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Comparative study for non-statistical fluctuation of net- proton, baryon, and charge

multiplicitiesDai-mei Zhou (IOPP/CCNU)

2014 CBCOS Workshop for Phenomenological Research on Heavy-Ion Collisions

May 9 - May 14

(2) D. M. Zhou, Z. Z. Luo, Y. Cheng, A. Limphirat, Y. L. Yan, Y. P. Yan, X. Cai and B. H. Sa, J. Phys. G: Nucl. Part. Phys. 41 (2014) 065103

(1) D. M. Zhou, A. Limphirat, Y. L.Yan, Y. Cheng, Y. P. Yan, X. Cai, Laszlo P. Csernai, and B. H. Sa, PHYSICAL REVIEW C 85, 064916 (2012)

Based on:

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Outline

Introduction

Non-statistical moments of conserved quantities

Results for moments and the products of conserved quantities

Summary

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Introduction1

Attempts were then made to locate the QCD critical point (CP), where the first order phase transition gives over to the ‘crossover’ in the QCD phase diagram

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Skewness:

In a static and infinite medium, various moments of conserved quantities are related to the correlation length

M. Asakawa, U. Heinz, B. Muller,PRL85(2000) 2072

Kurtosis:

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The products of higher moments related to the ratio of conserved quantity number susceptibilities

)2()3( /~ S

)2()4(2 /~ k

Conserved quantity event distribution becomes non-Gaussian and the susceptibility diverges when QCP is approached. This causes products to change significantly

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M. Asakawa et al., PRL103 (2009)262301M. A. Stephanov,PRL102(2009)032301

A crossing of the Phase boundary may results in a change of sign of skewness of net-proton distribution as a function of the energy density.

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M. A. Stephanov, PRL 107 (2011) 052301

The sign of the kurtosis of net- proton distribution could be negative as the critical point is approached from the crossover side of the QCD phase transition.

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net-proton, net-baryon,and net-charge excitation functions in Pb+Pb collisions behave rather differently: The net-proton and net-charge κσ2 are slightly negative but the net-baryon κσ2 keeps largenegative values

Nahrgang M, Schuster T, Stock R, Mitrovski M and Bleicher M 2012 Eur. Phys. J. C 72 2143 (UrQMD)

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as a function of the rapidity window size was also different:both the net-proton and net-charge are differently fluctuated around zero, but the net-baryon reaches a large negative value at the large window

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The opinion in “Kitazawa M and Asakawa M 2012 Phys. Rev. C 86 024904” is quite opposite:

They analytically derived a relation between the baryonnumber cumulant and the proton number cumulant with the assumptions that the conserved observable number distribution is a binomial function and that the strange baryon is considered approximately.

Thus the net-baryon and net-proton cumulants have a similar behavior.

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:)(xP Distribution of conserved quantity

dxxPxxxxM nnn )()()()(

Moments about mean

dxxPxx nn )(

Moments about zero

2 Non-statistical moments of conserved quantities

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Key moments:

A. Variance )2(2 MB. Skewness

2/3)2()3(33 )/ (/)( MMxxS C. Kurtosis

3-)/ (3/)( 2)2()4(44 MMxx D. Products )2()3( / MMS

)2()2()4(2 3-/ MMM

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The phase transition and the approach of the CP is a matter of dynamics

eliminate the finite size and limited statistics effectsTo pronounce the effect of dynamic fluctuation, one

should study non-statistical moment excitation functions :

)()()( nM

nR

nD MMM

)(nRMinstead of studying only, where

)(nRM)(n

MM is calculated from mixed events

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Real events: measured or generated events, with dynamical conservations such as momentum conservation etc.Mixed events: constructed randomly from real events ,by keeping the real event multiplicity. In mixed events dynamical conservations and correlations are gone, but <x> is not changed.

The PACIAE model is used to generate the events

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3 Results

Dai-mei Zhou, et al., PRC85 (2012) 064916 STAR, X.F. Luo, arXiv:1106.2926

16Dai-mei Zhou, et al., PRC85 (2012) 064916; STAR PRL105, (2010) 022302

17Dai-mei Zhou, et al., PRC85 (2012) 064916 STAR PRL105, (2010) 022302

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At higher beam energies the skewness is negative, indicating more dominance of the hadronic side of the phase transition. The kurtosis becomes significantly negative, although small at higher beam energies, indicating that the freeze-out is indeed in the phase transition domain.

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The effect of finite windows dramatically influences the

cnmulant of conserved observables.

Net-charge cumulant may be more advantageous for the investigation of the CP singularity

A. Bzdak and V. Koch, Phys. ReV. C 86, 044904 (2012)arxiV: 1206.4286v1 [nucl-th]

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Dai-Mei Zhou, Zeng-Zeng Luo, Yun cheng, Ayut Limphirat, Yu-Liang Yan, Yu-Peng Yan, Xu Cai and Ben-hao Sa, J. Phys. G: Nucl. Part. Phys. 41 (2014) 065103

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S 2Xiaofeng Luo for STAR Collaboration, arxiV: 1210.5573 [nucl-ex]

J. Phys. G: Nucl. Part. Phys. 41 (2014) 065103

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STAR Collaboration,2013 Acta Phys. Pol. Suppl. 6 437

The net-proton and the net-charge theoretical real excitation function of Sσ and in window I are comparable with the corresponding STAR data

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The net-proton, net-baryon, and net-charge real event higher moment excitation function of M and σ appear to have a similar dependence on the window size. But the dependence of S, κ, Sσ, and on the window size is rather complicated

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The dependence of the non-statistical Skewness and on the collisions energy become stronger with increasing the window size.

S

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Sudden drop to a negative value (or a turning point) may indicatesome kind of dynamical changes and have to be studied further

the net-baryon S and Sσ calculated in window III as well as κ in window I and II vary dramatically at the same √sNN

27One can not see any dramatic change of the net-charge non-statistical moments

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4 Summary

(1)We have calculated the real and non-statistical excitation functions of higher moment of the net-proton, net-baryon and net-charge number event distributions

(2) PACIAE model is used to generate real events and the mixed events are randomly generated according to the real events.

(3) The behavior of higher moments excitations function, both real and non-statistical strongly depend on the window size

(4) non-statistical fluctuation is stronger energy and window dependent than the statistical one

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4 Summary

(5)The real and of the net-proton and net-charge excitations functions are consistent with the corresponding STAR data

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(6) A sudden drop to negative value (or a turning point) may indicate some change in the dynamics.

Thanks for your attention！