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V. Greco Universita’ di Catania, Italy INFN-LNS

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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

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

Outline

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

In-medium

Non-abelian

energy-loss

- Strong (Flat) suppression explained by jet quenching
- Proton not suppressed ?!

H

Parton spectrum

Surprises…

Baryon/Mesons

Coalescence

Baryon

Au+Au

Coal.

Meson

p+p

Fragmentation

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

quenched

soft

hard

e ~ 0.8 GeVfm-3

dS/dy ~ 4800

L/l=3.5

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

p,r,w,K,K*,p,D,L,S...

Baryons vs Meson

r-> pp

TAMU

DUKE

v2q fitted from v2p

TAMU

OREGON

Fries et al., PRC68

Meson & Baryon Spectra

Au+Au @200AGeV (central)

sh

L/K

- Proton suppression hidden
by coalescence!

Greco-Ko-Levai, PRL90 (03)202302

PRC68(03) 034904

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

PRC68(03)44902

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

PHENIX, PRL (07)

Coalescence scaling

Enhancement of v2

- nq - not a mass effect
- Most of flow is partonic

z

y

x

v2 develops t<5fm

Hydro & cascade

x - p correlation neglected

narrow wave function

Molnar and Voloshin, PRL91 (2003)

baryons

mesons

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

- v2 pions from rho decay
- (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

but

S. Kelly,QM04

V2 of electrons

Greco-Ko-Rapp, PLB595 (04) 202

RAA , v2 of single e -pQCD

q

q

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

1.4Tc

[Asakawa+

Hatsuda ’03]

Spectral function in lQCD

A(w)=w2r (w)

Asakawa

J/Y

Similar from Potential model for J/Y

Mannarelli, Rapp - PRC72 (Bruckner-like)

Alberico, Beraudo, De Pace - PRD 72 & 75

Petrecsky,Mocsy,Wong….

J/y (p = 0) disappears

between 1.62Tc and 1.70Tc

- 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

PYTHIA (PDF’s + pQCD )

c,b quarks

HQ scattering in QGP

Langevin simulation

in Hydro bulk

sQGP

Hadronization

Coalescence + Fragmentation

c,b

K

D,B

Semileptonic decay

RAA & v2 of “non-photonic” e

e

ne

Charm reaching thermalization?!

Pythia

Therm+Flow

coalescence

+ fragment.

fq from p, K

Greco,Ko,Levai - PRL90

Hees, Greco, Rapp - PRC73

pQCD

Reson.

- 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

Ncoal/NINI

Greco, Ko, Rapp

PLB595(2004)

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

RHIC

LHC

bottom

bottom

charm

charm

- 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

RHIC

LHC

from D only

ALICE

- 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!

Summary

- 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.

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

pQCD

QGP- RHIC

“D”

Isotropicangular distribution sres essential for thermalization

What is the RAA and v2 ?

Transport approximated Fokker-Plank equation

Background not affected by heavy quarks

Single-Electron Decays

D-Mesons

- 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

function

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

Pythia

Therm+Flow

- LHC spectra considerably harder !
- At Tc charm nearly thermalized
- Resonances switched-off above 2 Tc