On the Mechanism of Baryon Formation in Hadronization of the QuarkGluon Plasma

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On the Mechanism of Baryon Formation in
Hadronization of the Quark-Gluon Plasma

• K.Terasaki and T.Matsui
• University of Tokyo
• March 22, 2005

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Outline

• Hadronization of QGP
• RHIC puzzles at moderate pT values
• ReCo (recombination/coalescence) model
• What can ReCo do for RHIC?
• Jet correlations in intermediate pT range
• Diquark fragmentation model
• Numerical results
• A Glance at LHC
• Conclusions

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Hadronization of QGP

• Relativistic heavy Ion Collision

collision
thermalization
Hydrodynamical expansion
hadronization
Freeze-out
QGP phase
Hadron phase
If phase space is filled with partons, How do
they turn into hadrons?
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RHIC puzzles at moderate pT values

• Anomalous baryon enhancement

p/?1 (pTgt2GeV) in central collisions
Fragmentation
p/?1
Limitation of fragmentation
Fragmentation energy loss seem to work above 6
GeV/c.
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• Difference in baryon and meson elliptic flow v2

Look at emission patterns using Fourier
expansion extract v2 components from the fits.

• Pressure gradient
• Collision plane gt
• Perpendicular plane

dN/d(f -YR ) N0 (1 2V1cos (f-YR) 2V2cos
(2(f-YR)) ... )
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Saturation of v2 at different PT and on different
levels.
Constituent Quark number of scaling of hadron
elliptic flow
It cant be explained by mass effect.
It might be a evidence for pre-hadronic
collective flow.
Hydrodynamical model seem to work under 2 GeV/c.
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Particle production vs PT
Mechanisms atintermediate pT?
Hydro
pQCD
Spectra, Rcp
???
Soft
Fragmentationand quenching of jets
pT
0
1-2 GeV/c
6-8GeV/c ?
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Recombination/coalescence idea
Recombination model (Duke model) R.J.Fries, B.
Müller, S. A. Bass C. Nonaka PRC68, 034904(2003)

• Basic assumpsions
• At low pT, the quarks and antiquark spectrum is
  thermal and they recombine into hadrons locally
  at an instant
• At high pT, the parton spectrum is given by a
  pQCD power law, partons suffer jet energy loss
  and hadrons are formed via fragmentation of
  quarks and gluons

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Recombination formalism

• Recombine thermal ensemble of massive quarks
  (constituent quarks) at the phase transition.

CM, CB Degeneracy factors
E791 ?- beam hard cc production recombine c
with d valence quark from ?- gt reco of c with d

• We will not take into account color octet and
  spin flip states.
• This is supported from work on recombination in
  pQCD (Leading particle effect).
• (Braaten, Jia, Mehen Phys. Rev. Lett. 89, 122002
  (2002))

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• Spectrum of thermal parton
• Add pQCD calc. using fragmentation and energy
  loss.

Hadr. hypersurface ? t5fm, T175 MeV Radial flow
v0.55c

• What can ReCo do for RHIC?

ReCo dominates up to 4-6 GeV/c
Good description of the different hadron species
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Jet correlations in intermediate pT range
The ratior(PT)R/(RF) For protons (red) and
pions (blue).
PHENIX experiment Trigger pT 2.5-4.0GeV/c Associa
ted pT 1.7-2.5GeV/c ?f0.0-0.94 Npart Number
of participant nucleons

• ReCo is free of particle correlations.
• ?RHIC experiment
• (especially for baryons)

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Diquark fragmentation model
In ReCo model, we did not take into account color
octet and spin flip states.
ReCo
Baryon
diquark
ReCo
Fragmentation
Meson
Diquark-jet
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Diquark fragmentation function
A.Bartl, H.Fraas and W.Majerotto, PRD26, 1061
(1982)

• Extend the equations of Feynman and Field to
  diquark fragmentation by adding two elementary
  processes.
• Tune the parameters to fit p, , p, p-, ? and
  neutrino-production data of BEBC (Big
  European Bubble Chamber).

M
M
B
B

• Emission of a baryon from quark-jet

• Emission of a meson from diquark-jet by
  diquark-breaking

• Emission of a baryon from diquark-jet

• Emission of a meson from quark-jet

µ-
W
µ
W-
?
(uu)-diquark
(ud)-diquark
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Fragmentation function (FF) of (uu)-diquark (red)
and u-quark (blue). We show proton (solid line)
and p (dashed line) .
ltSpectrum of diquark on hadr. hypersurface Sgt
This is same as meson spectrum, except for the
degeneracy factor.
CD3(13)12
Color
scalarvector
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Numerical result
Hadron spectra at midrapidity as a function of
transverse momentum PT for central AuAu
collisions with vs200GeV.
Proton
p
We show fragmentation (black line), diquark
effect (green), recombination (blue), and the sum
of all contributions (red).
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The ratio of recombined hadrons to the sum of all
contributions
Proton
p
The diquark effect contributes to 10-15 of
proton spectrum in 2.5-4.0GeV/c.
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A Glance at LHC PbPb central collisions with
vs5.5TeV at midrapidity
Hadr. hypersurface ? t9fm, T175 MeV, radial
flow v0.75c are assumed.
Proton
p
The diquark effect at LHC is larger than at RHIC.
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• Spectrum of thermal parton

radial flow velocity 0.55 (at RHIC) 0.75 (at LHC)
ReCo processes are enhanced by the fast flow and
strong jet quenching at LHC.
diquark
Spectra
Diquark processes are shifted to low transverse
momentum region by fragmentation.
fragmentation
proton
pT
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Conclusions

• ReCo explains differences between hadron species
  baryon enhancement, v2 scaling for central AuAu
  collisions at RHIC for PT lt 46 GeV/c.
• But ReCo doesnt give two particle correlations
  observed at PHENIX.
• Jet-like correlations may be explained by diquark
  fragmentation model.
• It is expected that the diquark fragmentation
  effect at LHC is even larger than at RHIC.
• We need to construct more dynamical model for
  diquark production and baryon formation.

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THE END