Elliptic and directed flow in heavy ion collisions

1
Elliptic and directed flow in heavy ion
collisions

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

2
Thanks to the UrQMD group_at_ 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)

3
Outline

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

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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)

phase boundary
Plot taken from H. Stöcker, E. Bratkovskaya et
al., J.Phys. G 31, 2005
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Introduction - directed flow
Fourier expansion of the azimuthal distribution
of the emitted particles
Directed flow
with
? measures the total amount of transverse flow
Reaction plane
(J.Y. Ollitrault, Phys. Rev. D, 46 A.M.
Poskanzer, S.A. Voloshin, Phys. Rev. C, 58)
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Introduction - elliptic flow
Second coefficient of the Fourier expansion of
the azimuthal particle distribution
Coordinate space asymmetry ? momentum space
anisotropy
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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

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Equation of state
Schematic picture of the EoS with a first order
phase transition
Connection between pressure and flow via
P/e
softest point
QGP
HG
A surface element
QGP
HG
Mixed phase
P pressure e energy density
e
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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

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v1 of protons _at_ 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
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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)
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Elliptic flow
Two competing effects lead to different signs of
v2
Squeeze-out py2 gt px2 ? v2 lt 0
In-plane flow px2 gt py2 ? v2 gt 0
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v2 (y) of pions _at_ 40/160 AGeV
PbPb
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v2(pt) of pions _at_ 40/160 AGeV
PbPb
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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)
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Partonic dof already _at_ 40 AGeV

• Underestimation of v2(pt) in model coincides
  with onset of partonic matter? signals onset
  of change of EoS in the early stage
• partonicfraction is always calculated at the
  time of highest energy density in the reaction

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

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Backup slides
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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 !

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Excitation function v2/ltptgt
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Model
UrQMD
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V2(y) of protons _at_40 AGeV

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