LI Na, LI Zhiming, LIU Lianshou and WU YuanfangLI Na, LI Zhiming, LIU Lianshou and WU Yuanfang(for the STAR Collaboration)(for the STAR Collaboration)

Institute of Particle Physics (IOPP)Institute of Particle Physics (IOPP)Huazhong Normal universityHuazhong Normal university

WuhanWuhan

A Longitudinal Property of the Charge Balance Function and its Transverse Momentum Dependence in Au-Au Collisi

ons at GeV200NNs

2008.4.27 2008.4.27 南京南京 李治明李治明 22

Outline:Outline:

1.1. IntroductionIntroduction ●● what does BF measurewhat does BF measure ●● current status and current status and problemsproblems

● ● motivationsmotivations

2. Experiment and data sample2. Experiment and data sample

3. 3. Results and discussionsResults and discussions ● ● Dependence of BFDependence of BF on on size and position ofsize and position of ηη windowwindow ● Independence of BIndependence of Bss on size and position of η window on size and position of η window ● ● Transverse momentum dependence of BTransverse momentum dependence of Bss

4. Summary and conclusions4. Summary and conclusions

1.1. IntroductionIntroduction ●● what does BF measurewhat does BF measure ●● current status and current status and problemsproblems

● ● motivationsmotivations

2. Experiment and data sample2. Experiment and data sample

3. 3. Results and discussionsResults and discussions ● ● Dependence of BFDependence of BF on on size and position ofsize and position of ηη windowwindow ● Independence of BIndependence of Bss on size and position of η window on size and position of η window ● ● Transverse momentum dependence of BTransverse momentum dependence of Bss

4. Summary and conclusions4. Summary and conclusions

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1.Introduction: 1.Introduction: ☞ ☞ What does Balance Function What does Balance Function measuremeasure

})()()()(

{2

1)|(

n

ynyn

n

ynynYyB W

Definition :Definition :Definition :Definition :

1 2| |y y y Relative rapidity:

All the particles are within the rapidity window

counting the pairs that satisfy the criteria in the rapidity window

WY

WY( )n y

BF measures how BF measures how the conserved electric charges compensate in the conserved electric charges compensate in the phase spacethe phase space, i.e., how the surrounding electric charges are , i.e., how the surrounding electric charges are rearranged if the charge at any selected point changes.rearranged if the charge at any selected point changes.

It tells how the production of charged particles in the whole It tells how the production of charged particles in the whole phase space is constrained by phase space is constrained by global charge balanceglobal charge balance, thus , thus provides a direct access to collision dynamics.provides a direct access to collision dynamics.

BF measures how BF measures how the conserved electric charges compensate in the conserved electric charges compensate in the phase spacethe phase space, i.e., how the surrounding electric charges are , i.e., how the surrounding electric charges are rearranged if the charge at any selected point changes.rearranged if the charge at any selected point changes.

It tells how the production of charged particles in the whole It tells how the production of charged particles in the whole phase space is constrained by phase space is constrained by global charge balanceglobal charge balance, thus , thus provides a direct access to collision dynamics.provides a direct access to collision dynamics.

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1.Introduction:1.Introduction: ☞ Motivation: ☞ Motivation: Difficulty in Difficulty in heavy ionheavy ion

The narrowing of the width of BF with centrality The narrowing of the width of BF with centrality

in Au+Au collisions atin Au+Au collisions at√s√sNNNN=130GeV, and =130GeV, and

in lighter nuclei collisions at√sin lighter nuclei collisions at√sNNNN=17.2GeV, =17.2GeV,

and with multiplicity in and with multiplicity in ππ++pp and and KK++pp Collisions at√s = 22GeV Collisions at√s = 22GeV

Current statusCurrent status:

J. Adams et al., (STAR Coll.), PRL90, 172301(2003); C. Alt et al., (NA49 Coll.), PRC71, 034903(200J. Adams et al., (STAR Coll.), PRL90, 172301(2003); C. Alt et al., (NA49 Coll.), PRC71, 034903(2005);5);

M. R. Atayan et al., (NA22 Coll.), PLB, 034903(2006).M. R. Atayan et al., (NA22 Coll.), PLB, 034903(2006).ProblemProblem:: acceptances in ηor ySTAR: [-1.3, 1.3]NA49: [ 2.6, 5.0]NA22: whole y

IncomparableIncomparable results!

