HuaZhong Normal University IWND09, August 22~25, Shanghai 1

Event-by-Event Fluctuations of Net-Baryon D istribution 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 2

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 3

motivation

QCD Phase Diagram RHIC beam energy scan program :

Locate the QCD critical point.

Draw the QCD phase boundary.

STAR Beam User Request

Key measurements:(1) PID hadron spectra, ratios, v2 … (2) Fluctuations: - Net-p Kurtosis - K/ - <pT>, <N> … JY Chen for STAR -CPOD2009

★ Mapping the QCD phase diagram

★ Searching the Critical Point

Figure 1

CP

HuaZhong Normal University IWND09, August 22~25, Shanghai 4

is Correlation length22 ~)( N

4 2 2 7( ) 3 ( )N

motivation

2nd Order Cumulant:

4th Order Cumulant:

M. A. Stephanov, PRL 102, 032301 (2009)

at the Critical Point

"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 "

4th Order Cumulant is more sensitive than 2nd Order Cumulant to study the CP

baryon number fluctuation is a highlight in heavy ion physics and studying the event-by-event fluctuations of observable provide useful tools to research the critical point

arXiv: 0606047arXiv: 0805.0236arXiv: 0809.0685arXiv: 0903.2911Phys. Rev. D 79, 074505 (2009)nayak(STAR Collaboration)@QM2009

...

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

HuaZhong Normal University IWND09, August 22~25, Shanghai 5

Figure 2

motivationM.Cheng et al. arXiv: 0811.1006 v3 [hep-lat]M.Cheng et al.Phys. Rev. D 79, 074505 (2009)

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 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.

☞☞ 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.

24 /

This maximum is most pronounced for the baryon number fluctuations.

Figure 3

HuaZhong Normal University IWND09, August 22~25, Shanghai 6

3

3

( )NSkewness

2

42,4 C

CR

analysis2nd Order Cumulant:

2 2 2 22 ( )C N N N

4th Order Cumulant:4 2 2

4 ( ) 3 ( )C N N

is Standard deviation

4

4

( )3

NKurtosis

a measure of the symmetry of a distribution

a measure of the peakedness of the distribution

for a Gaussian distribution, the value of skewness and kurtosis is 0

• MC data we used:

RQMD v2.4: 9.2 GeV ~4M Events 12.3GeV ~1M Events 17.3GeV ~1M Events 20 GeV ~3M Events

UrQMD v2.3: 9.2 GeV ~16M Events

AMPT v2.11: 9.2 GeV(3mb) Default ~2M Events

String Melting ~8M Events

☞ ☞ all for Au+Au collision☞ ☞ all for Au+Au collision

☞☞

☞☞

☞☞

☞☞

☞☞

HuaZhong Normal University IWND09, August 22~25, Shanghai 7

centrality dependence for Net-Baryon

from peripheral to central collisions: • Mean values <NB>, C2 increase smoothly• Skewness and Kurtosis: decreasing • C4 and R4,2 decreases rapidly in central collision

Au+Au 9.2GeVNNS

RQMD v2.4

0< pT <1.0 (GeV/c) |Y|<0.5 Figure 4

HuaZhong Normal University IWND09, August 22~25, Shanghai 8

transverse momentum dependence

• The results of different pT do not take effect distinctly although the value are not the same.

pT distribution for net-baryon

Figure 9

Figure 10

Net-Baryon

HuaZhong Normal University IWND09, August 22~25, Shanghai 9

rapidity dependence

different rapidity also do not play an active role

rapidity distribution

Figure 13

Figure 12

☞ ☞ rapidity window ① |Y|<0.5 ② |Y|<1.0

☞ ☞ rapidity window ① |Y|<0.5 ② |Y|<1.0

Net-Baryon

HuaZhong Normal University IWND09, August 22~25, Shanghai 10

rapidity dependence

they all have similar trendsalthough a diverge happened in central collision for C4 、 R4,2

Figure 14

Figure 15

☞ ☞ rapidity region☞ ☞ rapidity region

0.5< |Y| <1.0

Net-Baryon

0< pT <1.0(GeV/c)

HuaZhong Normal University 11IWND09, August. 22~25, Shanghai

energy dependence of C4

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.

Figure 5

Figure 6

Net-Baryon

HuaZhong Normal University 12IWND09, August. 22~25, Shanghai

energy dependence of KB

the right panel shows at 9.2, 12.3, 17.3, 20 GeV, KB exhibit similar behaviour.

the left panel shows energy dependence of KB, in central collision, the trend are seen the same

Figure 7 Figure 8

Net-Baryon

HuaZhong Normal University 13IWND09, August. 22~25, Shanghai

MC model differenceUrQMD for Net-Baryon

other MC models are used to check our results

Figure 16

HuaZhong Normal University IWND09, August 22~25, Shanghai 14

MC model differenceAMPT for Net-Baryon

we can find the trend of UrQMD and AMPT are similar to those of RQMD

Figure 17

HuaZhong Normal University IWND09, August 22~25, Shanghai 15

• We have presented a study of mean value <NB>, variance C2, skewness, kurtosis(KB), C4 and R4,2 of event-by-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

Summary and Outlook

HuaZhong Normal University IWND09, August 22~25, Shanghai 16

Thanks for your attention

also thanks to the Organizer of IWND2009

HuaZhong Normal University IWND09, August 22~25, Shanghai 17

backup

HuaZhong Normal University IWND09, August 22~25, Shanghai 18

analysis

how does the different cut effect the results of all observable

transverse momentum dependence rapidity dependence

①

②

T

centrality dependenceTcentral > Tperipheral

energy dependenceThighEnergy > TlowEnergy

observable

observable T

Critical Point

LGT

HuaZhong Normal University IWND09, August 22~25, Shanghai 19

• The quadratic fluctuations of light and strange quark number versus temperature (upper figure) and the ratio of s and u quark fluctuations on lattices of size × 4 and ×6,respectively.

316 324

• The quadratic fluctuations of light and strange quark number versus temperature (upper figure) and the ratio of s and u quark fluctuations on lattices of size × 4 and ×6,respectively.316 324

HuaZhong Normal University IWND09, August 22~25, Shanghai 20

transverse momentum dependence

mean 、 C2 、 skewness 、 KB have the similar trendC4 and R4,2 seems different in four PT regions

0.0 < PT<0.50.5 < PT <1.01.0 < PT <1.51.5 < PT <2.0

Figure 11

☞ ☞ PT region☞ ☞ PT region

0.5<PT<1.0(GeV/c)

Net-Baryon

HuaZhong Normal University

The fluctuations of net-baryon number in a subsystem are of the order of the root of the average net-baryon number in this subsystem.

The fluctuations of net-baryon number in a subsystem are of the order of the root of the average net-baryon number in this subsystem.

arXiv:0903.2911v2 [hep-ph]arXiv:0903.2911v2 [hep-ph]