Dynamical fluctuations in relativistic collisions of nuclei

1
Dynamical fluctuations in relativistic collisions
of nuclei
Frankfurt Institute for Advanced Studies
Elena Bratkovskaya Heavy-Ion Reactions at
Ultrarelativistic Energies Trento, 27.06.06
2
Thanks
Volodymyr Konchakovski Mark Gorenstein Steph
ane Haussler Marcus Bleicher Horst
Stöcker
HSD UrQMD Collaboration
3
The phase diagram of QCD

• UrQMD initial energy density is higher than the
  boundary from LQCD
• Tri-critical point reached somewhere between 20
  and 30 A GeV
• -gt we are probing a new phase of matter already
  at AGS!
• FAIR is located in the right place!

4
Lattice QCD Critical Point
Fluctuations of the quark number density
(susceptibility) at mqgt0 Karsch et al.

• Lattice QCD predictions
• cq (quark number density fluctuations) will
  diverge at critical chiral point gt
• Experimental observation look for
• baryon number fluctuations
• charge number fluctuations

5
Fluctuations as experimental signatures of the
critical point
Event-by-event fluctuation and correlation
measurements provide information on
susceptibilities of matter rapid changes
reflect the order of the phase transition Goal
for experiment Locate the critical point using
correlation/fluctuation measurements
lt(X - ltXgt)2gt

• Observables (examples)
• multiplicity fluctuations
• baryon number fluctuations
• charge fluctuations
• particle ratio fluctuations (K/p, p/p)
• mean pT fluctuations
• 2 particle correlations
• ...

vs
Enhanced Fluctuations near Critical Point
6
Origin of fluctuations

• statistical fluctuations
• exist for all non-conserved quantities (e.g.
  baryon number or charge at mid-rapidity)

• dynamical fluctuations
• exist due to interactions between particles
• fluctuations of the initial energy deposited
  inelastically in the collision yield fluctuations
  of all thermodynamical parameters (total entropy,
  strangeness content, pressure and temperature)
• sensitive to the EoS of the matter

7
Multiplicity fluctuations

• The early stage energy and entropy fluctuations
  are not directly observable
• Systems entropy is related to the mean particle
  multiplicity

(averaging over events which have identical
initial conditions, i.e. the same amount of
energy is deposited for the particle production)

• Dynamical entropy fluctuations are related to
  the dynamical multiplicity fluctuations

However, the multiplicity N measured on
event-by-event basis varies not only due to
dynamical fluctuations, but predominantly due to
the statistical fluctuations at freeze-out

• The relative dynamical fluctuations can be
  expressed through the total relative the
  fluctuations - scaled variance w

w1 - Poissonian multiplicity distribution no
dynamical fluctuations
8
NA49 Multiplicity Fluctuations
Multiplicity fluctuation w of negatively,
positively and all charged particles as a
function of the number of projectile participants
Npproj
NA49 observed non-trivial system size
dependence of multiplicity fluctuations (similar
for transverse momentum fluctuations!) HIJING
gives basically poissonian fluctuations What is
the nature of the maximum at Npartproj 35 ?!
NA49 PRC70 (2004) 034902
9
NA49 acceptance
Note NA49 is NOT a 4p detector! 1) f-pT
acceptance
What is the influence of acceptance cuts on
multiplicity fluctuations ? 2) Fluctuations are
measured for fixed projectile participants NPproj

NPprojA-NSproj
10
Study of fluctuations within transport models
HSD Hadron-String-Dynamics transport
approach UrQMD Ultra-relativistic-Quantum-Molecu
lar-Dynamics

• Transport models allow to study
• statistical and dynamical fluctuations
• event-by-event analysis similar to the
  experiment
• the centrality dependence
• the energy dependence of fluctuations
• the influence of the experimental acceptance
• on the final results on fluctuations

11
Dense baryonic matter average quantities

• enormous energy and baryon densities are reached
  (e gt ecrit1 GeV/fm3)

• baryon density in central cell (AuAu, b0 fm)

12
Energy density fluctuations (UrQMD)
PbPb at 160AGeV
e (GeV/fm3)
Large fluctuations in space due to fluctuations
in collision number and mass production in NN
collisions!
X (fm)
y (fm)
Dz1fm
M. Bleicher et al, Nucl.Phys.A638391,1998
13
Multiplicity fluctuations in projectile and
target hemispheres

• HSD and UrQMD show strong multiplicity
  fluctuations of dynamical origin
• f-pT acceptance cuts strongly decrease
  fluctuations !

2) Fluctuations in target hemisphere are larger
than in projectile hemisphere 3) HSD and UrQMD
show strong multiplicity fluctuations in 4p
full acceptance, however, the observed (by
NA49) non-trivial system size dependence of
multiplicity fluctuations is not reproduced by
HSD and UrQMD
PRC 73 (2006) 034902
14
Fluctuations in the number of participants in HSD
UrQMD
NPprojA-NSproj projectile participant
NPtargA-NStarg target participant
15
Fluctuations in the number of participants in HSD
UrQMD
wPtarg is the scaled variance for the
fluctuations of the number of target participants
Nptarg
in each sample with Npprojconst the number of
target participants Nptarg fluctuates
considerably wptarg 3 at Npproj 25
16
Model of independent sources
Gazdzicki, Gorenstein, hep-ph/0511058
Number of independent sources is proportional to
number of participants
wi is the fluctuation from a single NN source
fluctuation in the number of nucleon
participants in AA
w- 1.5 w 1.1 wch 2.5
HSD NN (averaged over ppnnpn)

