V. GrecoUniversità di Catania, ItalyINFN-LNS

Coalescence models for

hadronization in uRHIC

?

International Workshop XXXVIII on Gross Properties of Nuclei and Nuclear ExcitationsInternational Workshop XXXVIII on Gross Properties of Nuclei and Nuclear ExcitationsHirschegg, Austria, January 17 - 23, 2010Hirschegg, Austria, January 17 - 23, 2010

Relevance for : the Heavy-Quark Sectorthe Heavy-Quark Sector /s of sQGP/s of sQGP A role in the Mach Cones ?A role in the Mach Cones ?

Observation at RHIC hadronization modified RAA-RCP-V2 for baryon and mesons

Ou

tlin

eIntro to Basic Idea & Relevance for sQGP

Basic Theory of coalescence (phase –space) coal. vs fragm. - application to RHIC RAA – v2 and B/M in the coalescence mechanism

Extensions from early realizations Robustness and open issues Formulation from Boltzmann collision integral

Surprises…

In vacuum pp collisions: p/ ~ 0.3

Hadronization has been modifiedHadronization has been modified1< p1< pTT < 5-6GeV !? (> 10 T < 5-6GeV !? (> 10 Tmaxmax))

PHENIX, PRL89(2003)

Baryon/MesonsBaryon/Mesons

Protons appear not suppressed!

QuenchingQuenching

Au+Au

p+p

Jet quenching should affect both

suppression: evidence of jet quenching

before fragmentation

Hadronization in Heavy-Ion CollisionsInitial state: no partons in the vacuum but a thermal ensemble of partonsThe bulk hadronization dynamics much less violent (t ~ 4 fm/c)dense parton systems no need for creation and splitting of partons

Parton spectrum

H

Baryon

Meson

Coal.

Fragmentation

V. Greco et al./ R.J. Fries et al., PRL 90(2003)

Fragmentation: energy needed to create quarks from vacuum hadrons from higher pT

partons are already there $ to be close in phase space $

ph= n pT ,, n = 2 , 3 baryons from lower momenta (denser)

Coalescence:

ReCo pushes out soft ReCo pushes out soft physicsphysicsby factors x2 and x3 !by factors x2 and x3 !

Basic TheoryDiscard details of dynamics -> adiabatic approximation:instantaneous projection of initial state onto final cluster

- Go in the momentum frame- Neglect the transverse momentum- Neglect r,p correlations -> only p-space- direct production (no resonances)

M(r,q) Meson wave function

All fairly good approximationsAt pT > 2 GeV/cxi light-cone momentum fraction

ababMbbbaaba

aM qrprfprfPd

dN,),(),(

,3

Approximation in FMNB (Hwa-Yang)

CM spin-isospin color factor

fragmenting:Ph = z pq, z<1

Recombining :X1Ph+x2Ph=Ph

Fries, QM’04

1

0 21212133,)()(

)2(xxPxfPxfdxdx

PdC

Pd

dNMbaM

M

Fries-Nonaka-Muller-Bass, PRC68(03)

Specific features of Reco in HICSpecific features of Reco in HIC

ReCo for ReCo for power lawpower law jet jet spectraspectra

Tpth Aef /

Bpf jetnn

jet pBC BpFjet

)1(nTp

F

CEven if eventually Fragmentation takes over …

Need of Coalescence + Fragmentation modelNeed of Coalescence + Fragmentation model

Both mesons and baryons have the same distribution at variance with fragmentation

P-> ∞ or m=0

1 ba xx

TPTPxxTPxTPx eeee baba //)(// Meson

ReCo is very effective for ReCo is very effective for thermal thermal spectraspectra::

Fragmentation for Fragmentation for power lawpower law spectra: spectra:

shift small power enhancement Suppressed by a power n=# of quarks

TPTPxxxTPxTPxTPx eeeee bbacba //)(/// Baryon

for power law spectra

Phase-Space Coalescence (GKL)

)(δ)...,...(),()π2(

σ 111

3

3

i2 iTTnnH

n

iiiq

iiH

T

H ppppxxfpxfpd

dpgpd

dN

)(δ)...,...(),()π2(

σ 111

3

3

i2 iTTnnH

n

iiiq

iiH

T

H ppppxxfpxfpd

dpgpd

dN

ffHH hadron Wigner hadron Wigner functionfunction 2

21

2

21

22

21

2 )()()(2

π9mmppxxf pxM 2

21

2

21

22

21

2 )()()(2

π9mmppxxf pxM

3D-geometry with radial flow space-momentum correlation

ET ~ 740 GeV

T ~ 170 MeV(r)~ 0.5 r/R

GeVfm-3

dS/dy ~ 4800

Experiments

lQCD Tc

like Hydro

L/

T=170 MeV

P. Levai et al., NPA698(02)

quenched

soft hardBulk matter consistent with hydro, experiments,

lQCD

Bulk matter consistent with hydro, experiments,

lQCD

x =p

Meson & Baryon Spectra

V. Greco et al., PRL90 (03)202302 PRC68(03) 034904R. Fries et al., PRL90(03)202303 PRC68(03)44902R. C. Hwa et al., PRC66(02)025205

Au+Au @200AGeV (central)ππρ

Proton suppression hidden by coalescence!

sh

GKL FMNB

ReCo dominates up to 4 (meson)6(baryon) GeV/c; Fragmentation + energy loss takes over above.

