Energy Dependence of Multiplicity Fluctuations in Heavy Ion - - PowerPoint PPT Presentation

Energy Dependence of Multiplicity Fluctuations in Heavy Ion Collisions

Benjamin Lungwitz, IKF Universität Frankfurt for the NA49 collaboration

Benjamin Lungwitz, IKF Universität Frankfurt 2

Outline

• Introduction
• Analysis of energy dependence
• Energy dependence of multiplicity fluctuations

– Acceptance scaling – Model comparison

• Summary

Benjamin Lungwitz, IKF Universität Frankfurt 3

Motivation

• Anomalies in energy dependence seen at low SPS

energies -> hint for onset of deconfinement ?

• Models predict large fluctuations near onset of

deconfinement or critical point

(GeV)

NN

s 1 10

2

10 〉

+

π 〈 / 〉

+

K 〈 0.1 0.2

A+A: NA49 AGS RHIC

p+p

(GeV)

NN

s 1 10

2

10 T (MeV) 100 200 300

): p p+p (

S

K

+

K

+

K

√sNN (GeV)

ω

?

Benjamin Lungwitz, IKF Universität Frankfurt 4

Centrality Selection

• Veto calorimeter -> projectile spectators,

number of projectile participants NP

Proj

• Target spectators not measured in NA49 !

Veto calorimeter VCAL EVeto≈(AProj - NP

Proj)*Ekin

NP

Proj

AProj

Benjamin Lungwitz, IKF Universität Frankfurt 5

Var(n)/<n>

0.5 1 1.5 2

negative

p+p Pb+Pb

PROJ P

N

50 100 150

System Size Dependence of n- Fluctuations

• NP

Proj experimentally fixed, NP Targ fluctuate

• Peripheral collisions: Large NP

Targ fluctuations may cause

large ω in forward hemisphere (e.g. mixing)

• Central collisions: NP

Targ fluctuations negligible

50 100 150 200 1 2 3 4 HSD UrQMD

Pb+Pb, 158 A GeV

ω ω ω ω

targ P

N

proj P

t

158A GeV

see talk of M. Rybczynski

see talk of M. Gorenstein,

• V. Konchakovskyi et al.
• Phys. Rev. C 73 (2006)

034902

Benjamin Lungwitz, IKF Universität Frankfurt 6

Track Selection

• Only hadrons in a limited forward acceptance (projectile

hemisphere) were selected (158A GeV: equal to M. Rybczynski)

– Safe acceptance (no problems with efficiency etc.)

158A GeV

y in cms system

50 100 150 200 250 300

[deg] φ

• 150
• 100
• 50

50 100 150

[GeV/c]

T

p

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

• (pT, φ) cut:
• C. Alt et al.,

Phys.Rev.C70:064903, 2004

• y-cut:

20A – 80A GeV: 1<y<ybeam 158A GeV: 1.08<y<2.57

1.4<y<1.6

h-

) π y(

• 4
• 3
• 2
• 1

1 2 3 4 T

p

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Benjamin Lungwitz, IKF Universität Frankfurt 7

NN

s 6 8 10 12 14 16 18 20 p 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

small standard

Experimental Acceptance

• Strong energy dependence of experimental acceptance

– Difficult to compare different energies

• Small acceptance (1<y<(ybeam-1)/2+1) used to study

acceptance effects

h-

Benjamin Lungwitz, IKF Universität Frankfurt 8

Multiplicity Distributions

• Multiplicity distributions for

central collisions are significantly narrower than Poisson distribution !

all data are preliminary !

40A GeV

)

• N(h

10 20 30 40 50 60 70 200 400 600 800 1000 1200 1400 1600 )

• N(h

10 20 30 40 50 60 70 data/poisson 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 )

• N(h

60 80 100 120 140 160 180 100 200 300 400 500 600 700 800 )

• N(h

60 80 100 120 140 160 180 data/poisson 0.5 1 1.5 2

158A GeV h- at NP

Proj=195

black: data red: Poisson distribution

)

• N(h

1 2 3 4 5 6 7 data/poisson 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 )

• N(h

1 2 3 4 5 6 7 1000 2000 3000 4000 5000 6000 7000 8000

Pb+Pb Pb+Pb p+p

Benjamin Lungwitz, IKF Universität Frankfurt 9

Centrality Dependence at all Energies

Proj P

N 160 165 170 175 180 185 190 195 200 205 ω 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