We want to measure B (B (δ δ ηη ||ηηww ) as a function of ) as a function of δδ ηη

but this function but this function depends on the observed windowdepends on the observed window ηηww !!

We want to measure B (B (δ δ ηη ||ηηww ) as a function of ) as a function of δδ ηη

but this function but this function depends on the observed windowdepends on the observed window ηηww !!

AimAim:: Study the dependence of BF on Study the dependence of BF on ηηww and try to findand try to find a measure independent of observed windowa measure independent of observed window.

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NA22 experiment resultsNA22 experiment results full 4full 4ππ acceptance acceptance 0.001GeV/c < 0.001GeV/c < ppTT < 10 GeV/c< 10 GeV/c

M.R. AtayanM.R. Atayan, et al., Phys. Lett. B 637 (2006) 39-42;, et al., Phys. Lett. B 637 (2006) 39-42;M.R. AtayanM.R. Atayan, et al., Phys. Lett. B 637 (2006) 39-42;, et al., Phys. Lett. B 637 (2006) 39-42;

Boost invariance of BF is Boost invariance of BF is valid over the whole valid over the whole

rapidity space.rapidity space.

Boost invariance of BF is Boost invariance of BF is valid over the whole valid over the whole

rapidity space.rapidity space.

ππ++ p p and and K K ++ p p at 22GeV at 22GeVππ++ p p and and K K ++ p p at 22GeV at 22GeV

( | ) ( | ) (1 )ww

yB y Y B y Y

BF in different finite rapidity BF in different finite rapidity windows can be obtained from BF in windows can be obtained from BF in whole phase space due to boost whole phase space due to boost invariance.invariance.

BF in different finite rapidity BF in different finite rapidity windows can be obtained from BF in windows can be obtained from BF in whole phase space due to boost whole phase space due to boost invariance.invariance.

( | )( )

(1 )

ws

w

BB

2008.4.27 2008.4.27 南京南京 李治明李治明 66

1.1. The longitudinal property of BF comes from the special longiThe longitudinal property of BF comes from the special longitudinal interaction of charged particles under the tudinal interaction of charged particles under the constraint constraint of global electric charge balanceof global electric charge balance..

2.2. The range of The range of ppT T of final state particles is supposed to be relateof final state particles is supposed to be relate

d to its emitted proper time.d to its emitted proper time.

1.Introduction:1.Introduction: ☞ Motivation: ☞ Motivation: why why ppTT dependence dependence

Hydrodynamic expansion:

gradient pressure acts

Gradient of density leads to non-zero

collective velocities

Yu M. S., et al., PRL 89 052301 Yu M. S., et al., PRL 89 052301 (2002) (2002) Yu M. S., et al., PRL 89 052301 Yu M. S., et al., PRL 89 052301 (2002) (2002) J. Adams et al., (STAR Coll.), NPA757, 102(2005)J. Adams et al., (STAR Coll.), NPA757, 102(2005)J. Adams et al., (STAR Coll.), NPA757, 102(2005)J. Adams et al., (STAR Coll.), NPA757, 102(2005)

3. Since a subset of particles can behave collectively only if they 3. Since a subset of particles can behave collectively only if they are produced at the same proper-time, therefore, examine thare produced at the same proper-time, therefore, examine the e ppT T dependence will provide direct experimental access on tdependence will provide direct experimental access on t

his subject.his subject.

