# Presentation: 479189

## Elliptic and directed flow in heavy ion collisions 

-     Hot Quarks 2006, 16.05.06, Villasimius, Sardinia
-     Hannah Petersen, Universität Frankfurt

- Hannah Petersen, Hot Quarks 2006

## Thanks to the UrQMD group@ Frankfurt

- Mohammed Abdel-Aziz (fluctuations)
- Marcus Bleicher
- Stephane Haussler (fluctuations)
- Qingfeng Li (EoS, HBT)
- Diana Schumacher (dileptons)
- Horst Stöcker
- Sascha Vogel (resonances)
- Xianglei Zhu (elliptic flow and charm)

## Outline

- Motivation
- Introduction
- Equation of state (EoS)
- Directed flow results
- Elliptic flow results
- Summary

## Motivation

- No direct detection of the quark gluon plasma    indirect observables like flow are needed

- Transverse collective flow is                          intimately connected to pressure
- Flow is sensitive to changes in     the equation of state and therefore to phase transitions
- (H.Stöcker,W.Greiner Phys.Rep. 137 (1986) 277)

- Plot taken from H. Stöcker, E. Bratkovskaya et al., J.Phys. G 31, 2005

- phase boundary

## Introduction - directed flow

- Fourier expansion of the azimuthal distribution of the emitted particles :

- Directed flow

-  measures the total amount of transverse flow

- with

- Reaction plane

- (J.Y. Ollitrault, Phys. Rev. D, 46; A.M. Poskanzer, S.A. Voloshin, Phys. Rev. C, 58)

## Introduction - elliptic flow

- Coordinate space asymmetry  momentum space anisotropy

- Second coefficient of the Fourier expansion of the azimuthal particle distribution:

## Time evolution

- Pressure      develops sharp maximum in the early stage of the reaction
- Pressure gradients lead to flow
- v2 builds up directly after this maximum

## Equation of state

- QGP

- HG

- Mixed phase

- Schematic picture of the EoS with a first order phase transition

- Connection between pressure and flow via

- A : surface element

- P: pressure
- : energy density

- 

- P/

- HG

- QGP

- softest point

## The UrQMD model

- Non-equilibrium transport model
- All hadrons and resonances up to 2.2 GeV
- String excitation and fragmentation
- Cross sections are fitted to available data, parametrized via AQM or calculated by detailed balance
- Generates full space-time dynamics of hadrons and strings
- Known event-plane

## v1 of protons @ 40 AGeV

- Comparison of rapidity spectra between model and data:
-  Largest flow at high rapidity values
-  Centrality dependence visible

- Data from C.Alt et al., Phys. Rev. C 68, 2003

## v1 of protons

- Slope around midrapidity characterizes shape of the rapidity distribution

- Extracted from normalized rapidity distribution via polynomial fit
- At low energies:             potentials are important
- At high energies:        data developes negative slope   ́wiggle ́
- QGP-signal?
- (L.P. Csernai,  Phys.Lett. B 458,1999)

## Elliptic flow

- Two competing effects lead to different signs of v2:

- Squeeze-out
- py2 > px2
-  v2 < 0

- In-plane flow
- px2 > py2
-  v2 > 0

## v2 (y) of pions @ 40/160 AGeV

- Pb+Pb

## v2(pt) of pions @ 40/160 AGeV

- Pb+Pb

## Excitation function of elliptic flow

- At low energies:                  squeeze-out effect visible and inclusion of nuclear potential needed
- At high energies:         underestimation of flow by calculation because of lack of pressure
- Data and calculation for mid-central events
- „HMw“= mean field from a hard equation of state with momentum dependence and medium-modified NN-cross section                      (Qingfeng Li, nucl-th/0602032)

**Notes:**
 - „HMw“= nuclear potential from a hard equation of state with momentum dependence and modified NN-cross section (Qingfeng Li ́s Rechnung)

## ‘Partonic’ dof already @ 40 AGeV

- Underestimation of v2(pt) in model coincides  with onset of ‘partonic’ matter signals onset of change of EoS in the early stage
-  ́partonic ́fraction is always calculated at the time of highest energy density in the reaction

- (see also H. Weber et al., Phys. Lett. B 442, 1998)

## Summary

- Flow is connected to pressure and therefore to the EoS
- Slope of v1(y) becomes negative around 40 AGeV
- Clear underestimation of elliptic flow at high energies in the transport model
- Phase transition around Elab ~40 AGeV ?

## Backup slides

- Hannah Petersen, Hot Quarks 2006

## Elliptic flow scaling

-  Data shows saturation of scaled   v2
-  High mass resonances  like in UrQMD can not explain  v2 above 40 AGeV
-  Strong hint for    initial QGP pressure from   30 AGeV on !

## Excitation function v2/<pt> 

## Model

## V2(y) of protons @40 AGeV

- Experimental situation unclear
- Transport model calculation is compatible with the data