Baryon/Meson ratio

TAMU

FMNB Hwa-Yang

Strange particlesfrom a common

quark flow

A Coalescence process carries with it A Coalescence process carries with it another featureanother feature

thanks to non-equilibrium thanks to non-equilibrium

x

yz

px

py

22

22

2 2cosyx

yx

pp

ppv

22

22

xy

xyx

c2s=dP/d

Mass-dependence of v2(pT) suggests common transverse velocity field large At higher pT v2 for Baryon=Mesons in both - hydrodynamics - jet fragmentation

Again surprise Baryon Again surprise Baryon ≠≠ Mesons : vMesons : v22 larger for Baryons larger for Baryons

Elliptic flow at intermediate pT

Coalescence carries another features …Coalescence carries another features …

/3)(p3v)(pv

/2)(p2v)(pv

Tq2,TB2,

Tq2,TM2,

Enhancement of vEnhancement of v22Coalescence scalingCoalescence scaling

n

p

nT

2V1

baryons

mesons

Molnar and Voloshin, PRL91 (2003)

2

22)2()(

T

T

q

T

T

M ppd

dNαp

pd

dN

3

22)3()(

T

T

q

T

T

B ppd

dNp

pd

dN

)2cos(v21φ 2

TT

q

TT

q

dpp

dN

ddpp

dN

Considering only momentum space x - p correlation neglected

narrow wave function collinear approximation

v2 for baryon is larger and saturates at higher pT

v2q fitted from v2

GKL

Quark number scaling!

Again agreement with Again agreement with unexpected observationunexpected observation

No free parameter !No free parameter !

Better scaling vs KET/nq <–> energy conservation

Scaling widely confirmed for all species and centralitiesScaling widely confirmed for all species and centralitiesR. Lacey, PoS CFRNC2006:021,2006. e-Print: nucl-ex/0610029

Is the vIs the v22 (p (pTT) needed by coalescence ) needed by coalescence compatible with a fluid compatible with a fluid /s /s ~ 0.1-0.2~ 0.1-0.2 ? ?

0mmKE TT

But it also means that vBut it also means that v2q2q ~ ~ vv2h2h/2/2

Motivation for a Transport approachMotivation for a Transport approachSolved discretizing the space in x, ycells

It is a 3+1D (viscous hydro 2+1D till now) No gradient expansion, full calculation valid also at intermediate pvalid also at intermediate pTT out of equilibrium out of equilibrium QNS QNS valid at high valid at high /s /s study the effect of the hadronic phasestudy the effect of the hadronic phase include hadronization by coalescence+fragmentationinclude hadronization by coalescence+fragmentation Extension to Bulk viscosity Extension to Bulk viscosity (related also to chiral mass generation)(related also to chiral mass generation)

Simulate a fluid at constant shear viscositySimulate a fluid at constant shear viscosity

sn

pTr trtr /

1

15

1)),(( ,

=cell index in the r-spaceTime-Space dependent cross Time-Space dependent cross

section evaluated locallysection evaluated locally

(see also D. Molnar arXiV:0806.0026)

cost.15

1

n

p

s tr

Relativistic Kinetic theory Cascade code

G. Ferini, PLB670(2009)325V. Greco, Prog. Part. Nucl. Phys. 62 (2009) 562Extensions to NJL dynamics -Plumari et al., 1001.2736 [hep-ph] - yesterday

4/s >3 too low v2(pT) at pT1.5 GeV/c even with coalescence

4/s =1 not small enough to get the large v2(pT) at pT2 GeV/c

without coalescence

Agreement with Hydro at low pT

Parton Cascade at fixed shear viscosity

Role of Reco for /s estimate

Hadronic Hadronic /s included /s included

shape for vshape for v22(p(pTT) )

consistent with that consistent with that

needed needed

by coalescenceby coalescence

20-30% centrality

A quantitative estimate needs an EOS with phase transition: vs

2(T) < 1/3 -> v2 suppression ~~ 30%

-> /s ~ 0.1 may be in ~ 0.1 may be in

agreement agreement with coalesccencewith coalesccence

RRcpcp~~1 with large v1 with large v22

Coalescence revertsreverts the correlationbetween RAA & v2: both are enhanced

This rules out other explanations:Baryon junctions, hydro+jets

This effect is essential also for thestudy of charm quark interaction !

