Light and heavy quark coalescence
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Light and heavy quark coalescence In Heavy-ion collisions. V. Greco Universita’ di Catania, Italy INFN-LNS. ?. Work done in collaboration with Van Hees, Ko, Levai, Rapp. Zimanyi 75 Memorial , July 2007 – Budapest (Hungary). First proceedings on QGP I looked at…. Before instead

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Light and heavy quark coalescence

In Heavy-ion collisions

V. Greco

Universita’ di Catania, Italy



Work done in collaboration with

Van Hees, Ko, Levai, Rapp

Zimanyi 75 Memorial , July 2007 – Budapest (Hungary)

First proceedings on QGP

I looked at…

Before instead

I was working on RMFT

“In the ALCOR model we assume that just before the hadronization the dense matter can be described as a mixture of dressed up, massive quarks andantiquarks. The effetive mass of the gluons at this point is much larger than that of the quarks [9], consequently the gluon fission into quark-antiquark pairs is enhanced and massive gluons disappear from the mixture.”

[9] Heinz & Levai, PRC57

Hadronization mechanism & QGP structure

Light Hadrons and intermediate pT

  • Modification of hadronization mechanism

    • coalescence + fragmentation (RAA&v2 Bar. – Mes.)

    • Robustness – developments - open issues


Relevance of Coalescence in the Heavy-Quark sector

  • presence of heavy-light Qq resonances (lQCD)

    • Heavy quark thermalization

    • RAA –v2 correlation of single e

  • link J/Y – D : one underlying HQ distribution

  • From RHIC to LHC (new QGP phase)?!

    • SimilarRAA & v2 proof of Qq resonances in the RHIC-QGP

Nuclear Modification Factor




  • Strong (Flat) suppression explained by jet quenching

  • Proton not suppressed ?!


Parton spectrum










PHENIX, PRL89(2003)

In the vacuum p/p ~ 0.3

due to Jet fragmentation

Use medium and not vacuum

More easy to produce baryons

Hadronization has been modified

pT < 4-6GeV !?

Greco, Ko, Levai, PRL 90 –PRC68

Phase-Space Coalescence

T=170 MeV

ET ~ 730 GeV

T ~ 170 MeV

b(r)~ 0.5 r/R




e ~ 0.8 GeVfm-3

dS/dy ~ 4800


P. Levai et al., NPA698(02)

3D geometry with radial flow space-momentum correlation

just overlap of fq with wave function

  • fqinvariant parton distribution function

  • thermal with radial flow(b=0.5r/R)

  • quenched minijets (GLV- L/l = 3.5)

fHhadron Wigner function

Dx = 1/Dp

Bulk matter consistent

with hydro, experiments, ec


Baryons vs Meson

r-> pp



v2q fitted from v2p



Fries et al., PRC68

Meson & Baryon Spectra

Au+Au @200AGeV (central)



  • Proton suppression hidden

    by coalescence!

Greco-Ko-Levai, PRL90 (03)202302

PRC68(03) 034904

R. Fries et al., PRL90(03)202303


Hwa and Yang, PRC66(02)025205

ReCo dominates up to 4-6 GeV/c; fragmentation

and energy loss takes over above.

A message from the early stage


Coalescence scaling

Enhancement of v2

  • nq - not a mass effect

  • Most of flow is partonic




v2 develops t<5fm

Hydro & cascade

x - p correlation neglected

narrow wave function

Molnar and Voloshin, PRL91 (2003)



x-p correlation in Greco-Ko-Levai

still small scaling violation

Ok, but this is really too naive… (!?)

already included

Greco-Ko-Levai, PRC68 & 70

(less important at high pT)

high pT no problem …

but at lower pT

is not so drammatic

  • Resonances

  • Wave function finite width

  • Gluons

    • ALCOR, TAMU-coalescence : mass suppressed, splitting, quark dressing

    • Higher-Fock state, Fries-Muller-Bass, PLB618 (05)

  • 4) Energy Conservation

    • not large 17% in PRC68, resonances decay & v2

    • Ravagli-Rapp arXiv:0705.0021 for v2(KET)

  • 5)Entropy Conservation

    • 15% like energy – Dynamical coalescence V(r,T)

