Anisotropic flow, Azimuthal Balance Function,Anisotropic flow, Azimuthal Balance Function,and Two-charged-particle Azimuthal Correlationsand Two-charged-particle Azimuthal Correlations

in RQMD and AMPTin RQMD and AMPT

We are very grateful to We are very grateful to Zhixu LiuZhixu Liu and and Jiaxin DuJiaxin Du for offering us the data for offering us the data samples of samples of RQMDRQMD and and AMPTAMPT..

1.1. IntroductionIntroduction

2. Behaviors of these three measurements 2. Behaviors of these three measurements

in RQMD and AMPTin RQMD and AMPT

3. Conclusions and Suggestions3. Conclusions and Suggestions

1.1. IntroductionIntroduction

2. Behaviors of these three measurements 2. Behaviors of these three measurements

in RQMD and AMPTin RQMD and AMPT

3. Conclusions and Suggestions3. Conclusions and Suggestions

IOPP, Central China Normal University, Wuhan, China

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1. Introduction1. Introduction

The observed large flow at RHIC has been argued as an The observed large flow at RHIC has been argued as an indicator of early thermal equilibrium. Its flavor dependence is indicator of early thermal equilibrium. Its flavor dependence is supposed to be highly relevant to interpretation of strongly supposed to be highly relevant to interpretation of strongly interacting QGP.interacting QGP.

The observed large flow at RHIC has been argued as an The observed large flow at RHIC has been argued as an indicator of early thermal equilibrium. Its flavor dependence is indicator of early thermal equilibrium. Its flavor dependence is supposed to be highly relevant to interpretation of strongly supposed to be highly relevant to interpretation of strongly interacting QGP.interacting QGP.

22

22

2 )(yx

yxt pp

pppv

► ► Anisotropic collective Anisotropic collective flow is caused by initial flow is caused by initial spatially-anisotropic participant zone and interactions spatially-anisotropic participant zone and interactions in non-central nucleus-nucleus collisions,in non-central nucleus-nucleus collisions,

J. Adams, et al, (STAR Coll.), Nucl. Phys. A 757, 102(2005);J. Adams, et al, (STAR Coll.), Nucl. Phys. A 757, 102(2005); K. Adcox, et al, (PHENIX Coll.), Nucl. Phys. A 757, 184(2005).K. Adcox, et al, (PHENIX Coll.), Nucl. Phys. A 757, 184(2005).Miklos Gyulassy, Larry McLerran, Nucl. Phys. A 750, 30-63(2005). Miklos Gyulassy, Larry McLerran, Nucl. Phys. A 750, 30-63(2005). B. M\"uller, Annu. Rev. Nucl. and Part. Phys.,1(2006).B. M\"uller, Annu. Rev. Nucl. and Part. Phys.,1(2006).

)(2cos)(2 Rv

ψψR R is azimuthal angle of reaction plane is azimuthal angle of reaction plane

defined on an event-by-event base.defined on an event-by-event base.

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1. Introduction (cont.)1. Introduction (cont.)

►►Azimuthal charge balance functionAzimuthal charge balance function

nnn

nnn

B)()()()(

21

)(

P. Bozek, Phys. Lett. B 609, 247(2005).P. Bozek, Phys. Lett. B 609, 247(2005).

☺☺Another independent constraint Another independent constraint on the temperature and the on the temperature and the amount of transverse flow at the amount of transverse flow at the freeze-out.freeze-out.☺☺It is expected from theIt is expected from the thermal thermal modelmodel that thethat the higher higher temperature temperature and theand the smallersmaller elliptic flow, theelliptic flow, the wider the wider the azimuthal balance functiazimuthal balance function.on.

It is interesting to see how azimuthal charge balance function It is interesting to see how azimuthal charge balance function behaves in the dynamical models RQMD and AMPT.behaves in the dynamical models RQMD and AMPT.

__ T T ff = 90 MeV, = 90 MeV, ββ=0.6=0.6

- - T T f f = 165 MeV = 165 MeV ββ=0.5=0.5

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1. Introduction (cont.)1. Introduction (cont.)

ab

ababn

nC

)()(

ab

ababn

nC

)()(

► ► Two-charge-particle azimuthal corr. Two-charge-particle azimuthal corr.

