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## Particle number fluctuations and correlation

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Particle number fluctuations and correlation

Marcus Bleicher

Institut für Theoretische Physik

Goethe Universität Frankfurt

Germany

Marcus Bleicher, Santiago de Compostela 2006

Outline of the talk

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

Marcus Bleicher, Santiago de Compostela 2006

Motivation

At RHIC: look for signals of freely moving partons.At FAIR/SPS:look for the mixed phase and the onset of deconfinement

E. Bratkovskaya, M.B. et al., PRC 2005

Marcus Bleicher, Santiago de Compostela 2006

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)

Dz=1fm

M. Bleicher et al, Nucl.Phys.A638:391,1998

Marcus Bleicher, Santiago de Compostela 2006

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

Marcus Bleicher, Santiago de Compostela 2006

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

Marcus Bleicher, Santiago de Compostela 2006

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

Marcus Bleicher, Santiago de Compostela 2006

Fluctuations/Correlations II

- String mass: P(m2)~1/m2Multiplicity fluctuations at fixed Ecm
- Fluctuations of string tension (A. Bialas 2000)strangeness and pT fluctuations
- Resonance decays
- Flow
- Jets

Marcus Bleicher, Santiago de Compostela 2006

Ratio fluctuations

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

Marcus Bleicher, Santiago de Compostela 2006

The ‘famous’ D: The first smoking gun prediction

Bleicher, Jeon, Koch, PRC (2000)

Marcus Bleicher, Santiago de Compostela 2006

Similar results from other models

Marcus Bleicher, Santiago de Compostela 2006

Zhang, Topor Pop, Jeon, Gale, hep-ph/0202057

and why it doesn’t work

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

qMD calculation by S. Scherrer

Marcus Bleicher, Santiago de Compostela 2006

Multiplicity fluctuations

Pb+Pb (158 AGeV)

in the NA49 acceptance

(1.1<yCM<2.9)

Extraction of the multiplicity distribution for every NparNote: Calculation is narrower than the data

Marcus Bleicher, Santiago de Compostela 2006

Multiplicity fluctuations at SPS:The 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, w=1

Marcus Bleicher, Santiago de Compostela 2006

Multiplicity fluctuations at SPS:Not a problem?

There seems not to be a problem in string cluster approaches.

Marcus Bleicher, Santiago de Compostela 2006

Where is the problem?

Pb+Pb (158 AGeV)

in the NA49 acceptance

(1.1<yCM<2.9)

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

Marcus Bleicher, Santiago de Compostela 2006

Analysis of different windows

- the normalized variance :
- flat in the projectile hemisphere
- larger in the mirror acceptance
- even larger in 4p
- maximum around Np=40

Marcus Bleicher, Santiago de Compostela 2006

The number of participants

Calorimeter : measure of the energy

deposited by the projectile spectators

TPC’s : measure of the particles multiplicities

In the UrQMD, the number of participant spectators is determined with a rapidity cut on the nucleons

Marcus Bleicher, Santiago de Compostela 2006

Fluctutions in target region

- the fluctuation has a maximum
- around Np=25
- introduces an asymetry between
- projectile and target participants
- leads to an increase of the multiplicity
- fluctuation in the target hemisphere

Marcus Bleicher, Santiago de Compostela 2006

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

Marcus Bleicher, Santiago de Compostela 2006

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. Gorenstein:arXiv:hep-ph/0511058

Marcus Bleicher, Santiago de Compostela 2006

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

Marcus Bleicher, Santiago de Compostela 2006

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/T2=0.53 and cus+ cds=0, CBS~1consistent with a weakly interacting QGP

R.V. Gavai and S.Gupta Phys. Rev. D 67/65

A. Majumder, V. Koch, J. Randrup arXiv:nucl-th/0510037

Marcus Bleicher, Santiago de Compostela 2006

Baryon-Strangeness Correlations 2

- Limiting cases for CBS:
- Large mB: CBS3/2
- large acc. window: CBS0Explored with help of increasing rapidity window inAu+Au 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

Marcus Bleicher, Santiago de Compostela 2006

Baryon-Strangeness Correlations 3

Energy dependence of CBS

allows to study the onset of deconfinement transition

Note that the QGP result is for m=0

Here |ymax|<0.5

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

Haussler, Stoecker, Bleicher,hep-ph/0507189

Marcus Bleicher, Santiago de Compostela 2006

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 m=0

|ymax|<0.5, Ecm=200AGeV

- 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

Marcus Bleicher, Santiago de Compostela 2006

Summary

- The D puzzle is solved: hadronization destroys all initial state correlations
- Hadron-string models fail to reproduce the
- measured multiplicity fluctuationsmight 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.

Marcus Bleicher, Santiago de Compostela 2006

Thanks

- Diana Schumacher
- Hannah Petersen
- Stephane Haussler
- Diana Schumacher

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

Marcus Bleicher, Santiago de Compostela 2006

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