1. STAR 1 Azimuthal Anisotropy: The Higher Harmonics Art Poskanzer for the Collaboration STAR

2. 2 Peter Kolb v 4 - a small, but sensitive observable for heavy ion collisions: PRC 68, 031902(R) Strong potential to constrain model calculations and carries valuable information on the dynamical evolution of the system Magnitude, and even the sign, sensitive to initial conditions of hydro Kolb peanut shape v2v2 v4v4 isotropic momentum space

3. STAR 3 v 2 determines the reaction plane v 1 (STAR talk by Aihong Tang), v 4 v 6 and v 8 using second harmonic particles Possible because v 2 is so large at RHIC and event plane resolution is so good in STAR 4 th harmonic of one subevent relative to 2 nd harmonic of other subevent Correlation of two event planes: Normalized v 4 is positive

4. STAR 4 Terminology n = harmonic number Common usage v n = harmonic order n with respect to event plane of same order v n {N} = N-particle cumulant for v n New addition v n {EP 2 } = harmonic order n with respect to event plane of order 2

5. STAR 5 for v 2 for v 4 for v 6 Method Described in methods paper: Poskanzer and Voloshin, Phys. Rev. C 58, 1671 (1998) v = v observed resolution v 8 vs. 2 nd Square-root of subevent correlation Signal to fluctuation noise Same harmonic v 4 vs. 2 nd v 6 vs. 2 nd

6. STAR 6 v 4 (p t ) 200 GeV/A Au + Au

7. STAR 7 v 4 (p t )

8. STAR 8 v 4 (p t ) 1.2 v 2 2 1.2 v 2 3 v n ~ v 2 n/2 Ollitrault

9. STAR 9 v 4 (p t ) Scaling 1.2 Definitely greater than 1.

10. STAR 10 v 4 from f 2 Kolb only f 2 1.2 Blast Wave Therefore, f 4 is greater than zero Fit v 2

11. STAR 11 Blast Wave v 4 fit f 2 = 1.2 % s 2 = 7.4 % T = 0.1 GeV  0 = 1.08 f 4 = 0.15 % s 4 = 1.2 % v2v2 v4v4 (1 + 2 s 2 cos(2 phi) + 2 s 4 cos(4 phi))

12. STAR 12 Parton Coalescence and Scaling 2 for mesons quarks Voloshin, Kolb, Chen, Ko, and Lin Therefore, v 4 q is even greater than simple parton scaling would indicate 1/4 + 1/2 (v 4 q /(v 2 q ) 2 ) Assuming coalescence of quarks:, but experimentally it is 1.2 Assuming scaling for quarks: v n q = (v 2 q ) (n/2) 1/4 + 1/2 = 3/4, but experimentally it is 1.2 Therefore, v 4 q is greater than zero

13. STAR 13 The Peanut Waist No waist: v 4 = (10 * v 2 - 1) / 34 fit Kolb 16.5% v 2 3.8% v 4 both High p t

14. STAR 14 v 4 (p t,cent) Centrality 70 - 80 % 60 - 70 % 50 - 60 % 40 - 50 % 30 - 40 % 20 - 30 % 10 - 20 % 5 - 10 %

15. STAR 15 v 4 (centrality)

16. STAR 16 v 4 (centrality)

17. STAR 17 v 4 (centrality) 1.4 v 2 2 1.4 v 2 3

18. STAR 18 v triply integrated in MTPC v% 25.18 +/- 0.005 40.44 +/- 0.009 60.043 +/- 0.037 8-0.06 +/- 0.14 Two sigma upper limit is 0.1%

19. STAR 19 Conclusions v 4 Integrated, a factor of 12 smaller than v 2 v 2 2 scaling Small, but significant v 6 Probably another factor of 10 smaller Consistent with v 2 3 scaling Blast Wave f 4 finite, s 4 needed for good fit Parton coalescence v 4 q finite and greater than (v 2 q ) 2 Hydro Predicts a waist, but not observed

20. STAR 20 spares v 4 {EP 4 } 3x high because of either fluctuations or nonflow Hydro v 4 seems to fit v 6 is zero instead of negative from hydro

21. STAR 21 v 4 and v 6 Hydro Points: centrality 20-30% data for charged particles Lines: Kolb hydro at b=7 fm for positive pions Kolb

22. STAR 22 v 4 and v 6 Hydro Points: centrality 20-30% data for charged particles Lines: Kolb hydro at b=7 fm for positive pions Kolb

23. STAR 23 Search for higher harmonics Long History Voloshin at CERES Me and Voloshin with NA49 data Large, and decreasing slowly with harmonic number Probably all non-flow effects Except Voloshin and Zhang at AGS E877: PRL 73, 2532 (1994) Q distribution method

24. STAR 24 Non-flow and/or Fluctuations For v 2, about 20% reduction from v 2 {2} to v 2 {4} For v 4, up to a factor 3 difference!

25. STAR 25 v 4 at high  v 2 / 3 v4v4 Signal in the FTPCs consistent with 0 Drop of v 4 from TPC to FTPC faster than for v 2 See poster by Markus Oldenburg 2 M events 70 k events