  • 6) Relation to jet-like correlations

  • Fries et al.,PRL94 but need of transport description

  • 7) Space-momentum correlations affect v2 scaling

  • (Pratt-Pal PRC71, Molnar nucl-th/0408044, Greco-Ko nucl-th/0505061 )

  • (At LHC they will still be so nice ?!)

w.f. + resonance decay

p from

K & p


Effect of Resonances & wave function

K, L, p …v2 not affected

by resonances!

p coal. moved towards p data

Greco-Ko, PRC 70 (03)

About Energy & Entropy …

  • On v2 it is mainly a shift in pt ->KET

    • v2 pions from rho decay

      (Greco-Ko-Levai, PRC68&70)

    • Q value effect in a Boltzmann approach

  • (Ravagli-Rapp, arXiv:0705.0021 [hep-ph] )

  • Entropy- Energy Conservation

  • 15% violation, No factor 2 :

  • resonances

  • mass of the particle

  • degeneracies

Greco-Ko-Levai, PRC68

But, the energy is not conserved !

Dynamical coalescence

with interaction effects

can conserve the entropy …

Deeper questions… and difficult answers

  • Dynamical coalescence (no sudden f.o. - Molnar-QM05)

  • Where is confinement ?

  • V(r,T) (beyond sudden approx.) especially for heavy quarks - lQCD

  • 3) How to go from thermal to chiral masses?

  • Although thermal quark mass does not breal chiral Symmetry and similar magnitude

  • of both quantities near Tc may facilitate the formation of hadrons from 2- and

  • 3-quark clusters ( Heinz and Levai, PRC57).

  • 4) Quasiparticle with spectral function

  • quark mass distribution (Zimanyi-Birò-Levai, JPG31 (05) 771)

  • -> good p,p specra and ratio

  • Take home messages from the light sector

  • Hadronization from 2-3 body phase SPACE (pT< 5-6 GeV):

    • dense medium decrease vacuum role

    • massive quarks close in phase space

    • hadrons at pt comes from quarks pt/n (change of soft scale)

  • Universal elliptic flow (dynamical quarks “visible”):

    • carried by quarks

    • enhanced by coalescence

Fries, Greco, Lacey, Sorensen - Ann. Rev. Part. Sci. (2008)

What happens

to heavy quarks?

Some years ago…

V2q from p, p, K, L

Flow mass effect

v2D 5% no c interaction


S. Kelly,QM04

V2 of electrons

Greco-Ko-Rapp, PLB595 (04) 202

RAA , v2 of single e -pQCD



S. Wicks et al.,nucl-th/07010631(QM06)

N. Armesto et al., PLB637(2006)362

  • Radiative energy loss not sufficient

  • sQGP: non perturbative effect

lQCD resonant (bound) states persist

for QQ and qq -> Qq (D-like) resonant scattering

“Light”-Quark Resonances



Hatsuda ’03]

Spectral function in lQCD

A(w)=w2r (w)



Similar from Potential model for J/Y

Mannarelli, Rapp - PRC72 (Bruckner-like)

Alberico, Beraudo, De Pace - PRD 72 & 75


J/y (p = 0) disappears

between 1.62Tc and 1.70Tc

Open-Charm Resonances in QGP

  • effective model with pseudo/scalar

  • + axial/vector “D-like” mesons

  • [chiral + HQ symmetry]

with dimensional regularization

or form factors

  • cross sectionISOTROPIC

  • more microscopic

  • from lQCD potential+many-body

  • [Mannarelli et al.,in preparation]

Ok, but can it describe RAA and v2?

  • t eqdown to 5 fm/c at RHIC !

The model

Hard production


c,b quarks

HQ scattering in QGP

Langevin simulation

in Hydro bulk



Coalescence + Fragmentation




Semileptonic decay

RAA & v2 of “non-photonic” e



Charm reaching thermalization?!



Single-Electronv2andRAAat RHIC


+ fragment.

fq from p, K

Greco,Ko,Levai - PRL90

Hees, Greco, Rapp - PRC73



  • Uncertainty:

  • better estimate of B/C contribution

  • Improvements:

  • include radiative E-loss

  • resonances from lQCD – potential model

  • no-sudden coalescence (full transport)

  • resonant scatteringmore effective forRAA – v2correlation

  • coalescenceincreases bothRAAandv2(anti-correlation)

No feed-down

No direct contr.

J/Y coal.