Proj P

N 160 165 170 175 180 185 190 195 200 205 ω 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

Proj P

N 160 165 170 175 180 185 190 195 200 205 ω 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

Proj P

N 160 165 170 175 180 185 190 195 200 205 ω 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

Proj P

N 160 165 170 175 180 185 190 195 200 205 ω 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

• Not corrected for

resolution of veto calorimeter

• 190<NP

Proj<200

selected

20A GeV 30A GeV 40A GeV 80A GeV 158A GeV

h-

Benjamin Lungwitz, IKF Universität Frankfurt 10

Corrections and Biases

• Correction applied for finite size of centrality bins

in the order of 2%

• Known uncorrected biases:

– NP

Proj fluctuations due to finite Veto calorimeter

resolution (estimated to be <2%)

– A possible NP

Targ fluctuations contribution to projectile

hemisphere

• > They both increase fluctuations

bw=〈n〉 Var N P

Proj

〈 N P

Proj〉 2

Benjamin Lungwitz, IKF Universität Frankfurt 11

NN

s 6 8 10 12 14 16 18 20 ω 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

NN

s 6 8 10 12 14 16 18 20 ω 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

NN

s 6 8 10 12 14 16 18 20 ω 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

Energy Dependence of n- Fluctuations

• Scaled variance for h+, h- smaller than 1
• ω for h+- < 1 for low energies, ω+− > 1 for higher energies
• ω(p+p) ≈ ω(central Pb+Pb) at 158A GeV

h+ h- h+-

Note: different acceptance for different energies !

• nly statistical

errors shown

(GeV) (GeV) (GeV)

blue: Pb+Pb red: p+p

Benjamin Lungwitz, IKF Universität Frankfurt 12

Effect of Limited Acceptance

• Assuming no correlations in momentum space
• ω(4π) > 1 <=> ω(acc) > 1, ω(4π) < 1 <=> ω(acc) < 1

acc=4­1⋅pacc1

p(acc) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (acc) ω 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

ρ π+ π-

• Formula (*) not valid if more than one

daughter particle of a decay is detected

– very few particles decay into 2 h- – many particles decay into h+ and h-

(*)

Benjamin Lungwitz, IKF Universität Frankfurt 13

Acceptance Scaling for h-

• Data comparable with acceptance scaling and no (or

weak) energy dependence of multiplicity fluctuations in 4π

p 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 ω 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

20A GeV 30A GeV 40A GeV 80A GeV 158A GeV

h-

<ω(4π)> ≈ 0.3

small and standard acceptance

Benjamin Lungwitz, IKF Universität Frankfurt 14

Statistical Model

• Grand canonical ensemble (no charge conservation):

– ω>1 for all energies

• Canonical ensemble (B,Q,S conserved):

– ω<1 for h+ and h- , ω crosses 1 for h+-

• Final state: resonance decays

NN

S 1 10

2

10

3

10

+

ω

0.2 0.4 0.6 0.8 1 1.2 1.4 AGS

SPS RHIC

Primordial GCE Final GCE Primordial CE Final CE

NN

S 1 10

2

10

3

10

• ω

0.2 0.4 0.6 0.8 1 1.2 1.4

AGS SPS RHIC

Primordial GCE Final GCE Primordial CE Final CE

NN

S 1 10

2

10

3

10

ch

ω

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 AGS SPS RHIC

Primordial GCE Final GCE Primordial CE Final CE

see talk of M. Gorenstein,V. Begin

• M. Hauer et. al. nucl-th/0606036

h+ h- h+-

4π acceptance !

Benjamin Lungwitz, IKF Universität Frankfurt 15

NN

s 6 8 10 12 14 16 18 20 ω 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

data canonical model grand canonical model

NN

s 6 8 10 12 14 16 18 20 ω 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

data canonical model grand canonical model

Statistical Model and Data

• 4π values scaled down to exp. acceptance assuming no

correlations in momentum space (eg. due to resonance decays)

• Grand canonical model overpredicts fluctuations
• Canonical model works better, but its fluctuations are also too

high (energy conservation needed ?)

h+ h-

(GeV) (GeV)

Benjamin Lungwitz, IKF Universität Frankfurt 16

NN

s 6 8 10 12 14 16 18 20 ω 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

data Venus HSD

NN

s 6 8 10 12 14 16 18 20 ω 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

data Venus HSD

String Hadronic Models: Venus, HSD

• HSD: works good for 20A – 40A GeV, but overpredicts data

at 80A and 158A GeV

• Venus overpredicts data for energies > 20A GeV

h+ h-

HSD: V. Konchakovski, priv. com.

