side,0

• At SPS At SPS = = 0.0430.043±0.023±0.023


Discussion and CommentsDiscussion and Comments

• Good agreement between new and old CERES results Good agreement between new and old CERES results as well NA49 for 158 and 80 AGeV, analysis for 40 as well NA49 for 158 and 80 AGeV, analysis for 40 AGeV in progressAGeV in progress

• azimuthal anisotropy of Razimuthal anisotropy of Routout as expected, however as expected, however

• no significant azimuthal anisotropy of the source no significant azimuthal anisotropy of the source observedobserved by R by Rsideside radii radii. Possible softening by bayron-. Possible softening by bayron-

meson mixed state. meson mixed state. • Possible source of RPossible source of Rlong long oscillation - initial collision oscillation - initial collision

conditioncondition• More azimuthal anisotropy studies are need (RHIC low More azimuthal anisotropy studies are need (RHIC low

energy runs)energy runs)


More from SPSMore from SPS

• Hydro calculation for SPS – works well for flow and pt-spectra Hydro calculation for SPS – works well for flow and pt-spectra but fails to reproduce HBT radii, see presentation form but fails to reproduce HBT radii, see presentation form D.Miśkowiec (WPCF 2007)D.Miśkowiec (WPCF 2007)

• 3D source imaging technique applied to SPS/NA49 data 3D source imaging technique applied to SPS/NA49 data arXiv:0807.4892arXiv:0807.4892


BackupBackup


s

CERES/NA45 SetupCERES/NA45 Setup

System Pb+Au @ 17.2, 12.3, 8.8 GeVTarget 13/8 gold disks (diameter 600 m, thickness 25 m)

SiDC1+2 Vertex reconstructionRICH1+2 Electron IDTPC Charge particle ID

Acceptance 2.03 < < 2.65Momentum resolution p/p = 2% 1%·p/GeVEnergy loss resolution (dE/dx)/(dE/dx)=10%

Radial drift field (1/r), azimuthal deflection


Data set - Pb+Au @ 158 AGeVData set - Pb+Au @ 158 AGeV

• 30 M events with centrality 7%• 2 M events with centrality 20 %• 500 k minimum bias events

Track cuts

Available statistics

• good fit quality from tracking• high number of fitted hits (long

track) • matching between TPC and SD

< 2 • partial PID via dE/dx vs.

momentum


Data set – Pair cutsData set – Pair cuts

Different minimum opening cuts needed for the two topologies:

Sailor Cowboy

Sailor Cowboy


Coulomb interactionCoulomb interaction

Schrödinger equation describing particle in the Coulomb field is

wave function squared

Coulomb correlation function: square of the non-relativistic

wave function averaged over finite Gaussian source.

rkErkrrV coulpcoul

,,

2 12

2

q

m

k

krrikiFe

erk kri

coul

2

12

2

;1;1

2,


Previous HBT radii resultsPrevious HBT radii resultsanalysis by Heinz Tilsner and Harald

Appelshäuser

Nucl. Phys. A714 (2003) 124


Effect of the Coulomb Effect of the Coulomb correctioncorrection

attenuated by λ full strength


Effect of the Coulomb Effect of the Coulomb correctioncorrection

attenuated by λ full strength


Correction for momentum Correction for momentum resolutionresolution

• example: highest p bin

(the largest correction)• determined by Monte Carlo• lines: various attempts to

parameterized effect• correction applied to the

radii obtained from the fit


Extracting source parametersExtracting source parameters

ffgeomside TmRR 21

/GEOM 0-2.5 %

/GEOM 15-25 %/GEOM ~ 17.5 %

System size, transverse flow velocity

f

ffflong

TmK

TmK

mT

R1

2

System lifetime

Chapman, Phys. Rev C52(1995) 2694

Sinyukov, Z. Phys. C39(1998) 69,Herrmann, Bertsh, Phys. Rev.

C51(1995)328

assuming Tassuming Tff=0.12 GeV=0.12 GeV


Pair acceptance Pair acceptance

- – standard HBT analysis

midrapidity = 2.91


Centrality dependence of Centrality dependence of f f , R, RGG and and ff

22/T/Tff

1.3 < Y<2.8 fix TTff=0.12 GeV=0.12 GeV


Fitting the HBT correlation Fitting the HBT correlation functionsfunctions

111 )-q(F))qG(()kλ(N)k,qC( coul

where

• N is a normalization and (k) is a correlation strength

• with i,j = out, side, long

• Fcoul(q) is a Coulomb correlation function

• Standard Gaussian fit used• Maximum likelihood assuming Poison distribution• Coulomb included in the fit, calculated for a

similar source size and attenuated by

ji

jiji qqR)qG(,

2,exp


HBT radii vs. kHBT radii vs. k┴ ┴ for 158 AGeVfor 158 AGeV

Comparison to CERES previous results

centrality 0-5%

Nucl. Phys. A714 (2003) 124

Comparison toNA49 preliminary results

centrality 0-7.5%

PRC 77, 064908 (2008)

Documents

Two pion correlations at SPS energies Dariusz Antończyk Institut fuer Kernphysik Frankfurt 11-14.09.2008 Workshop on Particle Correlations and Femtoscopy