Quarkonium <-> Heavy-Quark

  • Till now we have looked only at J/Y yield,

    but thanks to such a strong collective dynamics …

  • Regeneration is revealed in :

  • - pt spectra

  • elliptic flow

v2Y from v2D :

measure of


Greco, Ko, Rapp


Tdiss(pT) decrease – AdS Liu et al. hep-ph/0607062

Coalecence only

pT- Quarkonia

from regeneration

consistent with Open!?

Suppression only

From RHIC to LHC?

For min. bias.

Hydro bulk dN/dy=1100

Tinit= 3 Tc

Radial flow bmax=0.68

V2q light quark =7.5 % (hydro or numerology)

v2q(pT) from a cascade [VG, Colonna, Ferini, Di Toro]

Resonances off T>2Tc

From RHIC to LHC - RAA







  • Suppression: RAA similar at RHIC and LHC!

    • Harder initial spectra at LHC

    • Resonance ineffective (“melted” T>2Tc) at early stage!

From RHIC to LHC – v2 electrons



from D only


  • v2 similar at RHIC and LHC!

    • Resonance effective when anisotropy is reduced

    • Strong drag with the bulk flow at later stage!

    • v2 slightly higher at low pt

Warning! Radiative energy loss to be included!


  • Coalescence from a bulk consistent with exp. and hydro

    • Yields, ratios, D-fluctuations

    • RAA, Rcp,V2/nq vs pT

  • Beyond naïve coalescence -> better data description

    • 3D, resonances, wave function, Fock states, energy conservation

  • RAA - v2e anti-correlation for HQ entails:

    - presence of Q-q resonances (lQCD)

  • Similar RAA & v2 at RHIC- LHC:

    - if from RHIC to LHC a new QGP phase is created !

  • Consistency of D and J/Y with one underlying distribution ?!

    • better insight into coalescence at low pT– V(r,T)

2-3 body phase-space

behind hadronization

Relevance of Coalescence in the Heavy-Quark sector

Back up slides


coal.+ fragm.

G = 0.75 GeV

Baryon contamination due to coalescence …

P. Soresen, nucl-ex/0701048

G. Martinez-Garcia et al., hep-ph/0702035

  • Contamination of Lc in single e :

  • enhance v2e: v2Lc > v2D

  • enahencement modest + BRe 4.5%

  • but if one can verify those prediction …

Apparent reduction if Lc/D ~1

consistent with RHIC data

(pt~2-4 GeV)

Heavy-Flavor and jet quenching- Workshop, Padova 29-9-2005

Thermalization w “D”-Mesons

Cross section

Equilibration time




Isotropicangular distribution sres essential for thermalization

What is the RAA and v2 ?

Transport approximated Fokker-Plank equation

Background not affected by heavy quarks

Heavy-Flavor Baseline Spectra at RHIC

Single-Electron Decays


  • bottom crossing at 5GeV !?

  • strategy: fix charm with D-mesons,

  • adjust bottom in e±-spectra

Inclusion of radiative E-loss

w/o gluon radiation

I. Vitev, A. Adil, H. van Hees, hep-ph/0701188

Improve treatment of fluctuations (not Gaussian)

Include hadronization: coal+ fragmentation

RAA & v2 for D/B mesons at LHC

  • D and B via coalescence+ fragmentation!

    • coalescence leads to increase both RAA and v2

    • resonant scattering factor 3 in v2

What happens at lower energy –RHIC @62?

Uncertainties: amount of quenching,

bulk properties (ET, mb,..), p fragmentation


Without changing any

coalescence parameter!

p+/pincrease by 20%

p-/pdecrease slight decrease

Greco ,Ko, Vitev - PRC71

Balance between fragmentation

(w quenching) and coalescence

What happens at higher energy - LHC?

  • Uncertainties:

  • - radial flow (b=0.65-075)

  • jet quenching

  • What about the v2 ?

  • we will see the scaling?

  • r-p correlation will be so nice at LHC?

Fries, Muller, EPJ C34:S279 (2004).

Similar trend for MICOR + pQCD(quenched)

P. Levai - ALICE Week- February 2007

Charm reaching thermalization?

Shadowing not included yet!

Spectra same parameter of PPR-ALICE



  • LHC spectra considerably harder !

    • At Tc charm nearly thermalized

    • Resonances switched-off above 2 Tc

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