Scaling properties of multiplicity fluctuations in heavy-ion collisions simulated by AMPT model

Yi-Long Xie

China University of Geosciences, Wuhan

（ Xie Yi-Long, Chen Gang ， et al ， Nucl. Phys. A 920 (2013) 33–44 ）

Content

• Nonlinear Dynamics

• AMPT model

• Results of NFM Analysis

• Discussion of FM’s Scaling

• Summary

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1. Nonlinear Dynamics

Big local fluctuation implied dynamical factors.

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Bialas ： describe the fluctuation with NFM as follow:

M

mq

m

mmmq

n

qnnn

MMF

1

111

1. Nonlinear Dynamics

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Self-similar Fractal Self-affine Fractal

Criterion for existence of fractal qMMFq

1. Nonlinear Dynamics

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Characterize of Self-similar Fractal:

Characterize of Self-affine Fractal

Isotropic partition the phase-space

Anisotropic partition the phase-space with calculated Hurst exponent

Fitting the 1-d NFM with saturation exponents

1 ln

1 lnj i

iji j

H

( ) iq i i i iF M A BM

Calculate the Hurst exponent with saturation exponent

Wu Y F, Liu L S. Phys Rev Lett, 1993, 70(21):3197-3200

collision at region

1. Nonlinear Dynamics

Self-similar Fractal

0Z

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Self-affine Fractal

Hadron collision

Agababyan N M, Atayan M R, Charlet M, et al. Phys Lett B, 1996, 382(3):305-311

Abreu P, Adam W, Adye T, et al. Nucl Phys B, 1992, 386(2):471-492

ee

The final state system in collisions at region is self-affine fractal

1. Nonlinear Dynamics

0Zee

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The final state system in hadron collisions is self-affine fractal

Does fractal exist in heavy ion collisions?

Which kind of fractal?

Experiments has shown that:

So:

A Pictorial View of Micro-Bangs at RHIC:

1. Initial Condition 2. Partonic Cascade 3. Hadronization 4. Hadronic Rescattering

2 AMPT model

2 AMPT model

(a) AMPT v1.11 (Default) (b) AMPT v2.11 (String Melting)

3.1 Results of NFM Analysis

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ty p

Tab.1. Fitting parameters for 1-D NFM (q=2).

1. 1-D NFM tends to saturate

2. Saturation exponents:

3. Identical Hurst exponents:

Fig.1. 1-D NFM: (q=2).MF 2

3.2 Results of NFM Analysis

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Fig.2. The logarithm distribution of 2-D NFM, i.e.

Fitting formula ：

Show good Scaling Conclusion: Self-Similar Fractal

)92( lnln qMFq

3.3 Results of NFM Analysis

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1. Fitting Formula:

Same Conclusion: Scaling Feature and Self-similar Fractal

Fig.3. The logarithm distribution

of 3-D NFM:

Tab.2. Fitting parameter for 3-D NFM Tab.3. Effect Fluctuation Strength

2. Fluctuation in heavy ion collision is larger than those in hadron collisions and collisions.

Effect Fluctuation Strength:

QGP

ee

MFq lnln

4. Discussion of FM’s Scaling

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Scaling property is checked again.

Fig.4. The distribution of 3-D NFM: Fig.5. Parameter are obtained when fitting the

relation：

1. .2.

2lnln FFq qvsq . )( 2q

2lnln FcFq )1( qq

1.3040.131.86ν tpy

Fitting Formula:

Fitting Formula:

DD 32

Not phase transition in AMPT.

RudophC. Hwa, M. T. Nazirov, Phys. Rev. Lett. 69 (1992) 1741.

4. Discussion of FM’s Scaling

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Fig.6. The loglog distribution of 2-D NFM in the plane at various intervals

qF ),( y tp

1. Expectation:

2. Indeed, Fluctuation with tp

）（）（ 5.4,5.30.1,5.0 tt pp

3. Due to the limited events, quantitative analysis can’t be made.

4. Discussion of FM’s Scaling

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Fig.7. The distribution of 2-D NFM as a

function of , with partition number M=1

),(ln yfq

tp

),( yfq tp rapidly with .

Fluctuation in high is actually much larger than that in low .tp

tp

2D FM on plane(M=1):

qm

mmmq

n

qnnnyf

)1()1(),(

),( y

5 Summary

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1. With the data of Au-Au collision events at 200Gev generated by AMPT model, the 1-D NFM is obtained. The obtained Hurst exponent approximately equal to 1 within the error range.

2. Partitioning the phase-space according to Hurst exponent, then calculate the 2-D and 3-D NFMs. They both show good scaling, which means the final state system is self-similar fractal.

3. According to the calculated effect fluctuation strengths, the fluctuation in heavy ion collisions is found to be much smaller than those in hadron-hadron collisions and electron-positron collisions, which may be the signal of QGP.

4. When checking the scaling property again, the parameter can be obtained. Our results is larger than v =1.304 derived in Ginzburg-Landau type of phase transition. AMPT does not include the phase transition.

5. Splitting the pt range into smaller intervals, the in high is expected to be larger than that in low . Due to the limited events, quantitative analysis can’t be made. But if considering the 2D FM on (M=1), we actually see the increasing of fluctuation with the increasing of pt.

13.086.1 tpy

tptp

),( y

Thank you !