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Charged Particle Fluctuation in Heavy Ion Physics
ZHOU You , WU Kejun & LIU Feng
Institute Of Particle Physics (IOPP)HuaZhong Normal University (HZNU)
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outline• Motivation• Results and Discussion • Summary and Outlook
new measurements of higher order cumulantsSkewness ,KurtosisdynQQQD ,, ,, discuss the properties and the behaviors of
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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
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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
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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
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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
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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
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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)
centrality dependence
S. Mro´wczyn´ski, Phys. Rev. C 66, 024904 (2002)M. Gaz´dzicki et al. Z. Phys. C 54, 127(1992)
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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
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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.
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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
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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
centrality dependence
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
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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
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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>
centrality dependence
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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
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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
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beam energy dependence
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
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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)
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Thanks for your attention !
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backup
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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
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normalized variance fluctuation
(PHENIX)
4)()( Q
ch
DNQVQ
22)( QQQV
Normalized Variance
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 ModelAMPT: A Multiphase transport model