Download Event-by-Event Fluctuations of Net-Baryon distribution and higher

Event-by-Event Fluctuations of Net-Baryon
Distribution and Higher Order Cumulants
ZHOU You ,
LIU Feng
Institute Of Particle Physics (IOPP)
HuaZhong Normal University
(HZNU)
HuaZhong Normal University
IWND09, August 22~25, Shanghai
1
outline
• Motivation
• Some definitions and MC data
• Results of centrality dependence,
transverse momentum dependence,
rapidity dependence,
& energy dependence,
of fluctuations of Net-Baryon distribution
and higher order cumulants
• Summary and Outlook
HuaZhong Normal University
IWND09, August 22~25, Shanghai
2
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
HuaZhong Normal University
Key measurements:
(1) PID hadron spectra, ratios, v2 …
(2) Fluctuations:
- Net-p Kurtosis
- K/
- <pT>, <N> … JY Chen for STAR -CPOD2009
IWND09, August 22~25, Shanghai
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motivation
baryon number fluctuation is a highlight in
heavy ion physics and studying the event-byevent fluctuations of observable provide
useful tools to research the critical point
arXiv: 0606047
arXiv: 0805.0236
arXiv: 0809.0685
arXiv: 0903.2911
Phys. Rev. D 79, 074505 (2009)
nayak(STAR Collaboration)@QM2009
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
2
2
2nd Order Cumulant:  (N ) ~ 
4th Order Cumulant:  ()4  3  ( N )2 2   7

is Correlation length
 is a measure of the range over which fluctuations in one region of space are correlated with those in another
• Sensitive to long range correlations
• Shows large non-monotonic behaviour as a function of T
4th Order Cumulant is more sensitive than 2nd Order Cumulant to study the CP
HuaZhong Normal University
IWND09, August 22~25, Shanghai
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motivation
M.Cheng et al. arXiv: 0811.1006 v3 [hep-lat]
M.Cheng et al.Phys. Rev. D 79, 074505 (2009)
Figure 2
Figure 3
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.
This maximum is most pronounced for the baryon number
fluctuations.
the value  4 /  2 for net-baryon is about 1.0 when T<
200MeV which consist with HRG. It is closed to SB limit
when T >200MeV
☞ The measurement of higher order cumulants of
net-baryon distribution and its variations will provide
the connection between experimental observable and
Lattice Gauge Theory calculations.
HuaZhong Normal University
IWND09, August 22~25, Shanghai
5
analysis
☞
C2  ( N ) 2  N 2    N  2   2

☞
☞
• MC data we used:
2nd Order Cumulant:
is Standard deviation
 ( N )3 
 ( N )4 

4
3
a measure of the peakedness of the distribution
for a Gaussian distribution, the
value of skewness and kurtosis is 0
☞
R4, 2
C4

