Duke University

1
Hadron production in heavy ion collisionFragment
ation and recombination

• Duke University
• ?? ??

in Collaboration with R. J. Fries (Duke), B.
Muller (Duke), S. A. Bass (Duke RIKEN)
PRL90,202303(2003), nucl-th/0306027,
nucl-th/0308051
2003?9?9?_at_?????? 2003????????
2
Outline

• Introduction
• Hadronization mechanism
• Experimental data
• Elliptic Flow, Proton Puzzle, RAA
• Hadronization mechanism
• Recombination Fragmentation Model
• Comparison with Experimental data
• Hadron Spectra, Hadron ratio, RAA,
• Centrality dependence of hadron spectra
• Elliptic Flow
• Summary

3
Hadronization mechanism

• Relativistic Heavy Ion Collision
• Schematic sketch (ex. Hydro)
• Experiments

t
?
freezeout hadron production
hydrodynamical expansion
hadronization
thermalization
collision
hadron phase
QGP production
phase transition
We have to find the hints about hadronization in
experimental data.
4
Experimental Data ( I )
AuAu at sqrt(sNN)200GeV
r.p. h34
min. bias
(STAR nucl-ex/0306007)

• Saturation in v2 of baryon occurs
• at higher PT than one of meson.

PHENIX nucl-ex/0305013
Hydro Huovinen et al., PLB503,58(2001)
5
Experimental Data ( II )

• Proton Puzzle at RHIC

• Hadronization from Fragmentation
• at high PT

p/p
g
(PHENIXnucl-ex/0307022)
p/p ratio 1 (PTgt2 GeV) in central
collisions
p/p ratio ltlt 1
6
Experimental Data ( III )

• Suppression in RAA of baryon occurs
• at higher PT than one of meson.

• There are some correlations between
• RAA and v2.

Sorensen_at_SQM2003
7
Recombination Fragmentation Model

• Recombination at moderate PT
• Recombination occurs
• in an instant.
• The parton spectrum is
• shifted to higher pT in the hadron
• spectrum.
• Entropy and energy conservation
• No gluon dynamics
• Fragmentation at high PT
• The parton spectrum has a power law tail (quarks
  and gluons) from pQCD.
• The parton spectrum is shifted to lower pT in the
  hadron spectrum.

Recomb.
Frag.
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Formalism of Recombination ( I )

• Number of meson

parton
meson
Meson states with momentum P
density matrix for systems of parton

• Covariant form on hadronizaion hypersurface S

• Integral over q in terms of light cone
  coordinates

Effective wave function
9
Formalism of Recombination ( II )

• Recombination from thermal phase
• Baryon/Meson ratio

• Important feature

This depends on hadron momentum !
ex.
10
Recombination vs. Fragmentation

• Fragmentation

• Important feature

i. Parton spectrum
(exponential)
Recomb.
Frag.
ii. Parton spectrum
(power law)
Recomb.
Frag.
Recombination exponential parton
spectrum Fragmentation power law parton
spectrum
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Input for Quantitative Calculation

• Recombination

Spectrum of parton
ga fugacity factor, D rapidity width f(r,f)
transverse distribution
T175 MeV, t5 fm, vT0.55

• Fragmentation

• K1.5 roughly account for higher order
• corrections
• C, B, b are taken from a leading order pQCD
• calculation

Spectrum of parton
Energy Loss
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Comparison with Experimental Data I
Hadron spectra, Hadron ratio, Central dependence
of hadron spectra
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Hadron Spectra ( I )
14
Hadron Spectra ( II )
15
Hadron Ratios vs. PT
R F
R
Statistical model

• Up to 4 GeV, thermal
• model describes data well.

• supports
• transition from recomb to
• fragmentation at
• intermediate PT.

16
Centrality dependence

• Fragmentation

The values of Ncoll(b) are given by PHENIX
collaboration

• Energy loss

• Recombination

Transverse area of the overlap zone
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Centrality dependence
p/p0

• In peripheral collision, fragmentation
• becomes more and more important.

• Centrality dependence of

nucl-th/0306027
18
Nuclear Modification Factors ( I )

• Central collision
• Both results are consistent with
• data.
• Peripheral collision
• Uncertainty in pQCD is large.
• Jet quenching effects are much
• weaker.

19
Nuclear Modification Factors ( II )
Nuclear modification factor
R

• 2 lt PT lt 4 GeV
• RCP (baryon) gt RCP (meson)
• Recombination
• 4 lt PT lt 6 GeV
• steep drop
• Transition from Recom.
• to Frag.
• High PT suppression
• Fragmentation

F
20
Comparison with Experimental data II
Elliptic Flow
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Elliptic Flow ( I )

• Elliptic flow is sensitive to initial geometry.

At moderate PT recombination
At high PT fragmentation

• Pressure gradient
• Collision plane gt
• Perpendicular plane

• Energy loss
• Perpendicular plane gt
• Collision plane

• Total elliptic flow

r(pt) relative weight of the recombination
contribution in spectra
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How to construct v2 of hadrons ?

• Parton number scaling

up to intermediate PT
Input Parton Ouput Hadron
(STARnucl-ex/0306007)

• v2 of parton

• v2 of hadron

R
F
relative weight of recombination in
hadron yield
23
Elliptic Flow ( I )

• Consistent with experimental data.
• Small deviation between full calculation
• and d-function approximation.

• v2 of baryons saturates at a higher value
• than for mesons.
• At high PT, v2 is dominated by fragmenta-
• tion.
• v2 of baryon and meson is identical.
• We do not take into account bounding
• energy at low PT.

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Elliptic Flow ( II )

• We use the same fragmentation functions
• of K (L) for that of f ( W, X).

• input

Mesons

• v2 of f is almost the same as that of K.

Hydrodynamical model

• For saturation feature, the mass effect in
• v2 is negligible.

of valence quarks

• Hadrons with high mass may be disfavored
• by the fragmentation process.

Baryons
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Comparison with Hydrodynamical Model

• Hydrodynamical Model

(Blast wave model)

• Low PT

• Mass effect

• Recombination Fragmentation

Model

• Intermediate PT

• Saturation feature

• of valence quarks

• High PT

v2 is sensitive to hadron structure !

• Fragmentation

Universal v2 curve
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Summary

• We can reproduce the experimental data.

• Hadron spectra
• Hadron ratio
• Centrality dependence
• High PT suppression of RAA and RCP
• Elliptic Flow

Recombination Fragmentation Model provides the
solution of understanding RHIC data !