Charged Particle Fluctuation in Heavy Ion Physics

QNP09, Sept. 21~26 Beijing 1

Charged Particle Fluctuation in Heavy Ion Physics

ZHOU You , WU Kejun & LIU Feng

Institute Of Particle Physics (IOPP)HuaZhong Normal University (HZNU)


outline• Motivation• Results and Discussion • Summary and Outlook

new measurements of higher order cumulantsSkewness ,KurtosisdynQQQD ,, ,, discuss the properties and the behaviors of


motivationQCD 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: - Kurtosis - K/ - <pT>, charged particle …

★ Mapping the QCD phase diagram ★ Searching the Critical Point

Figure 1

CP


motivation

i. Electric Chargeii. Baryon Numberiii. Strangenessiv. ...

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.

Fluctuations of Conserved Quantities


analysis• Monte Carlo data we used: 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 ~1M Events 9.2 GeV ~4M Events 12.3GeV ~1M Events 17.3GeV ~1M Events 20 GeV ~3M Events 27 GeV ~1M Events

AMPT v2.11: (A Multi-Phase Transport) AMPT is a Monte Carlo transport model for heavy ion collisions at relativisti

c 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

☞ ☞ all for Au+Au collision


charged particle ratio fluctuation D-measure

(STAR) Phys. Rev. C 68, 044905 (2003)

(PHENIX) Phys. Rev. Lett. 89 082301(2002)

Experimental Value

(central Au+Au collisions at )

GeVSNN 130

1.02.3 D3~D

ch

Q N

QD

2

4

QGP phase Hadron phasePredictions

1~D 4~DPhys. Rev. Lett. 85, 2076 (2000)

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.

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.

Q is net charge Nch is the total number of charged particles


charged particle ratio fluctuation

AMPT-StringMelting 3.072 ± 0.006

AMPT-Default 3.772 ± 0.009

RQMD 2.977 ± 0.001 DQ quantity depend on the acceptance

Figure 2

Y cut Figure 4

pT cut Figure 3|Y|<0.5

D-measure

pT cut doesn’t take effect

large acceptance leads to small DQ

centrality dependence


Φ is free of the effect of charge conservation

Φ measure Φ measure

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)

chch

NNQ

QZ 224

chN

NNz

Results from different Monte Carlo models proved that Φ is weakly depend on the collision centrality.

Figure 5

Φ is insensitive to the collision centrality and sensitive to the dynamics. Phys. Rev. C 66, 024904 (2002)


S. Mro´wczyn´ski, Phys. Rev. C 66, 024904 (2002)M. Gaz´dzicki et al. Z. Phys. C 54, 127(1992)


Φ measure

pT cut Y cut

Φ measure depends on the acceptance

Figure 7Figure 6

Φ measure weakly depends on pT Φ measure depends on the rapidity


Γ measureS. Mro´wczyn´ski, Phys. Rev. C 66, 024904 (2002)

M. Gaz´dzicki et al. Z. Phys. C 54, 127(1992)

pT cut

Y cut Figure 10

Figure 9

Figure 8

also depend on the acceptance

measure

accommodates for situation with non-symmetric 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.


dynamical charge fluctuation

NNNN

NN

dyn11

2

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)

S. Mro´wczyn´ski, Phys. Rev. C 66, 024904 (2002)

Y cut

pT cut

Figure 12

Figure 11

V+-,dyn is a hopeful observable, it almost doesn't depend on the acceptance

Dynamical Charge Fluctuation


beam energy dependence

Figure 14

Figure 15

dynamical charge fluctuation

We observed that the dynamical charge fluctuations are nonvanishing at all energies and exhibit a modest dependence on beam energy


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.

Figure 13


a measure of the range over fluctuations in one region of space are correlated with those in another

22 ~)( Q

is Correlation length

higher order cumulants fluctuation

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 "

higher order cumulant is more sensitive than 2nd order cumulant to study the CP

• Sensitive to long range correlations • Show large non-monotonic behaviour as a function of T

7224 ~3 QQ

3rd Order Cumulant: 5.43 ~ Q


22

4

CCKQ

higher order cumulants fluctuation

from peripheral to central collisions: • Mean values <NB>, C2 increase smoothly• Skewness , Kurtosis : decreasing

22 QC

3

3

QSkewness

standard definitions

a measure of the symmetry of a distribution

a measure of the peakedness of the distribution

☞☞

☞☞

☞☞

RQMD v2.4

34

4

Q

Figure 17

☞☞ <NQ>



transverse momentum dependence

☞ ☞ pT window

① 0 < pT < 0.5 ② 0 < pT < 1.0 ③ 0 < pT < 1.5

RQMD v2.4

skewness and kurtosis almost don't dependent on acceptance

Figure 20

Figure 23


rapidity dependence

☞ ☞ rapidity window ① |Y| < 0.5 ② |Y| < 1.0 ③ |Y| < 1.5

Figure 21

RQMD v2.4

different rapidity windows don’t affect Skewness and Kurtosis

Figure 23

Figure 22



Figure 25Figure 24

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.★

RQMD v2.4


summary and outlook• We have presented a study of various observable of charge particle fl

uctuation. 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)


Thanks for your attention !


backup


Figure 17

higher order cumulantsM.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-charge is between 1 to 2 when T< 200MeV which consist with HRG. It is closed to SB limit when T >200MeV

24 /

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


normalized variance fluctuation

(PHENIX)

4)()( Q

ch

DNQVQ

22)( QQQV

Normalized Variance

Figure 6

Figure 7

the same trend compared to D certainly



large fluctuations for C4 and R4,2 turn to monotonic behaviour

QNP09, Sept. 21~26 Beijing

Two versions of AMPT ModelAMPT: A Multiphase transport model

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Charged Particle Fluctuation in Heavy Ion Physics