Charged Particle Fluctuation in Heavy Ion Physics
ZHOU You , WU Kejun & LIU Feng
Institute Of Particle Physics (IOPP)
HuaZhong Normal University (HZNU)
QNP09, Sept. 21~26 Beijing
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outline
• Motivation
• Results and Discussion
discuss the properties and the behaviors of
DQ ,  Q , Q ,  ,dyn
new measurements of higher order cumulants Skewness ,Kurtosis
• Summary and Outlook
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motivation
QCD Phase Diagram
RHIC beam energy scan program :
 Locate the QCD critical point.
Figure 1
 Draw the QCD phase boundary.
CP
STAR Beam User Request
★ Mapping the QCD phase diagram
★ Searching the Critical Point
Key measurements:
(1) PID hadron spectra, ratios, v2 …
(2) Fluctuations:
- Kurtosis
- K/
- <pT>, charged particle …
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motivation
Fluctuations of Conserved Quantities
i. Electric Charge
ii. Baryon Number
iii. Strangeness
iv. ...
Phys.Rev. Lett. 85, 2076 (2000)
Phys.Rev. Lett. 89, 082301 (2002)
Phys. Rev. C 66, 024904 (2002)
Phys. Rev. C 68, 044905 (2003)
Phys. Rev. C 68, 034902 (2003)
Phys. Rev. C 71, 051901(R) (2005)
Phys. Rev. C 79, 024904 (2009)
...
The event-by-event fluctuations of conserved charges, like electric charge,
baryon number and strangeness, are generally considered to be sensitive
indicators for the existence of a critical point .
If at non-vanishing chemical potential a critical point exists in the QCD
phase diagram, this will be signaled by divergent fluctuations.
Charged particle fluctuations should also enable a direct measurement of
the degree of thermalization reached in heavy ion collisions.
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analysis
• Monte Carlo data we used: ☞ all for Au+Au collision
RQMD v2.4: (Relativistic Quantum Molecular Dynamics)
Relativistic Quantum Molecular Dynamics (RQMD) is a semiclassical microscopic
model which combines classical propagation with stochastic interactions.
7.7 GeV
9.2 GeV
12.3GeV
17.3GeV
20 GeV
27 GeV
~1M
~4M
~1M
~1M
~3M
~1M
Events
Events
Events
Events
Events
Events
AMPT v2.11:
(A Multi-Phase Transport)
AMPT is a Monte Carlo transport model for heavy ion collisions at
relativistic energies. It uses the Heavy Ion Jet Interaction Generator
(HIJING) for generating the initial conditions, the Zhang's Parton Cascade
(ZPC) for modeling the partonic scatterings, and A Relativistic Transport
(ART) model for treating hadronic scatterings.
9.2 GeV(3mb)
Default
~2M Events
String Melting ~8M Events
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charged particle ratio fluctuation

D-measure
DQ  4
Q 2
N ch
Q is net charge
Nch is the total number of charged particles
Predictions
QGP phase
D ~1
Experimental Value
Hadron phase
D~4
Phys. Rev. Lett. 85, 2076 (2000)
D  3.2  0.1
(STAR) Phys. Rev. C 68, 044905 (2003)
D~3
(PHENIX) Phys. Rev. Lett. 89 082301(2002)
(central Au+Au collisions at
S NN  130GeV )
D-measure in a quark gluon plasma is expected to be significantly smaller (by a factor 3–
4) than in hadronic gas.
The experimental values from STAR and PHENIX equal to about 3, which are much larger
than expected D value in QGP and closed to the predicted D value in Hadron phase.
But it is not possible to draw a firm conclusion concerning the existence or
nonexistence of a deconfined phase during the collisions from these results since,
incomplete thermalization could lead to larger fluctuations than expected for a QGP.
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charged particle ratio fluctuation

D-measure
pT cut
Figure 3
|Y|<0.5
centrality dependence
Figure 2
pT cut doesn’t take effect
Y cut
AMPT-StringMelting
3.072 ± 0.006
AMPT-Default
3.772 ± 0.009
RQMD
2.977 ± 0.001
Figure 4
DQ quantity depend on the acceptance
large acceptance leads to small DQ
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Φ measure

Φ measure
M. Gaz´dzicki et al. Z. Phys. C 54, 127(1992)
S. Mro´wczyn´ski, Phys. Rev. C 66, 024904 (2002)
centrality dependence
Figure 5
Z Q
Q
N ch
N ch
z2 
4 N N
N ch
2
Φ is free of the effect of charge conservation
In "background" model Φ measure is ‘blind’ to
the impact parameter variation as long as the
‘physics’ does not change with the collision
centrality.
Phys. Rev. C 66, 024904 (2002)
Φ is insensitive to the collision centrality and
sensitive to the dynamics.
Phys. Rev. C 66, 024904 (2002)
Results from different Monte
Carlo models proved that Φ
is weakly depend on the
collision centrality.
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Φ measure
pT cut
Figure 6
Y cut
Φ measure weakly depends on pT
Figure 7
Φ measure depends on the rapidity
Φ measure depends on the acceptance
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Γ measure

 measure
M. Gaz´dzicki et al. Z. Phys. C 54, 127(1992)
S. Mro´wczyn´ski, Phys. Rev. C 66, 024904 (2002)
Figure 9
pT cut
 accommodates for situation with nonsymmetric charge distribution and varying
global multiplicity. It is insensitive to the
distribution of the independent particle
sources.
It measures both the dynamical and
statistical fluctuation.
Y cut
Figure 10
Figure 8
 also depend on the acceptance
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dynamical charge fluctuation

pT cut
Dynamical Charge Fluctuation
S. Mro´wczyn´ski, Phys. Rev. C 66, 024904 (2002)
Figure 11
J. Adams et al.(STAR Collaboration), Phys. Rev. C 68, 044905 (2003)
B.I.Abelev et al.(STAR Collaboration),Phys. Rev. C 79, 024906 (2009)
Y cut
Figure 12
2
 N
 1
N 
1 
 dyn        

