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

1. 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

2. Outline: • 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

3. Relative rapidity: 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

4. 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

5. NA22 experiment results 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

6. 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

7. 2.Experiment and data sample: STAR experiment Relativistic Heavy Ion Collider (RHIC), BNL, Upton, NY, USA 李治明

8. 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

9. 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

10. 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

11. STAR Preliminary 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

12. QGP Signal 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

13. 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

14. 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

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

16. 21.5% 19.9% 2. Results and discussions:☞ Centrality dependence of the width of BF If 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