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2.2. Experiment and data sample: STAR Experiment and data sample: STAR experimentexperiment

Relativistic Heavy Ion Collider (RHIC), Relativistic Heavy Ion Collider (RHIC), BNL, Upton, NY, USABNL, Upton, NY, USARelativistic Heavy Ion Collider (RHIC), Relativistic Heavy Ion Collider (RHIC), BNL, Upton, NY, USABNL, Upton, NY, USA

2008.4.27 2008.4.27 南京南京 李治明李治明 88

Au-Au collision at √sNN = 200 GeV on STAR of Run 4

STAR / TPC acceptance: η : [-1.3, 1.3]

φ : full

Event cuts: |Vertexx|<1, |Vertexy|<1, |Vertexz|<25, MinTrack≥5

Track cuts: 0.15 < pT < 2.0, DCA<2, Fitpts>15,

FitPts/FitMax>0.52

Number of events: 5.7 million minimum bias events are selected!

2.2. Experiment and data sample: data Experiment and data sample: data samplesample

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STAR Preliminary

STAR Preliminary

BF strongly depends on the size of BF strongly depends on the size of ηw and becomes wider with increasing size of ηw.

BF’s in five different positions with same size are equal to each other, i.e., BF is invariant under a longitudinal translation within (-1,1).

Bs for different widths and positions of ηw coincide with each other, indicating that Bs is independent of the size and place of observed window.

BF strongly depends on the size of BF strongly depends on the size of ηw and becomes wider with increasing size of ηw.

BF’s in five different positions with same size are equal to each other, i.e., BF is invariant under a longitudinal translation within (-1,1).

Bs for different widths and positions of ηw coincide with each other, indicating that Bs is independent of the size and place of observed window.

3. Results and discussions:3. Results and discussions: dependence of BF on the size and position of☞ dependence of BF on the size and position of☞ ηηww

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3. Results and discussions:3. Results and discussions: Longitudinal property of BF in different subsamples☞ Longitudinal property of BF in different subsamples☞

STAR Preliminary

STAR Preliminary

In the left two subsamples, the global net charge is out of balance, and the lIn the left two subsamples, the global net charge is out of balance, and the longitudinal charge correlation is uniformly changed.ongitudinal charge correlation is uniformly changed.

The farther the charge is out of balance, the more seriously the longitudinal property of BF is violated.

In the right subsample, the longitudinal property of BF keeps well since the global charge balance maintains in each event in this case. So, the global charge balance is a necessary condition for the observed longitudinal property of BF!

In the left two subsamples, the global net charge is out of balance, and the lIn the left two subsamples, the global net charge is out of balance, and the longitudinal charge correlation is uniformly changed.ongitudinal charge correlation is uniformly changed.

The farther the charge is out of balance, the more seriously the longitudinal property of BF is violated.

In the right subsample, the longitudinal property of BF keeps well since the global charge balance maintains in each event in this case. So, the global charge balance is a necessary condition for the observed longitudinal property of BF!

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3. Results and discussions:3. Results and discussions: Transverse momentum dependence of B☞ Transverse momentum dependence of B☞ ss

STAR Preliminary

STAR Preliminary

The points at a given relative psudorarapidity in a restrict The points at a given relative psudorarapidity in a restrict ppT T interval are clinterval are cl

ose to each other.ose to each other.

It shows that both the special property of longitudinal interaction of charged particles and the global charge conservation are kept in the subset of particles within a give ppTT range.

This is in consistent with the scenario that particles in same restricted ppTT range are produced at the same proper-time of expansion with well balanced electric charge.

The points at a given relative psudorarapidity in a restrict The points at a given relative psudorarapidity in a restrict ppT T interval are clinterval are cl

ose to each other.ose to each other.

It shows that both the special property of longitudinal interaction of charged particles and the global charge conservation are kept in the subset of particles within a give ppTT range.

This is in consistent with the scenario that particles in same restricted ppTT range are produced at the same proper-time of expansion with well balanced electric charge.

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The width of Bs becomes narrower with the increase of ppTT, which is consistent to the expected delayed hadronization of high ppTT particles in the thermal model [S. Jeon et al., PRC 65, 044902(2002)].

The width of Bs becomes narrower with the increase of ppTT, which is consistent to the expected delayed hadronization of high ppTT particles in the thermal model [S. Jeon et al., PRC 65, 044902(2002)].

QGP SignalQGP SignalThe balance function is expected to be narrower for a scenario with delayed hadronization ,and is therefore sensitive to the conjecture that a quark-gluon plasma may be produced. [S. A. Bass et al., PRL 85, 2689 (2000) ].