N 
N  
 N
 N
V+-,dyn is a hopeful observable, it almost
doesn't depend on the acceptance
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dynamical charge fluctuation
centrality dependence
beam energy dependence
Figure 14
Figure 13
Figure 15
The observed monotonic reduction of the
magnitude of ν+−,dyn arises from the
progressive dilution of the charge
conservation effect when the number of
charged particle multiplicity is increased.
We observed that the dynamical
charge fluctuations are nonvanishing
at all energies and exhibit a modest
dependence on beam energy
QNP09, Sept. 21~26 Beijing
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higher order cumulants fluctuation
M. A. Stephanov, PRL 102, 032301 (2009)
"non-Gaussian moments (cumulants) of fluctuations of experimental observable
are very sensitive to the proximity of the critical point, as measured by the
magnitude of the correlation length "
at the Critical Point
2nd Order Cumulant: (Q) 2 ~  2
3rd Order Cumulant:
Q 3
~  4.5
4th Order Cumulant: Q 4  3 Q 2
2
~7
 is Correlation length
a measure of the range over fluctuations in one region of space are correlated with those in another
• Sensitive to long range correlations
• Show large non-monotonic behaviour as a function of T
higher order cumulant is more sensitive than 2nd order cumulant to study the CP
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higher order cumulants fluctuation
centrality dependence
standard definitions
RQMD v2.4
☞ <N >
Q
☞ C2 
Q 2
☞ Skewness 
Q 3
Figure 17
3
a measure of the symmetry
of a distribution
C4
K

Q
2
☞
C2
Q 4

3
4

a measure of the peakedness
of the distribution
from peripheral to central collisions:
• Mean values <NB>, C2 increase smoothly
• Skewness , Kurtosis : decreasing
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transverse momentum dependence
RQMD v2.4
Figure 20
Figure 23
☞ pT window
① 0 < pT < 0.5
② 0 < pT < 1.0
③ 0 < pT < 1.5
skewness and kurtosis almost don't dependent on acceptance
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rapidity dependence
RQMD v2.4
Figure 22
Figure 23
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☞ rapidity window
① |Y| < 0.5
② |Y| < 1.0
③ |Y| < 1.5
different rapidity windows don’t affect Skewness and Kurtosis
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beam energy dependence
RQMD v2.4
Figure 24
Figure 25
★
We studied the beam erergy dependence of skewness and kurtosis in order to find the
diverage which is indicated the existence of critical point.
★
Only smooth trend of skewness and kurtosis can be found from RQMD model. This will
provides baseline predictions to the higher order cumulants of net-charge distribution.
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summary and outlook
• We have presented a study of various observable of charge particle
fluctuation. DQ、ΦQ、ΓQ depend on the experimental acceptance.
—V+-,dyn is a hopeful observable, it has a weak dependence on the acceptance.
• Also we studied the higher order cumulants, Skewness, Kurtosis(KQ)
of net-charge distribution.
—Skewness and Kurtosis(KQ) almost don't depend on the acceptance, both of them
are promising observables in experiments.
•
This work presents baseline predictions of charged particle fluctuation and
higher order cumulants of net-charge distribution, it will help us to
understand the expectations from experimental results for the forthcoming
RHIC Beam Energy Scan Program.
•
Next to do:
1 Centrality dependence of Net-Charge fluctuation at high Energy
2 Hadronlization and rescattering effect on the Net-Charge fluctuation (using
modified AMPT model)
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Thanks for your attention !
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backup
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higher order cumulants
M.Cheng et al. arXiv: 0811.1006 v3 [hep-lat]
M.Cheng et al.Phys. Rev. D 79, 074505 (2009)
Figure 17
Figure 18
The quadratic(2nd order) and quartic(4th order) show a
large fluctuation around 200MeV, this fluctuation are
predicted as a signal of the existence of a critical point
in all cases the quadratic(2nd order) fluctuations rise
rapidly in the transition region and approach to SB limit
where the quartic(4th order) fluctuations show a maximum.
the value  4 /  2 for net-charge is between 1 to 2 when
T< 200MeV which consist with HRG. It is closed to SB
limit when T >200MeV
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normalized variance fluctuation

Normalized Variance
V (Q) DQ
 (Q) 

N ch
4
V (Q)  Q 2  Q
(PHENIX)
2
Figure 6
Figure 7
the same trend compared to D certainly
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beam energy dependence
large fluctuations for C4 and R4,2
turn to monotonic behaviour
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Two versions of AMPT Model
AMPT: A Multiphase transport model
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