1. 2010/4/18 1 南昌 Correlation between event multiplicity and observed collective flow 周代梅 华中师范大学粒子物理研究所

2. 2010/4/18 2 南昌 Contents Introduction and higher harmonics Collective flow and higher harmonics Results & discussions Conclusion

3. 2010/4/18 3 南昌 I. Introduction The charge particle emitted from the fireball created in relativistic nucleus-nucleus collision exhibit transverse collective flow Represented by the elliptic flow parameter (v_2) and other harmonic parameters (v_n, n=0,1,3,4,…) The expected phase transition to QGP should have a dramatic effect on those harmonic parameters The study of collective flow can provide information on the initial state dynamics and the degree of equilibration attained in heavy-ion collisions v 2 play crucial role in the evidence of QGP

4. 2010/4/18 4 南昌 A, Present status In basic paper of PR,C58(1990)1671,start from triple differential distribution and define that, where <> indicates an average over all particle in all events. and higher harmonics II. Collective flow and higher harmonics

5. 2010/4/18 5 南昌 : isotropic flow : first harmonic, directed flow : second harmonic, elliptic flow (elliptic component ） (n=3,4,…): higher harmonics For the particle number distribution, the coefficient That is widely accepted in theoretical calculations

6. 2010/4/18 6 南昌 is the azimuthal angle of the reaction plane In theory, if the beam direction Impact parameter vector reaction plane is between reaction plane and axis particle azimuthal angle is just the angle spanned by relative to axis

7. 2010/4/18 7 南昌 B, What we do Doubts about the method of averaging ? ● Transfer into cylindrical system, substitute by y (rapidity), and use The normalized particle multiplicity distribution is ● ● We first make a transparent derivation starting from invariant particle multiplicity distribution

8. 2010/4/18 8 南昌 the event multiplicity and the integrals are taken over entire ranges of the variables entire ranges of the variables This normalized particle multiplicity distribution is a three dimensional distribution. The dimension can be reduced by integrating over a certain variable ● If one studies, one should take integral over, the three dimensional distribution function reduces to a two dimensional distr. function

9. 2010/4/18 9 南昌 In numerical calculation a rapidity interval,, is used Instead of a single y value, the corresponding normalized particle multiplicity distribution becomes Here the normalization should be

10. 2010/4/18 10 南昌 ● Since is a periodic and even function, it can be expanded by a Fourier series ● is the normalized distributions density function of is the number of particles emitted into at azimuthal angle without constraint on but is constrained in

11. 2010/4/18 11 南昌 where is the average of over particles in a single event As the event multiplicity fluctuates event-by-event, one always has to generate multiple events and to take average over events generated means an average over all events event-wise average

12. 2010/4/18 12 南昌 Applying recursion formula of cosine function and is an average of first over particles in an event and then average over events (event-wise average)

13. 2010/4/18 13 南昌 rather than an average over all particles in all event (particle-wise average) Only if the is independent of constrained event multiplicity the reduces to In fact, the and correlate with each other (negatively correlate)

14. 2010/4/18 14 南昌 Elliptic flow and higher harmonics should be event-wise average rather than particle-wise average. The latter one should be corrected by event multiplicity. The parton and hadron cascade model AMPT was used to study the correlation between event multiplicity and observed collective flow. III. Results & discussions

15. 2010/4/18 15 南昌 The correlate between and

16. 2010/4/18 16 南昌 AMPT calculations for 0 － 40% of top multiplicity Au+Au events at RHIC energy: event-wise av. Is nearly 20% larger than particle-wise.

17. 2010/4/18 17 南昌 The correlation between impact parameter and charged multiplicity 1 fm change of impact parameter make a change of ～ 100 charged particles in multiplicity. An about 20% increase in multiplicity corresponds to about 2 fm decrease in impact parameter

18. 2010/4/18 18 南昌 20%mutiplicity change V_2 is strongly correlated to impact parameter b

19. 2010/4/18 19 南昌 IV. Conclusion (A) Elliptic flow and higher harmonics should be event-wise average rather than particle-wise average. The latter one should be corrected by event multiplicity (B) Only if the is independent of constrained event multiplicity the reduces to (C) In fact, the and correlate with each other (negatively correlate) (D) AMPT model shown that charged multiplicityand v_2 are strongly correlated with impact parameter b

20. 2010/4/18 20 南昌 (E) The change of v_2 caused by the different impact parameters in the sample is ~(15-40)% of the maximum! This is a very significant change, which should not be overlooked! (F) This correlation is important to take into consideration unless very narrow multiplicity bins are discussed.

21. 2010/4/18 21 南昌 Thank you !