( | )

( | )s i w ii

s i wi

B

B

3. Results and discussions:3. Results and discussions: ☞ ☞ ppTT dependence of the width of Bdependence of the width of Bss

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4. Summary & conclusions:4. Summary & conclusions:

Within the pseudorepidity range (-1,1), the balance function is independWithin the pseudorepidity range (-1,1), the balance function is independent of the position of the pseudorapidity window with the same size.ent of the position of the pseudorapidity window with the same size.

The scaled BF BThe scaled BF Bss, i.e., B (δ, i.e., B (δηη ||ηηww ) measured in an observed window ) measured in an observed window ηηww ddivided by (1-δivided by (1-δηη ||ηηww ) is found to be independent of the choice of observe) is found to be independent of the choice of observed pseudorapidity window.d pseudorapidity window.

The longitudinal property of the balance function is further found to be The longitudinal property of the balance function is further found to be valid for the particles in same restricted transverse-momentum range, valid for the particles in same restricted transverse-momentum range, which is in consistent with the scenario that particles in same restricted which is in consistent with the scenario that particles in same restricted transverse-momentum range are produced simultaneously with well baltransverse-momentum range are produced simultaneously with well balanced electric charge, and provides for the first time an experimental suanced electric charge, and provides for the first time an experimental support for the successful study of the pport for the successful study of the ppTT dependence of elliptic flow. dependence of elliptic flow.

Moreover, the higher the Moreover, the higher the ppTT of the particles, the narrower the scaled bal of the particles, the narrower the scaled balance function, as expected from the thermal model.ance function, as expected from the thermal model.

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Appendix IAppendix I

● ● on the measure of charge balance functionon the measure of charge balance function

)(

),()|(

,

,

s

Q

s

QQ

s

QQ

y

yyyy

s

s

s

)|()|(),|( ,,

s

Q

s

Q

ssyyyyyQyq ss

Associated particle densityAssociated particle density::

the density of particles of charge Q at rapidity ythe density of particles of charge Q at rapidity y under the condition that under the condition that

a particle of charge Qa particle of charge Qss is detected at the rapidity y is detected at the rapidity ys.s.

Associated net charge densityAssociated net charge density::

the net charge density at rapidity ythe net charge density at rapidity y under the condition that there existsunder the condition that there exists

a particle of charge Qa particle of charge Qss at the rapidity y at the rapidity ys.s.

Associated charge density Associated charge density balancebalance::

A measure of the change of the associated net charge density, A measure of the change of the associated net charge density, when the when the

charge of the selected particle(s) is changed from negative to positive.charge of the selected particle(s) is changed from negative to positive.D. Drijard, et al., (ACCDHW Coll.) , Nucl. Phys. B166(1980)233-242;

D. Drijard, et al., (CCHK Coll.) , Nucl. Phys. B155(1979)269.

)]|()|([)]|()|([ ssss yyyyyyyy

),|(),|()|( sss yyqyyqyyq

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[S. Jeon and S. Pratt, PRC 65, 044902 (2002) ]

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2. Results and discussions:2. Results and discussions: ☞ ☞ Centrality dependence of the width of BFCentrality dependence of the width of BF

21.5%

19.9%

The width of B(The width of B(δδηη |∞).|∞). is wider than that ofis wider than that of B(B(δδηη ||ηη ww))

The width of B(The width of B(δδηη |∞)|∞) decreases with centrality decreases with centrality faster than that of faster than that of B(B(δδηη ||ηη ww) )

The width of all centralities is 0.553±±0.003, which is smaller than 0.683±±0.015 for pp collision at √s =200GeV and 0.991±±0.008 for π+p and K+p collisions at √s =22GeV.

The width of all centralities is 0.553±±0.003, which is smaller than 0.683±±0.015 for pp collision at √s =200GeV and 0.991±±0.008 for π+p and K+p collisions at √s =22GeV.

i wi

i iwiB

B

)|(

)|(

If B(If B(δδηη||ηηww) is replaced by B) is replaced by B

((δδηη|∞) in,|∞) in,