1. Narrowing of Balance Function and Hadronization Time at RHIC Energy Du Jiaxin, and Liu Lianshou Institute Of Particle Physics, Huazhong Normal University (CCNU)

2. 2/13 dujx@iopp.ccnu.edu.cn Outline  About Balance Function About Balance Function  A Brief Introduction to AMPT Model A Brief Introduction to AMPT Model  The Time Evolution in AMPT The Time Evolution in AMPT  Our Result of Balance Function Our Result of Balance Function  Summary Summary

3. 3/13 dujx@iopp.ccnu.edu.cn Why (changed) balance function? Clocking Hadronization Clocking Hadronization QGP Signal QGP Signal BF is expected to be narrower for a scenario with delayed hadronization, due to the formation of a quark-gluon plasma. Early Hadronization  Large  y Late Hadronization  Small  y Bass, Danielewicz, and Pratt, Phys. Rev. Lett. 85, 2689 (2000). Charge-anticharge pairs are correlated in rapidity. Those who created earlier can separate further in rapidity.

4. 4/13 dujx@iopp.ccnu.edu.cn Relative rapidity All the particles are within the rapidity window Charge Balance Function in Yw The width of the BF is defined by: In our calculation

5. 5/13 dujx@iopp.ccnu.edu.cn Result given by STAR The narrowing of balance function as the increase of multiplicity is clearly discovered by experiments. STAR, QM04.

6. 6/13 dujx@iopp.ccnu.edu.cn A brief Introduction to AMPT Model initial state pre-equilibrium QGP and hydrody- namic expansion hadronization hadronic phase and freeze-out Characteristic:  Quark-Parton phase included  Complete time evolution after parton produced Two versions are available, we use the default version(v1.11).

7. 7/13 dujx@iopp.ccnu.edu.cn Four main components :  Initial Conditions: HIJING model  Partonic Interactions: ZPC model  Hadronization: LUND string fragmentation mechanism (PYTHIA).  Hadronic Interactions: ART model Zi-Wei Lin, Che Ming Ko, Bao-An Li and Bin Zhang, Phys. Rev. C72 064901 (2005).

8. 8/13 dujx@iopp.ccnu.edu.cn AMPT is based on non-equilibrium dynamics. No equilibrium phase transition from parton phase to hadron phase. A parton comes to hadronization only when it cease to interact with other partons. Hadronization time in AMPT Model No unique hadronisation time for the whole system. Each parton has its own hadronisation time.

9. 9/13 dujx@iopp.ccnu.edu.cn We defined: as the characteristic hadronization time for an event. Where is the number of partons in the event, is the freeze out time of the parton. Fig.2 distribution for b>7 and b<7 correspondingly

10. 10/13 dujx@iopp.ccnu.edu.cn Two preliminary questions : Balance Function in AMPT BF become narrowing Multiplicity increase BF become narrowing Delayed hadronization Is the narrowing of Balance Function only caused by the multiplicity increase or really due to delayed hadronization?  How does the hadronization time vary as the multiplicity increase?  How does the BF width vary when hadronization time increase but the multiplicity keep constant?

11. 11/13 dujx@iopp.ccnu.edu.cn Fig.3..vs. for b>7 and b<7 correspondingly  Two centrality samples:  Each centrality sample is divided into sub-samples according to multiplicity intervals;  The resulting sub-samples are further divided into sub- samples by different mean hadroniztion time intervals.

12. 12/13 dujx@iopp.ccnu.edu.cn FIG. 3: for different and Au-Au@ 200 GeV. Our result:  The width of BF decreases with the increasing of multiplicity.  In the same multiplicity interval, the width of BF is consistent of being constant, independent of the hadroni- zation time.  Using the narrowing of BF as a measure of hadroniza- tion time and as a signal of QGP is doubtful.

13. 13/13 dujx@iopp.ccnu.edu.cn Summary We use the average of hadronization time as the unique hadronization time of the whole system. We calculate the width of BF in different multiplicity interval and hadronization time interval. The width of BF decreases with the increasing of multiplicity. In AMPT model, the width of balance function is consistent with being independent of hadronization time in a fixed multiplicity interval. Based on our calculation of AMPT model, We concludes that using the narrowing of balance function in RHIC as a measure of hadronization time and as a signal of QGP is doubtful.