C2
Events
Events
Events
Events
3
a measure of the symmetry of a distribution
☞ Kurtosis 
all for Au+Au collision
RQMD v2.4:
9.2 GeV ~4M
12.3GeV ~1M
17.3GeV ~1M
20 GeV ~3M
4th Order Cumulant:
C4  ( N ) 4  3  ( N ) 2  2
Skewness 
☞
HuaZhong Normal University
UrQMD v2.3:
9.2 GeV ~16M Events
AMPT v2.11:
9.2 GeV(3mb)
Default
~2M Events
String Melting ~8M Events
IWND09, August 22~25, Shanghai
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centrality dependence for Net-Baryon
Au+Au S NN  9.2GeV
RQMD v2.4
0< pT <1.0 (GeV/c)
|Y|<0.5
Figure 4
from peripheral to central collisions:
• Mean values <NB>, C2 increase smoothly
• Skewness and Kurtosis: decreasing
• C4 and R4,2 decreases rapidly in central collision
HuaZhong Normal University
IWND09, August 22~25, Shanghai
7
transverse momentum dependence
Net-Baryon
pT distribution for net-baryon
Figure 9
Figure 10
•
The results of different pT do not take effect distinctly although the value are
not the same.
HuaZhong Normal University
IWND09, August 22~25, Shanghai
8
rapidity dependence
Net-Baryon
rapidity distribution
Figure 12
Figure 13
☞ rapidity window
① |Y|<0.5
② |Y|<1.0
different rapidity also do not play an active role
HuaZhong Normal University
IWND09, August 22~25, Shanghai
9
rapidity dependence
☞ rapidity region
Net-Baryon
0< pT <1.0(GeV/c)
0.5< |Y| <1.0
Figure 15
Figure 14
they all have similar trends
although a diverge happened in central collision for C4、R4,2
HuaZhong Normal University
IWND09, August 22~25, Shanghai
10
energy dependence of C4
Net-Baryon
Figure 6
Figure 5
the right panel shows at 9.2, 12.3, 17.3, 20 GeV, C4 exhibit unlike
behaviour. But we can get non-monotonic behaviour at all time.
HuaZhong Normal University
IWND09, August. 22~25, Shanghai
11
energy dependence of KB
Net-Baryon
Figure 7
Figure 8
the left panel shows energy dependence of KB, in central collision, the trend
are seen the same
the right panel shows at 9.2, 12.3, 17.3, 20 GeV, KB exhibit similar behaviour.
HuaZhong Normal University
IWND09, August. 22~25, Shanghai
12
MC model difference
UrQMD for Net-Baryon
Figure 16
other MC models are used to check our results
HuaZhong Normal University
IWND09, August. 22~25, Shanghai
13
MC model difference
AMPT for Net-Baryon
Figure 17
we can find the trend of UrQMD and AMPT are similar to those of RQMD
HuaZhong Normal University
IWND09, August 22~25, Shanghai
14
Summary and Outlook
• We have presented a study of mean value <NB>,
variance C2, skewness, kurtosis(KB), C4 and R4,2 of eventby-event net-baryon distribution.
The trend of centrality dependence of different pT and Y window are similar
Calculations from UrQMD and AMPT model also support our conclusion
• This work present baseline predictions of Net-Baryon
distribution and higher order cumulants, it will help to
understand the expectations from experiment results for
the forthcoming RHIC Beam Energy Scan Program.
• Next to do:
1 Centrality
dependence Net-Baryon distribution at high Energy
2 Net-Charge Kurtosis
HuaZhong Normal University
IWND09, August 22~25, Shanghai
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Thanks for your attention
also thanks to the Organizer of IWND2009
HuaZhong Normal University
IWND09, August 22~25, Shanghai
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backup
HuaZhong Normal University
IWND09, August 22~25, Shanghai
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analysis
①
observable
LGT
T
Critical Point
centrality dependence
Tcentral > Tperipheral
observable
T
energy dependence
ThighEnergy > TlowEnergy
②
how does the different cut effect the results of all observable
transverse momentum dependence
HuaZhong Normal University
rapidity dependence
IWND09, August 22~25, Shanghai
18
• The quadratic fluctuations of light and strange
quark number versus temperature (upper figure)
and the ratio of s and •u quark
fluctuations on
T
3
3
24
lattices of size 16 × 4 and
×6,respectively.
h
e
q
22~25, Shanghai
HuaZhong Normal University IWND09, August
163 243
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transverse momentum dependence
Net-Baryon
☞ PT region
0.0 < PT<0.5
0.5 < PT <1.0
1.0 < PT <1.5
1.5 < PT <2.0
Figure 11
0.5<PT<1.0(GeV/c)
mean、C2、skewness、KB have the similar trend
C4 and R4,2 seems different in four PT regions
HuaZhong Normal University
IWND09, August 22~25, Shanghai
20
arXiv:0903.2911v2 [hep-ph]
The fluctuations of net-baryon
number in a subsystem are of the
order of the root of the average netbaryon number in this subsystem.
HuaZhong Normal University