► ► Why we choose these three measurements ?Why we choose these three measurements ?

☻☻ They are all anisotropic trans. momentum dis. related. They are all anisotropic trans. momentum dis. related.

☻☻ The behaviors of these three measurements in RQMD and AMPT will help The behaviors of these three measurements in RQMD and AMPT will help us in understanding the underlying dynamics.us in understanding the underlying dynamics.

☻ ☻ Both two-charge-particle azimuthal corr. and azimuthal charge balance Both two-charge-particle azimuthal corr. and azimuthal charge balance func. are reaction plane irrelevant and therefore easily to measure.func. are reaction plane irrelevant and therefore easily to measure.

nnabab((δφδφ): is the number of pairs of charged a and b particles satisfying the ): is the number of pairs of charged a and b particles satisfying the

criteria that their relative angle equals criteria that their relative angle equals δφδφ..nnabab: : is the total number of the same kind of pairs for all possible separated angles.is the total number of the same kind of pairs for all possible separated angles.

L. Foa, Phys. Reports 22(1975).L. Foa, Phys. Reports 22(1975).

K. Adcox, et al., (PHENIX Coll.), PRL 89, 212301(2002)K. Adcox, et al., (PHENIX Coll.), PRL 89, 212301(2002)

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1. Introduction (cont.)1. Introduction (cont.)

► ► Models Models

A MC generator of A MC generator of RRelativistic elativistic QQuantum uantum MMolecular olecular DDynamics ( hadronynamics ( hadron

), ),

Without hadron rescattering, vWithout hadron rescattering, v2 2 = 0;= 0;

With hadron rescattering, vWith hadron rescattering, v2 2 > 0, but smaller than the data.> 0, but smaller than the data.H. Sorge, Phys. Rev. C52, 3291 (1995).H. Sorge, Phys. Rev. C52, 3291 (1995).See Feng Liu’s talk in the same session.See Feng Liu’s talk in the same session.

Zi-Wei Lin, Che Ming Ko, Bao-An Li, Bin ZhangZi-Wei Lin, Che Ming Ko, Bao-An Li, Bin Zhangand Subrata Pal, Phys. Rev. {\bf C72}, 064901 (2005).and Subrata Pal, Phys. Rev. {\bf C72}, 064901 (2005).

A MC generator of A MC generator of AA MMulti-ulti-PPhase hase TTransport Model (parton + hadron) ransport Model (parton + hadron)

Default AMPT, vDefault AMPT, v2 2 > 0,> 0, but still smaller than data;but still smaller than data;

AMPT with string melting, where parton transportation, AMPT with string melting, where parton transportation,

hadron rescattering and quark coalescence at hadronization are hadron rescattering and quark coalescence at hadronization are

implemented in the model. This model reproduces vimplemented in the model. This model reproduces v2 2 (p(ptt) data ) data

at RHIC.at RHIC.

RQMD (v2.4)RQMD (v2.4):RQMD (v2.4)RQMD (v2.4):

AMPTAMPT:AMPTAMPT:

Au-Au collisions at Au-Au collisions at √s √s NNNN=200GeV=200GeVAu-Au collisions at Au-Au collisions at √s √s NNNN=200GeV=200GeV

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2. Behaviors of three measurements in models2. Behaviors of three measurements in models

► ► vv22 of all, positive and negative charged particles of all, positive and negative charged particles

RQMD without rescattering:RQMD without rescattering:

no vno v2 2 at all.at all.

RQMD with rescattering:RQMD with rescattering:

same middle values same middle values

of vof vcc22 , v , v--

22, v, v++22..

AMPT with string melting:AMPT with string melting:

same big values of same big values of

vvcc22 , v , v--

22, v, v++22

RQMD without rescattering:RQMD without rescattering:

no vno v2 2 at all.at all.

RQMD with rescattering:RQMD with rescattering:

same middle values same middle values

of vof vcc22 , v , v--

22, v, v++22..