• ni is the particle number of i-th type (i,-,ch)
  per participant Np Npproj Nptarg

• wPtarg is the scaled variance
• for the fluctuations of the number
• of target participants Nptarg

17
Model of independent sources
for Npproj Nptarg wPtarg0
Fluctuations in AA collisions are dominated by
the fluctuations of the particle number in single
NN collisions
18
Multiplicity fluctuations as a probe of
transparency,mixing and reflection of initial
flows in HIC
Gazdzicki, Gorenstein, hep-ph/0511058

• Model of independent sources favors mixing (but
  not extreme!) scenario
• HSD UrQMD show smaller mixing as follows from
  NA49 data,
• i.e. too transparent

19
Baryon number fluctuations (HSD)
Baryon number is a conserved quantity the net
baryon number in the full phase space equals to
the total number of participants Np Npproj
Nptarg at fixed Npproj the Np number
fluctuates due to the fluctuations of Nptarg in
the full phase space
target hemisphere
4p
projectile hemisphere
wB t gt wB p
nucl-th/0606047
20
Baryon number fluctuations (HSD) at fixed y
Proton rapidity distribution for central (b0.5
fm) and semi-peripheral (b8.5 fm) collisions
target hemisphere
projectile hemisphere
target hemisphere
projectile hemisphere
Scaled variances of baryon number fluctuations wB
in different rapidity intervals
Note wB p 0 in projectile hemisphere 0 for T-
and R-models, if wB p gt0, there is a mixing
21
Net-electric charge fluctuations
sensitive to the EoS at the early stage of the
collision and to its changes in the
deconfinement phase transition region
Gazdzicki, Mrowczynski, Z. Phys. C 54 (1992) 127
net-charge fluctuations are much smaller in QGP
than in a hadron gas
Definition of electric charge fluctuations
X single-particles variable N number of
particles in 1 event lt...gt - averaging
single-particle distribution over
events
GCC global charge conservation
if particles are correlated by global charge
conservation
22
NA49 Net-electric charge fluctuations
The decay of resonances strongly modifies the
initial QGP fluctuations!
23
Net-electric charge fluctuations XQ
target hemisphere
Q fluctuations in full acceptance (at fixed
Npproj) are due to the fluctuations of Nptarg
in the full phase space
projectile hemisphere
4p
estimates for XQ using existing experimental
data from NA49 for w and ltNgt
nucl-th/0606047
24
Particle ratio fluctuations K/p, p/p (UrQMD)
NA49 Preliminary

• K/p fluctuations increase towards lower beam
  energy
• Significant enhancement of measured ratio over
  hadronic cascade model UrQMD
• p/p fluctuations are negative
• indicates a strong contribution from resonance
  decays

25
Baryon-Strangeness Correlations
Definition
Idea Strangeness and baryon number carriers 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

UrQMD Marcus Bleicher et al.
26
Baryon-Strangeness Correlations (UrQMD)
Energy dependence of CBS allows to study the
onset of deconfinement transition Note that the
QGP result is for m0 Here ymaxlt0.5
UrQMD

• Deviations from the HG are expected at top SPS
  energies due to QGP onset

Haussler, Stoecker, Bleicher, hep-ph/0507189
27
Balance function
The Balance function is defined as a correlation
in y of oppositely charged particles, minus the
correlation of same charged particles, normalized
to the total number of particles
where P1 is any rapidity interval in the
detector P2 is relative rapidity interval
The width of Balance function
BF could give us insight about the time of
hadronization
28
Width of the Balance function
taken from Panos Christakoglou (NA49)
29
Energy dependence of Balance function
Panos Christakoglou, nucl-ex/0510045

• Preliminary results from the energy scan show
• a plateau of the parameter W in the energy range
  30-80AGeV
• W rises towards RHIC (LHC?) energies

30
Conclusions

• The fluctuations in the number of target
  participants for fixed projectile participants
  - strongly influence the baryon number and charge
  multiplicity fluctuations
• The fluctuations of the baryon number and
  electric charge in different acceptance are
  important to measure
• The actual numbers depend crucially on the
  mixing-transparency effects
• Because of their too high transparency the HSD
  and UrQMD transport models cannot reproduce the
  NA49 results on multiplicity fluctuations
• Correlations may provide information on the early
  stage
• of the reaction

31
Outlook
? ? ?
Theory
Experiment
Will we find the critical point by measuring
fluctuations?
Very difficult!
32
Basic concept of HSD UrQMD

• HSD Hadron-String-Dynamics transport approach
• UrQMD Ultra-relativistic-Quantum-Molecular-Dyna
  mics
• for each particle species i (i N, R, Y, p, r,
  K, ) the phase-space density fi follows the
  transport equations
• with collision terms Icoll describing
• elastic and inelastic hadronic reactions
• baryon-baryon, meson-baryon, meson-meson
• formation and decay of baryonic and mesonic
  resonances
• string formation and decay
• Implementation of detailed balance on the level
  of 1lt-gt2
• and 2lt-gt2 reactions ( 2lt-gtn multi-meson
  fusion reactions in HSD)

33
Degrees of freedom in HSD UrQMD

• hadrons - baryons and mesons including excited
  states (resonances)
• strings excited color singlet states (qq - q)
  or (q qbar)
• Based on the LUND string model
• perturbative QCD via PYTHIA
• leading quarks (q, qbar) diquarks
• (q-q, qbar-qbar)
• NOT included in the transport models presented
  here
• no explicit parton-parton interactions (i.e.
  between quarks and gluons) outside strings!
• no explicit phase transition from hadronic to
  partonic degrees of freedom
• QCD EoS for partonic phase