(GeV) (GeV)

Benjamin Lungwitz, IKF Universität Frankfurt 17

NN

s 6 8 10 12 14 16 18 20 ω 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

data Venus HSD

String Hadronic Models: Venus, HSD (2)

• All string hadronic models overpredict fluctuations of h+- for

energies > 20A GeV

h+-

(GeV)

Benjamin Lungwitz, IKF Universität Frankfurt 18

Summary

• Multiplicity fluctuations in central Pb+Pb collisions for h+, h-

and h+- at 20, 30, 40, 80 and 158A GeV were analysed

• ω− scales with p(acc) for h- at all energies
• > weak energy dependence of ω in 4π [ ω(4π) ≈ 0.3 ]
• ω+ and ω- smaller than 1 for all energies
• > Grand canonical ensemble does not work !
• Canonical statistical model shows similar trend as the data

but ω(data) < ω(CE)

• String hadronic models (Venus, HSD) work for lower

energies (20-40A GeV) but fail for higher (80-158A GeV)

Benjamin Lungwitz, IKF Universität Frankfurt 19

Backup

Benjamin Lungwitz, IKF Universität Frankfurt 20

Multiplicity Distributions

20 40 60 80 100 120 140

Nneg

10

• 3

10

• 2

0.1 P(Nneg)

Pb+Pb central Poisson

20 40 60 80 100 120 140

Nneg

Pb+Pb semi-periph. Poisson

2 4 6 8

Nneg

p+p Poisson

n=Varn 〈n〉 =〈n

2〉­〈n〉 2

〈n〉

Used measure of fluctuations: scaled variance

[ =1 for Poissonian distribution ]

158A GeV

negative hadrons, NP

Proj fixed

NP

Proj=178

NP

Proj=39

Benjamin Lungwitz, IKF Universität Frankfurt 21

P

/A

Proj P

N 0.2 0.4 0.6 0.8 1 Var(n)/<n> 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

p+p C+C Si+Si Pb+Pb

Centrality and System Size Dependence

• Var(n)/<n> increases with decreasing centrality
• Approximate scaling in NP

Proj/AProj

NA49 preliminary

Projectile hemisphere

158A GeV

h-

Benjamin Lungwitz, IKF Universität Frankfurt 22

Different Extreme Reaction Scenarios

• Multiplicity fluctuations sensitive to reaction scenario

spectators fixed spectators fluctuate

NP

Targ fluctuations contribute in both

hemispheres (most statistical models) NP

Targ fluctuations contribute in target

hemisphere (most string hadronic models) NP

Targ fluctuations contribute in

projectile hemisphere

• M. Gazdzicki,
• M. Gorenstein

arXiv:hep-ph/0511058

selected phase space for analysis

Benjamin Lungwitz, IKF Universität Frankfurt 23

Proj P

N 50 100 150 200 Var(n)/<n> 0.5 1 1.5 2 2.5

Data: p+p Pb+Pb

String hadronic models: HSD UrQMD HIJING

String Hadronic Models

• String hadronic models shown (UrQMD, HSD, HIJING)

belong to transparency class

• They do not reproduce data on multiplicity fluctuations

HSD, UrQMD:

• V. Konchakovskyi et al.
• Phys. Rev. C 73 (2006)

034902 HIJING:

• M. Gyulassy, X. N. Wang
• Comput. Phys. Commun. 83

(1994) 307 Simulation performed by:

• M. Rybczynski

Projectile hemisphere

NA49 preliminary

h-

Benjamin Lungwitz, IKF Universität Frankfurt 24

Proj P

N 50 100 150 200 Var(n)/<n> 0.5 1 1.5 2 2.5 3 3.5

Data: p+p Pb+Pb

statistical model: transparency mixing reflection

Reflection, Mixing and Transparency

• Significant amount of mixing of particles produced by

projectile and target sources

Model calculation:

• M. Gazdzicki,
• M. Gorenstein

arXiv:hep-ph/0511058

NA49 preliminary

Projectile hemisphere

h-