AMPT with string melting:AMPT with string melting:

same big values of same big values of

vvcc22 , v , v--

22, v, v++22

vv22 is the biggest for mid-central is the biggest for mid-central

coll. and is smaller for central coll. and is smaller for central and very peripheral collisions.and very peripheral collisions.

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Rescattering off: Rescattering off: ☺☺ No small angular corr. No small angular corr. ☺ ☺ LLarge angular corr. due toarge angular corr. due to momentum conservation.momentum conservation.

Rescattering off: Rescattering off: ☺☺ No small angular corr. No small angular corr. ☺ ☺ LLarge angular corr. due toarge angular corr. due to momentum conservation.momentum conservation.

Rescattering on: Rescattering on: ☺☺ Small angular corr. Small angular corr. appearappear! ! ☺☺ The diff. among them are The diff. among them are small but visible.small but visible.☺ ☺ LLarge angular corr. remains.arge angular corr. remains.

Rescattering on: Rescattering on: ☺☺ Small angular corr. Small angular corr. appearappear! ! ☺☺ The diff. among them are The diff. among them are small but visible.small but visible.☺ ☺ LLarge angular corr. remains.arge angular corr. remains.

► ► CCcccc, C , C ++++ , , CC–– and and CC+-+- in RQMD in RQMD

2. Behaviors of three measurements in models2. Behaviors of three measurements in models

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► ► Centrality dependence of CCentrality dependence of Ccccc, C , C ++++ , , CC---- , , CC+-+-, in RQMD, in RQMD

Rescattering on: Rescattering on: The small angular corr. are the strongest for theThe small angular corr. are the strongest for themid-central coll. , small for most central coll. and even smaller for the mmid-central coll. , small for most central coll. and even smaller for the most peripheral coll. This centrality dependence is the same as vost peripheral coll. This centrality dependence is the same as v22 . .

Rescattering on: Rescattering on: The small angular corr. are the strongest for theThe small angular corr. are the strongest for themid-central coll. , small for most central coll. and even smaller for the mmid-central coll. , small for most central coll. and even smaller for the most peripheral coll. This centrality dependence is the same as vost peripheral coll. This centrality dependence is the same as v22 . .

Rescattering off: Rescattering off: Momentum conservation leads to the observed largeMomentum conservation leads to the observed largeangular correlations, especially for the most peripheral collisions. angular correlations, especially for the most peripheral collisions.

Rescattering off: Rescattering off: Momentum conservation leads to the observed largeMomentum conservation leads to the observed largeangular correlations, especially for the most peripheral collisions. angular correlations, especially for the most peripheral collisions.

2. Behaviors of three measurements in models2. Behaviors of three measurements in models

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► ► Centrality dependence of CCentrality dependence of Ccccc, C , C ++++ , , CC---- , , CC+-+- in AMPT in AMPT

► ► CCcccc, C , C ++++ , , CC---- , , CC+-+- in AMPT in AMPT with string meltingwith string melting

Small angle corr. have the same centrality dependence as flow.Small angle corr. have the same centrality dependence as flow.Small angle corr. have the same centrality dependence as flow.Small angle corr. have the same centrality dependence as flow.

In AMPT, small angular corr. becomes stronger than large angular corr.In AMPT, small angular corr. becomes stronger than large angular corr.Difference among CDifference among Ccccc, C , C ++++ , C , C---- , and C , and C+- +- are very small. are very small.

In AMPT, small angular corr. becomes stronger than large angular corr.In AMPT, small angular corr. becomes stronger than large angular corr.Difference among CDifference among Ccccc, C , C ++++ , C , C---- , and C , and C+- +- are very small. are very small.

2. Behaviors of three measurements in models2. Behaviors of three measurements in models

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►► Two-charge-particle corr. from PHENIX Coll.Two-charge-particle corr. from PHENIX Coll.

K. Adcox, et al, Phys. Rev. Lett. 89, 212301(2002)K. Adcox, et al, Phys. Rev. Lett. 89, 212301(2002)

2. Behaviors of three measurements in models2. Behaviors of three measurements in models

Data show:Data show:●●A anisotropic corr.A anisotropic corr. pattern is symmetric pattern is symmetric about about ∆∆φφ●●This anisotropy This anisotropy increase with impact increase with impact parameter and pparameter and pt.t.

