V. Greco

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ReCo Overview Prospectives
V. Greco
BNL , 29 April 2005
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• Overview Early successes of RecoFragm.
• pT spectra ( enh. B/M ratio, RAA , Rcp )
• Elliptic Flow (scaling)

• Developments I Extensions
• Resonances (from QGP or hadron phase)
• Wave function (Widths, Higher Fock state)
• Insight on charm interaction
• v4M/v4B , v1M/v1B
• Charge Fluctuations

• Developments II Prospective
• Jet-like Dynamical Correlations
• Low pT (Energy, Entropy, conservation)
• Links to QCD

Relation to EOS-WG Topics
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Hadrons at RHIC
pions
protons
PHENIX, nucl-ex/0212014

• Fragmentation p/p 0.2
• Jet quenching should affect both

PHENIX, nucl-ex/0304022
p0 suppression evidence of jet quenching
before fragmentation
Fragmentation is not the dominant mechanism of
hadronization at pT lt 4-6GeV !?
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Coalescence vs. Fragmentation
H
Partonic Hydro behavior shifted at higher pT
Even if eventually Fragmentation takes over
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Phase-Space Coalescence
fq invariant parton distribution function thermal
(mq0.3 GeV, ms0.47 GeV) with radial flow
(b0.5) quenched minijets (L/l 3.5,
mq0.01GeV, ms0.175 GeV)
Mqq-gtm2 depends only on the phase space
weighted by wave function npQCD also encoded in
the quark masses (gluon dressing), mq0.3 GeV,
ms0.475 GeV.
fH hadron Wigner function
Dx 1/Dp 0.85 fm coalescence radius parameter
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TAMU implementation
Coalescence Integral solved in a 3D geometry,
with radial flow space-momentum correlation
(important to fix bulk parton distribution)
Locally v1, u1 not small
Coalescence on bulk matter consistent with
hydro, experiments, ec
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Meson Baryon Spectra
AuAu _at_200AGeV (central)
sh
V. Greco et al., PRL90 (03)202302
PRC68(03) 034904 R. Fries et al.,
PRL90(03)202303
PRC68(03)44902 R. C. Hwa et al., PRC66(02)025205

• Proton suppression hidden
• by coalescence!

ReCo dominates up to 4..6 GeV/c fragmentation
and energy loss takes over above.
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Baryon/Meson ratio
DUKE
TAMU
r -gt pp
OREGON
DUKE
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Elliptic Flow
v2,q from a fit to p data -gt v2 p, K, L ...
prediction
D. Molnar and S.A. Voloshin, PRL91 (03)
w.f. effect 5 B/M breaking (Dp 0.25 GeV) Large
breaking if Dp gtgt (OSU, PRC68)
Shape consistent with cascade (AMPT, MPC)
To be seen, breaking of the scaling !
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Effect of Resonances wave function
K, L, p v2 not affected by resonances!
p coal. moved towards p data
V.G., C.M. Ko, PRC 70 (03)
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Resonances II
K from QGP decays into a K with a v2 to K
directly produced

• HG resonances
• hadron final stage, h-h rescattering
• scaling with n4

r (pT ) is determined by experiments and related
to width of particles and cross section in the
hadronic medium.
C. Nonaka , PRC69, 31902 (2004)

• Medium effects
• m shift v2 of decay product

No sensitive to resonance width (Final p spectra
weak dependence)
ps from r
Can we learn more via the analisis of resonances
v2? Can we see evidence of chiral symmetry
restoration?
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Polarized QGP?
Global transverse polarization in the direction
orthogonal to the reaction plane
MECHANISM qq collision carry an angular
momentum that can be transferred to the spin due
to spin-orbital coupling
Z.T. Liang, X.N. Wang, PRL94,102301(05)
2p lt- r
Pq degree of quark polarization
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Higher Fock State
Costituent quark picture is a good description of
hadron PDF as Q2 lt 1 GeV2 (higher Fock state are
suppressed) Still contribution from higher terms
may not be negligible
Is v2 scaling preserved?
For narrow w.f. limit
Standard higher twist w.f
n Fock state, nn partons
B. Muller, nucl-th0503003
Spectra are also not affected (at least pT gtgt m )
s of sea quark
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Charmed elliptic flow
V2 of electrons
V.G. et al., PLB595 (04) 202
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Charm in a sQGP
Charm scatters with D hadronic (chiral restored)
resonances in the QGP (Van Hees, Rapp,
nucl-th/0412015 )
Isotropic cross section
Fokker-Plank approach on a hydro bulk evolution
Therm flow
At high pT even light quarks dont thermalize !
Do heavy Flavor Equilibrate (strongly interact)?
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What happens at lower energy?
Without changing any coalescence parameter!
Jet quenching from I. Vitev, PLB606, 303 (05)
Balance between fragmentation (w quenching) and
coalescence
Uncertainties amount of quenching, bulk
properties (ET, mb,..), p fragmentation function
p/p increase by 20 p-/p decrease slight decrease
V. G., C. Ko, I.Vitev, nucl-th/0412043
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Jet-like Correlation
Correlation in the parton distribution
Source of correlation are jets dump energy and
partons into medium

