Elliptic and directed flow in heavy ion collisions

Hannah Petersen, Hot Quarks 2006

Elliptic and directed flow in heavy ion collisions

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


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 flowFourier expansion of the azimuthal distribution of the emitted particles :

t

x

p

pv 1

1

cos212

1

iRi

tttt

ivdydpp

dN

dyddpp

dN

Directed flow

measures the total amount of transverse flow

22yxt ppp with

Reaction planeReaction 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:

2

2

2

2

2t

y

t

x

p

p

p

pv


Time evolutionPressure 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

t A

x dAdtSPp ),(~ QGP

HGMixed 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

fro

m C

.Alt

et

al.,

Ph

ys.

Rev.

C 6

8,

200

3


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 > px

2

v2 < 0

In-plane flow

px2 > py

2

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 pressureData 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)


‘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


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 !

data for h-


Excitation function v2/<pt>


UrQMD

Model


V2(y) of protons @40 AGeV

Experimental situation unclear

Transport model calculation is compatible with the data

Documents

Elliptic and directed flow in heavy ion collisions