Models show:Models show:► ► The small angle corr. The small angle corr. is related to anisotropy is related to anisotropy of pof ptt distribution distribution

►► The same symmetry The same symmetry structure structure iin AMPTn AMPT with string melting.with string melting.►► The same centrality The same centrality dependency in both dependency in both RQMD and AMPTRQMD and AMPT

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2. 2. Behaviors of three measurements in modelsBehaviors of three measurements in models

RQMD wRQMD w

► ► Azimuthal charge balance function in RQMDAzimuthal charge balance function in RQMD

The more central coll., the narrower BF, The more central coll., the narrower BF, which are diff. from centrality which are diff. from centrality dependence of vdependence of v2 2 ..

The more central coll., the narrower BF, The more central coll., the narrower BF, which are diff. from centrality which are diff. from centrality dependence of vdependence of v2 2 ..

No centrality dependence.No centrality dependence.This means that the corr. causeThis means that the corr. caused by momentum cons. d by momentum cons. are cancelled in the measurement.are cancelled in the measurement.

No centrality dependence.No centrality dependence.This means that the corr. causeThis means that the corr. caused by momentum cons. d by momentum cons. are cancelled in the measurement.are cancelled in the measurement.

RQMD w/oRQMD w/o

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2. 2. Behaviors of three measurements in modelsBehaviors of three measurements in models

► ► Azimuthal charge balance function in AMPAzimuthal charge balance function in AMPTT

In more central coll., the BF is narrower In more central coll., the BF is narrower In more periph. coll., the BF is wider.In more periph. coll., the BF is wider.

This is different from the eThis is different from the expectations from the therxpectations from the thermal model, where the smamal model, where the smaller elliptic flow, the wider ller elliptic flow, the wider azimuthal balance functioazimuthal balance function.n.

This is different from the eThis is different from the expectations from the therxpectations from the thermal model, where the smamal model, where the smaller elliptic flow, the wider ller elliptic flow, the wider azimuthal balance functioazimuthal balance function.n.

__ T T ff = 90 MeV, = 90 MeV, ββ=0.6=0.6

- - T T f f = 165 MeV = 165 MeV ββ=0.5=0.5

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3. Conclusions and suggestions3. Conclusions and suggestions

The behaviors of anisotropic flow, azimuthal chargeThe behaviors of anisotropic flow, azimuthal chargebalance function, and two-charge-particle azimuthal corr.balance function, and two-charge-particle azimuthal corr.in RQMD and AMPT are compared.in RQMD and AMPT are compared.

●● The large angular corr. are due to the constraint of The large angular corr. are due to the constraint of momentum conservation.momentum conservation.

●● The small angular corr. mainly come from anisotropic The small angular corr. mainly come from anisotropic transverse momentum distribution caused by hadron transverse momentum distribution caused by hadron level rescattering and/or parton level transportation.level rescattering and/or parton level transportation.

●● The centrality dependence of the small angular corr. The centrality dependence of the small angular corr. is the same as the centrality dependence of vis the same as the centrality dependence of v22

in both AMPT and RQMD.in both AMPT and RQMD.

●● To measure the two-charge-particle azimuthal corr.To measure the two-charge-particle azimuthal corr. at STAR detector, where TPC covers the whole at STAR detector, where TPC covers the whole azimuthal angle.azimuthal angle.

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3. Conclusions and suggestions3. Conclusions and suggestions

● From the behavior of two-charge-particle azimuthal corr., we see that azimuthal charge balance function (ACBF) well cancel the contributions caused by the constraint of momentum conservation.

● ACBF changes monotonically with centrality in both RQMD and AMPT models. This is different from the centrality dependence of v2 and what expected from thermal model.

● It is interesting to see how the B( ∆φ) behave in current heavy ion collisions.

● These three measurements are all sensitive to the anisotropic transverse momentum distributions.

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AppendixAppendix

AMPT defaultAMPT default