• Factorized Ansatz
• Gaussian correlations in azimuthal angle ? and
  rapidity y
• S01 inside a Vc ( Vc const , Vc Npart )
• f0 1 (weak pT dependence)
• C0 and f0 fixed to fit data

Different processes F-F, SS-SS, F-SH,
F-SS,SH-SH,SH-SS
Recombination enhances correlations in the parton
phase, ( amplification of elliptic flow)
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Numerical example
Baryons
Mesons
F-F and SS-SS with C00.08, VcNpart.
Large correlations from F-F, favoring baryon
triggers.
F-F and SS-SS with C00.08x100/Npart (Vcconst.)
Lower associated yield when adding SS-SS without
correlations (C00), especially for baryon
triggers.
F-SH (?-? only) v0.5

• Compatibility with jet-like correlation
• Microscopic theory desireable
• - how much comes from gluon radiation
• - relative strength of different correlation
  source
• Different pT window to constraint f0

from R. Fries, HQ04
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What Can we say?

• Constituent quark masses close in phase space
  hadronize to give
• intermediate pT hadrons with the baryon/meson
  pattern observed at RHIC
• - pT spectra ( enh. B/M ratio, RAA , Rcp, absence
  of baryon quenching )
• Elliptic Flow (scaling)
• Large D meson v2
• This is how QCD seems to work in a dense medium
  ( _at_ pq gt 0.75 GeV)
• Result robust against uncertainty in resonance
  decay, wave function
• (shape, presence of higher Fock state)

• Connection to QCD
• - Chiral Symmetry
• - Confinement
• Low pT
• - Energy conservation
• - Entropy conservation
• - Particle conservation

• Need further investigation
• Evolution with beam energy
• (breakdown point?)
• Jet-like Correlation
• Non Zero Rapidity

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From Fragmentation to ReCo

• Fragmentation 1 parton has to hadronize
• 
  (ee-,pp,...AA)
• With more partons around multiple parton
  fragmentation (higher twist)
• (pp,pA,AA)
• If phase space is filled with partons
  recombine/coalesce them into hadrons!

• Dilute system
• High virtualities

• Dense system
• Low virtualities

(AA)
At very low pT most hadrons are formed via
coalescence (Voloshin, NPA715 (03))
R. Fries,HQ04
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Bulk Charge Fluctuations
Neglecting Correlations cik
Hadronic diffusion Gluons
Close to the value used in V.G., PRC68 Nq
1100
Can we understand the results of fluctuations
measurements? Are they compatible with a
deconfined medium?
Recombination with all the quark converted into
baryon and meson
( ) nonet mesons octet decuplet baryons
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Entropy Conservation
Non-Relativistic/ no quantum effect
2) Our Coalescence (PRC68, 034904)
16 decrease
Volume expansion (t 4 fm/c)

• No factor 2 or more due to
• mass of the particle
• off- equilibrium effect

Moreover entropy in the quark phase May be
reduced by interaction C. Nonaka et al.,
nucl-th/0501028
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What is the role of the mass?
Massive quarks mu 0.3 GeV ms 0.5 GeV
What mass is it?
0.02 GeV
Its a thermal mass (zero component of vector
self energy)
0.3 GeV
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Thermal masses and energy conservation
Although thermal quark mass does not breal chiral
Symmetry and similar magnitude of both
quantities (Mq 300-350 MeV) near Tc may
facilitate the formation of hadrons from 2- and
3- quark clusters. (U . Heinz and P. Levai,
PRC57, (2003) 1879)
Thermal masses are related to EOS in a
quasi-particle picture, but interaction is still
important !
Self-consistent Dirac-Brueckner (DB) with a LQCD
potential -gt hadronic resonances with
chiral restored phase M.Mannarelli and R.Rapp,
work in progr.
Spectral function represents an effective way of
treating off-shell effect due to the presence of
the medium
Check Consistency with LQCD resonance spectral
function
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Recombination with thermal masses (from LQCD)

• Link to LQCD
• Energy Conservation
• (-gt Entropy , Resonances)

EOS
LQCD
DB
V(r)
Spectral function
To be checked properties of standard
coalescence are preserved
Input of Coalescence

• Confinement, or use of all Nquark is still
  pending

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Dynamical Coalescence
Quasi particle massive quarks interacting through
LQCD potential
Investigation of Coalescence-Clusterization like
in molecular dynamics

• Use of all quarks
• Energy - Entropy conservation?
• Need for string mechanism at low pT ?
• Effect of q-q potential (entropy, pT, link to
  EOS)
• Natural account for Correlation effect in the
  Fluctuation
• Jet-like Correlations

Better enviroment for
Does Coalescence work at low pT ?
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Summary

• Bulk used in coalescence consistent with present
  knoweledge
• (ET, S, D ..)
• Elliptic flow of resonances deep insight on ReCo
  and medium effect
• Polarization (further check inside into the
  scaling)
• Charge Fluctuation

• ReCo can be connected to QCD inside the validity
  of a
• massive interacting quasi-quark approach
• This will allow to base ReCo on microscopic
  many-body
• calculation based on LQCD
• - Link to EOS
• - Investigation of Energy, entropy ..

Heavy quark should be a better starting point for
a decription In term of q-q potential, more
sophisticated model for J/Y, Y
Of Course our hope is to invalidate
recombination! Right!
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