Particle number fluctuations and correlation

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Particle number fluctuations and correlation

• Marcus Bleicher
• Institut für Theoretische Physik
• Goethe Universität Frankfurt
• Germany

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Outline of the talk

• Introduction
• Ratio fluctuations- D- scaled variance
• Baryon-strangeness correlations
• Summary

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Motivation
At RHIC look for signals of freely moving
partons.At FAIR/SPSlook for the mixed phase
and the onset of deconfinement
E. Bratkovskaya, M.B. et al., PRC 2005
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Energy density fluctuations
Pb(160AGeV)Pb

• Hot spots in the thermal energy density
• Clusters of size 5 fm3

e (GeV/fm3)
X (fm)
y (fm)
Dz1fm
M. Bleicher et al, Nucl.Phys.A638391,1998
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The tool

• UrQMD Ultra-Relativistic Quantum Molecular
  Dynamics
• out-of-equilibrium transport model
• Particles interact via - measured and
  calculated cross sections - string
  excitation and fragmentation - formation
  and decay of resonances
• Provides full space-time dynamics of heavy-ion
  collisions

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What can transport models do?

• Provide baseline calculations,including
  resonances, jets, flow,Study energy/centrality
  dependence
• Provide a look behind the curtain,i.e. what is
  the origin of the observed effect
• Study acceptance effects, i.e. how does limited
  detector coverage and the trigger conditions
  influence the results

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Sources of fluctuations I

• Centrality determination- same volume?- same
  energy deposition?- same particle density?
• Number of (initial) collisions- elastic vs
  inelastic
• Collision energy spectrum of the individual
  collisions

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Fluctuations/Correlations II

• String mass P(m2)1/m2?Multiplicity
  fluctuations at fixed Ecm
• Fluctuations of string tension (A. Bialas
  2000)?strangeness and pT fluctuations
• Resonance decays
• Flow
• Jets

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Ratio fluctuations

• proposed by Jeon, Koch, Mueller, Asakawa (2000)
• E.g.

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The famous D The first smoking gun prediction
Bleicher, Jeon, Koch, PRC (2000)
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Similar results from other models
Zhang, Topor Pop, Jeon, Gale, hep-ph/0202057
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and why it doesnt work

• Hadronization (quark recombination) destroys the
  fluctuation
• Finite acceptance might also destroy the signal
  (Zaranek et al.)

qMD calculation by S. Scherrer
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Multiplicity fluctuations
PbPb (158 AGeV) in the NA49 acceptance (1.1ltyCMlt2
.9)
Extraction of the multiplicity distribution for
every NparNote Calculation is narrower than
the data
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Multiplicity fluctuations at SPSThe problem

• The fluctuation is quantified with the
• scaled variance
• Enhanced fluctuations for mid-
• peripheral collisions are observed

Similar results from HIJING, HSD and RQMD
Note - for a poisson distribution, w1
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Multiplicity fluctuations at SPSNot a problem?
There seems not to be a problem in string cluster
approaches.
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Where is the problem?
PbPb (158 AGeV) in the NA49 acceptance (1.1ltyCMlt2
.9)

• mean value correctly reproduced
• Variance reproduced for central and very
  peripheral events
• Failure for mid-peripheral events

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Analysis of different windows

• the normalized variance
• flat in the projectile hemisphere
• larger in the mirror acceptance
• even larger in 4p
• maximum around Np40

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The number of participants
Calorimeter measure of the energy deposited by
the projectile spectators
TPCs measure of the particles multiplicities
In the UrQMD, the number of participant
spectators is determined with a rapidity cut on
the nucleons
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Fluctutions in target region

• the fluctuation has a maximum
• around Np25
• introduces an asymetry between
• projectile and target participants
• leads to an increase of the multiplicity
• fluctuation in the target hemisphere

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Correlation length in rapidity

• Rapidity window dependence
• correlation length of the order of 1
• unit of rapidity
• ? target and projectile hemisphere are
• independent in hadron-string models

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Mixing and fluctuations

• I.e. the trigger condition marks projectile
  and target participants
• This allows to study the degree of mixing of
  the matter produced in HIC
• Data suggest strong mixing of hemispheres
• ? Hints to expanding initial fireball in
  contrast to string dynamics

M. Gazdzicki and M. GorensteinarXivhep-ph/05110
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Baryon-Strangeness Correlations
Definition
Idea Strangeness and baryon numbercarriers are
different in QGP and hadron gas.
First suggested by V. Koch et al., 2005

• HG strangeness is decoupled from baryon number
  (mesons) ? small CBS correlation
• QGP strangeness is fixed to baryon number
  (strange quark)? large CBS correlation

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Lattice estimate of CBS
CBS can be obtained from lattice simulations
- calculate off-diagonal susceptibilities -
vanishing chemical potential - quenched
approximation (no quarks of the sea)
with css/T20.53 and cus cds0, ?CBS1
consistent with a weakly interacting QGP
R.V. Gavai and S.Gupta Phys. Rev. D 67/65 A.
Majumder, V. Koch, J. Randrup arXivnucl-th/051003
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Baryon-Strangeness Correlations 2

• Limiting cases for CBS
• Large mB CBS ?3/2
• large acc. window CBS ?0Explored with help
  of increasing rapidity window inAuAu reaction
  at RHIC

• Present models yield similar results for small
  rapidity window
• Different handling of the fragmentation
  region/spectators influences results at large
  rapidities

Haussler, Stoecker, Bleicher,hep-ph/0507189
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Baryon-Strangeness Correlations 3
Energy dependence of CBS allows to study the
onset of deconfinement transition Note that the
QGP result is for m0 Here ymaxlt0.5

• Deviations from the HG are expected around high
  SPS energy region, due to QGP onset.

Haussler, Stoecker, Bleicher,hep-ph/0507189
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Baryon-Strangeness Correlations 4
Centrality dependence of CBS allows to study the
critical volume needed for QGP formation. Note
that the QGP result is for m0 ymaxlt0.5,
Ecm200AGeV

• Hadron-string transport models predict no
  centrality dependence of CBS
• A QGP transition leads to a strong centrality
  dependence

Haussler, Stoecker, Bleicher,hep-ph/0507189, PRC
in print
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Summary

• The D puzzle is solved hadronization
  destroys all initial state correlations
• Hadron-string models fail to reproduce the
• measured multiplicity fluctuations ? might
  indicate that the matter at CERN SPS is mixed
• Baryon-strangeness correlations allow to pin
  down the onset of the QGP transition.
• Fluctuations and correlations are valuable tools
  to study heavy ion reactions.
• However, the interpretation is usually difficult.

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Thanks

• Diana Schumacher
• Hannah Petersen
• Stephane Haussler
• Diana Schumacher

• Elena Bratkovskaya
• Manuel Reiter
• Sascha Vogel
• Xianglei Zhu
• Horst Stoecker