Flow in p p data

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Flow in pp data
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Collective Flow (radial and anisotropic)

• Only type of transverse flow in central collision
  (b0) is radial flow
• Integrates pressure history over complete
  expansion phase

• Elliptic flow (v2) , hexadecupole flow (v4) , v6,
  caused by anisotropic initial overlap region (b
  gt 0)
• More weight towards early stage of expansion.

• Directed flow (v1) , sensitive to earliest
  collision stage (b gt 0)
• pre-equilibrium at forward rapidity, at
  midrapidity perhaps different origin

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FlowC.) Elliptic Flow v2
Z
Reaction plane
Y
X
Pz
Py
Px
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Elliptic flow as a function of centrality
PHOBOS Phys. Rev. Lett. 89, 222301 (2002) 
STAR Phys. Rev. Lett. 86, 402 (2001)
RQMD
centrality
First time in Heavy-Ion Collisions a system
created which at low pt is in quantitative
agreement with hydrodynamic model predictions for
v2 up to mid-central collisions
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Main contribution to elliptic flow develops early
in the collision
Zhang, Gyulassy, Ko, Phys. Lett. B455 (1999) 45
6
How to compare elliptic flow in AuAu, dAu
and pp collisions ?

• v2 does not scale --- need to find a
  multiplicity (or Nbinary) independent quantity to
  compare azimuthal correlations between two
  different systems.

Multiplicity independent non-flow
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Azimuthal correlation in AuAu, dAu and pp
collisions
STAR Preliminary
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Radial and elliptic flow
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A.) Directed Flow
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Anisotropic Flow

• spatial
• anisotropy
• momentum
• anisotropy
• sensitive to the EoS

• peripheral collisions produce an asymmetric
  particle source in coordinate space

• Fourier transformation of azimuthal particle
  distribution in momentum space yields
  coefficients of different order

• v1 directed flow
• v2 elliptic flow

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Flow of nucleons
AuAu, EkinLab 8 A GeV

• Bounce off nucleons at forward rapidity show
  positive flow.
• If matter is close to softest point of EoS, at
  mid-rapidity the ellipsoid expands orthogonal to
  the longitudinal flow direction.
• Softening of the EoS can occur due to a phase
  transition to the QGP or due to resonances and
  string like excitations.
• At mid-rapidity, antiflow cancels bounce off.

Baryon density
QGP ? v1(y) flat at mid-rapidity.
J. Brachmann, S. Soff, A. Dumitru, H. Stöcker, J.
A. Maruhn, W. Greiner, L. V. Bravina, D. H.
Rischke, PRC 61 (2000), 024909.
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Stopping and space-momentum correlation

• collective expansion of the system implies
  positive space-momentum correlation
• wiggle structure of v1(y) develops
• shape of wiggle depends on
• centrality
• system size
• collision energy

R. Snellings, H. Sorge, S. Voloshin, F. Wang, N.
Xu, PRL 84 (2000), 2803.
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Directed Flow from data

• Directed flow weights are dependent on rapidity
  and have a sign change

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Radial Flow in transverse direction
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Thermal Flow Traditional Approach
Assume common flow pattern and common temperature
Tth
1. Fit Data ? T
2. Plot T(m) ? Tth, bT

• is the transverse expansion velocity. With
  respect to T use kinetic energy term ½ m b2
• This yields a common thermal freezeout
  temperature and a common b.

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Heavy (strange ?) particles show deviations in
basic thermal parametrizations
T tot T f0 mv2
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Blastwave a hydrodynamic inspired description of
spectra
Spectrum of longitudinal and transverse boosted
thermal source
bs
R
Ref. Schnedermann, Sollfrank Heinz, PRC48
(1993) 2462
Static Freeze-out picture, No dynamical evolution
to freezeout
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The Blastwave Function

• Increasing T has similar effect on a spectrum as
  
• increasing bs
• Flow profile (n) matters at lower mT!
• Need high quality data down to low-mT

