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

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

LI Na, LI Zhiming, LIU Lianshou and WU Yuanfang

(for the STAR Collaboration)

Institute of Particle Physics (IOPP)

Huazhong Normal university

Wuhan

- Introduction
- ●what does BF measure●current status and problems
- ● motivations
- 2. Experiment and data sample
- 3. Results and discussions
- ● Dependence of BFon size and position ofηwindow
- ● Independence of Bs on size and position of η window
- ●Transverse momentum dependence of Bs
- 4. Summary and conclusions

李治明

All the particlesare within the rapidity window

counting the pairs that satisfy the criteria in the rapidity window

1.Introduction: ☞ What does Balance Function measure

Definition :

- BF measures how the conserved electric charges compensate in the phase space, i.e., how the surrounding electric charges are rearranged if the charge at any selected point changes.
- It tells how the production of charged particles in the whole phase space is constrained by global charge balance, thus provides a direct access to collision dynamics.

李治明

1.Introduction:☞ Motivation: Difficulty in heavy ion

Current status:

The narrowing of the width of BF with centrality

in Au+Au collisions at√sNN=130GeV, and

in lighter nuclei collisions at√sNN=17.2GeV,

and with multiplicity in π+p and K+p Collisions at√s = 22GeV

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

M. R. Atayan et al., (NA22 Coll.), PLB, 034903(2006).

Problem:

acceptances in ηor y

STAR: [-1.3, 1.3]

NA49: [ 2.6, 5.0]

NA22: whole y

Incomparable results!

We want to measureB (δ η|ηw) as a function of δη

but this function depends on the observed windowηw!

Study the dependence of BF on ηwand try to find

a measure independent of observed window.

Aim:

李治明

π+ p and K + p at 22GeV

- full 4π acceptance
- 0.001GeV/c < pT< 10 GeV/c

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

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

- Boost invariance of BF is valid over the whole rapidity space.

李治明

1.Introduction:☞ Motivation: why pT dependence

- The longitudinal property of BF comes from the special longitudinal interaction of charged particles under the constraint of global electric charge balance.
- The range of pT of final state particles is supposed to be related to its emitted proper time.

Gradient of density leads to non-zero collective velocities

Hydrodynamic expansion: gradient pressure acts

Yu M. S., et al., PRL 89 052301 (2002)

J. Adams et al., (STAR Coll.), NPA757, 102(2005)

3. Since a subset of particles can behave collectively only if they are produced at the same proper-time, therefore, examine the pT dependence will provide direct experimental access on this subject.

李治明

2.Experiment and data sample: STAR experiment

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

李治明

2.Experiment and data sample: data sample

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 eventsare selected!

李治明

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

STAR Preliminary

- 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.

李治明

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

STAR Preliminary

- In the left two subsamples, the global net charge is out of balance, and the longitudinal 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!

李治明

3. Results and discussions:☞ Transverse momentum dependence of Bs

- The points at a given relative psudorarapidity in a restrict pT interval are close 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 pT range.
- This is in consistent with the scenario that particles in same restricted pT range are produced at the same proper-time of expansion with well balanced electric charge.

李治明

The 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) ].

3. Results and discussions:☞ pTdependence of the width of Bs- The width of Bs becomes narrower with the increase of pT, which is consistent to the expected delayed hadronization of high pT particles in the thermal model [S. Jeon et al., PRC 65, 044902(2002)].

李治明

4. Summary & conclusions:

- Within the pseudorepidity range (-1,1), the balance function is independent of the position of the pseudorapidity window with the same size.
- The scaled BF Bs, i.e., B (δη|ηw) measured in an observed window ηwdivided by (1-δη|ηw) is found to be independent of the choice of observed pseudorapidity window.
- The longitudinal property of the balance function is further found to be valid for the particles in same restricted transverse-momentum range, which is in consistent with the scenario that particles in same restricted transverse-momentum range are produced simultaneously with well balanced electric charge, and provides for the first time an experimental support for the successful study of the pT dependence of elliptic flow.
- Moreover, the higher the pT of the particles, the narrower the scaled balance function, as expected from the thermal model.

谢谢/Thanks!

李治明

Appendix I● on the measure of charge balance function

Associated particle density:

the density of particles of charge Q at rapidity yunder the condition that

a particle of charge Qs is detected at the rapidity ys.

Associated net charge density:

the net charge density at rapidity yunder the condition that there exists

a particle of charge Qs at the rapidity ys.

Associated charge density balance:

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

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.

李治明

19.9%

2. Results and discussions:☞ Centrality dependence of the width of BFIf B(δη|ηw) is replaced by B(δη|∞) in,

- The width of B(δη|∞).

is wider than that of

B(δη|ηw)

- The width of B(δη|∞)

decreases with centrality

faster than that of

B(δη|ηw)

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.

李治明

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