# Presentation: 885375

## Azimuthal Anisotropy:The Higher Harmonics

## 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

- v2

- v4

- isotropic

- momentum space

## v2 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 **

- 4th harmonic of one subevent
- relative to 2nd harmonic of
- other subevent

- Correlation of two event planes:

- v4 is positive

## 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****	**

## Method

**Method**

**Described in methods paper:**
**Poskanzer and Voloshin, Phys. Rev. C 58, 1671 (1998)**

## v4(pt)

- 200 GeV/A Au + Au

## v4(pt)

## v4(pt)

- Ollitrault

## v4(pt) Scaling

**v****4****(p****t****) Scaling**

- 1.2

- Definitely greater than 1.

## v4 from f2

**v****4**** from f****2**

- Kolb

- only f2

- 1.2

- Blast Wave

- Therefore, f4 is greater than zero

- Fit v2

## Blast Wave v4 fit

- f2  = 1.2 %   s2 = 7.4 %

- T  = 0.1 GeV   0 = 1.08

- f4  = 0.15 %   s4 = 1.2 %

- v2

- v4

-  (1 + 2 s2 cos(2 phi) + 2 s4 cos(4 phi))

## Parton Coalescence and Scaling

- Voloshin, Kolb, Chen, Ko, and Lin

- Therefore, v4q is even greater than simple parton scaling would indicate

- Assuming coalescence of quarks:

- , but experimentally it is 1.2

- Assuming scaling for quarks:

- vnq = (v2q)(n/2)

- , but experimentally it is 1.2

- Therefore, v4q is greater than zero

## The Peanut Waist

**The Peanut Waist**

**No waist:**
**v****4**** = (10 * v****2**** - 1) / 34**

- fit

- Kolb

- 16.5% v2   3.8% v4   both

- High pt

## v4(pt,cent)

- _Centrality_
- 70 - 80 %
- 60 - 70 %
- 50 - 60 %
- 40 - 50 %
- 30 - 40 %
- 20 - 30 %
- 10 - 20 %
-  5 - 10 %

- preliminary

## v4(centrality)

## v4(centrality)

**v****4****(centrality)**

## v4(centrality)

## v triply integratedin MTPC

| v | % |
| --- | --- |
| 2 | 5.18 +/- 0.005 |
| 4 | 0.44 +/- 0.009 |
| 6 | 0.043 +/- 0.037 |
| 8 | -0.06 +/- 0.14 |

- Two sigma upper limit
- is 0.1%

## 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**

## 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**

## v4 and v6 Hydro

**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

- preliminary

## v4 and v6 Hydro

**Points: centrality 20-30% data for charged particles **
**Lines: Kolb hydro at b=7 fm for positive pions**

- Kolb

- preliminary

## 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**

## Non-flow and/or Fluctuations

**Non-flow and/or Fluctuations**

- For v2, about 20% reduction from v2{2} to v2{4}

- For v4, up to a factor 3 difference!

## v4 at high 

- v2 / 3

- v4

**Signal in the FTPCs consistent with 0 **
**Drop of v****4**** from TPC to FTPC faster than for v****2**

- preliminary

- See poster by Markus Oldenburg

- 2 M events

- 70 k events