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Transverse mass spectra
X
STAR Preliminary
Variety of hadron species K? , K0s, K, ?, ?,
?, ?, ?(1520), S(1385), X(1530), ?? , p, D pp,
AuAu, dAu Same experimental setup!
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Spectral shapes
Blast-wave model
E.Schnedermann et al, PRC48 (1993) 2462.
?, K, p ? T 90MeV, b0.6 X, ? ?
T160MeV, b0.45
Common hydro description ? Kolb and Rapp, PRC 67
(2003) 044903. Sudden Single Freeze-out ? A.
Baran et al. nucl-th/0305075.
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Blastwave fits

• Source is assumed to be
• In local thermal equilibrium
• Strongly boosted

• ?, K, p Common thermal freeze-out at T90 MeV
  and lt??gt0.60 c
• ? Shows different thermal freeze-out behavior
• Higher temperature
• Lower transverse flow
• Probe earlier stage of the collision, one at
  which transverse flow has already developed
• If created at an early partonic stage it must
  show significant elliptic flow (v2)

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Kinetic Freeze-out
Kinetic FO temperature

• Sudden Single Freeze-out ?

Radial flow velocity

• p,K,p Tkin decreases with centrality
• X Tkin const
• ?, X and W flow

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Collective Radial Expansion
From fits to p, K, p spectra

• lt?r gt
• increases continuously
• Tth
• saturates around AGS energy

• Strong collective radial expansion at RHIC
• high pressure
• high rescattering rate
• Thermalization likely

Slightly model dependent here Blastwave model
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Statistical Model Fit
200 GeV AuAu

• Stable particle ratios well described with
• Tch 160?10 MeV,
• mB 24 ?5 MeV
• Thermalization ?

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Chemical Freeze-out Properties
200 GeV AuAu
Close to net-baryon free
p,K,p
Close to chemical equilibrium !
p,K,p,L,X
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Freeze-out Evolution
Lattice QCD Tc 170?10 MeV

• Chemical FO close to hadronization
• Strong flow at hadronization

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Time Scale
Tch ? Tkin For massless particles in
equilibrium Entropy density T3
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Basic Idea of Statistical Hadronic Models

• Assume thermally (constant Tch) and chemically
  (constant ni) equilibrated system
• Given Tch and ? 's ( system size), ni's can be
  calculated in a grand canonical ensemble

• Chemical freeze-out
• (yields ratios)
• inelastic interactions stops
• particle abundances fixed (except maybe
  resonances)
• Thermal freeze-out
• (shapes of pT,mT spectra)
• elastic interactions stops
• particle dynamics fixed

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Readings for next week
Space time evolution of heavy ion reaction,
particle production, strange particle and
resonance production Strangeness Production in
the Quark-Gluon PlasmaRafelski et al., Phys.
Rev. Letter 48 (1982) 1006 Rafelski et al., Phys.
Rev. Letter 56, 2334 Strangeness Production in
Heavy Ion Collisions Redlich et al., Nuc. Phys.
A698 (2002) 94c Resonance Production in
mediumC. Markert, nucl-ex/0503013 B. Abelev,
nucl-ex/0604019
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Microscopic models
If the Quark Gluon Plasma was formed, it will
only live for 10-23 s !!!! Nuclei are so thin
because of velocity nearly speed of light
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Microscopic models
Investigate Particle species,
Spectra, Flow,..
   Creation of dense hadronic matter at high
temperatures    Properties of nuclear matter,
Delta Resonance matter    Creation of
mesonic matter and of anti-matter    Creation
and transport of rare particles in hadronic
matter.    Creation, modification and
destruction of strangeness in matter   
Emission of electromagnetic probes
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Particle Production at SPS and RHIC
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Microscopic models
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Particle Production
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Microscopic Models
Essay on Microscopic models

• all decay
• - measured

Marcus Bleicher and Jörg Aichelin Phys. Lett.
B530 (2002) 81-87. M. Bleicher and Horst Stöcker
.Phys.G30 (2004) 111.
chemical freeze-out 5fm/c kinetic freeze-out
20-30 fm/c (long life time !)
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AA Excitation functions

• 4 and mid-y abundancies OK
• Energy dependence OK
• Hadron-string models work well

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