P.Sorensen

RRCPCP and v and v22 Correlation:putting together observations! Correlation:putting together observations!

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

1)1)ResonancesResonances (included in GKL)(included in GKL)

2)2)Finite width Wave functionFinite width Wave function

3)3)GluonsGluons ALCOR, GKL : mass suppressed, quark dressing,

splitting Higher Fock States, Fries-Muller-Bass, PLB618 (05)

4) 4) Energy ConservationEnergy Conservation not large 17% in GKL, resonances decay & v2

Boltzmann Collision Integral approach: Ravagli-Rapp PLB655(2007)

5) Entropy Conservation5) Entropy Conservation 15% like energy – mass, resonances, expansion

6) Relation to jet-like correlations6) Relation to jet-like correlations Consistent with ReCo- Fries et al., PRL94, but need of a

transport description

7) Space-momentum correlations affect v7) Space-momentum correlations affect v22 scaling scaling

Pratt-Pal PRC71, Molnar nucl-th/0408044 , Greco-Ko nucl-

th/0505061, Rapp-Ravagli PRC79

Less important at high pT

Stability of Reco results respect

uncertainties in their treatment

high pT the problem suppressed

by m/pT

but even at low pT

is not so drammatic

Resonances & v2 scaling

K, , p … v2 not affected by resonances!

coal. moved towards data Greco-Ko, PRC 70 (03)

w.f. + resonance decay

K & p

*

from

Does mesons & baryons from resonance decay preserve the QNS?

2 ->1->2 can exihibt the scaling!

Dependence on wave function of v2 scaling

p momentum width of w.f.Baryon-to-Meson breaking of the scaling

Wavefunction+ Resonance decays

Breaking :

increasing with p

decreasing with pT

Higher Fock StateCostituent quark picture is a good description of hadron PDFas Q2 < 1 GeV2 (higher Fock state are suppressed)

B. Muller et al., PLB618(05)

...321 qqqqcgqqcqqcM

vv22 scaling scaling is preservedis preserved

Spectra are not affected (at least pT >> m )

pn

n

n

nCp

pn

n

n

nCp

M

M

B

B

vBB

M

M

M

M

vMM

)(

)(

12)(

1

)()(

2

)(

)(

12)(

1

)()(

2

v)(v~

v)(v~

Fock state, n = # partons)5.11(

3

2

2

3

1

sv

s

s

n

n

s = # of sea partons

For narrow w.f. limit

Standard higher twist w.f

Entropy Conservation?Entropy Conservation?Assuming hadronization linear with t during a mixed phase with the spectra of the static GKL model (

SSEE // ZTT

ES log

1

Energy is also not conserved !

15% violation, No factor 2 :- resonances- mass of the particle- degeneracies

Entropy- Energy ConservationEntropy- Energy Conservation

Entropy violation is also related to energy conservation and not to ReCo

Greco, EPJ ST155(2008)35004000 HADQGP SS

Transport approach to Coalescence->Energy Conservation Transport approach to Coalescence->Energy Conservation Miao et al., PRC75(2007)Rapp-Ravagli, PLB655(2007)

Solve energy conservation (except Solve energy conservation (except ))Clarify relation to statistical modelClarify relation to statistical modelKeeps features of coalescence:Keeps features of coalescence:

- show a KET scaling of v- show a KET scaling of v22/n/nqq

- baryon/meson enhancement- baryon/meson enhancement

Equilibrium solution h>>eq

givesProductionAbsorption

meson

Essential property:Essential property:- Product f(pProduct f(p11)* f(p)* f(p22) of 2 distr. funct.) of 2 distr. funct.- suppressed when psuppressed when p11pp22 is too large is too large

r-p from Fokker Planck r-p from Fokker Planck still preservestill preserve

Quark Number ScalingQuark Number Scaling

Ravagli et al. PRC79 (2008)

Good quark number scaling except for too large Q value (<300 MeV) (similar to not too large width

and or non zero quark mass)

KET scaling down to low pT

VV22 quark # Scaling with Energy quark # Scaling with Energy ConservationConservation Scattering for q,Q in QGPScattering for q,Q in QGP

2

2)(

p

fD

p

pf

t

f qqq

Including space-momentum correlation

What happens What happens

to heavy quarks?to heavy quarks?

G.D. Moore and D. Teaney, PRC70 (2005) nucl-th/0412346

Problematic relation of RAA and V2 for heavy quarks

Up-Scaling elastic scattering from pQCD

Too low RAA or

too low v2

Coalescence modifyv2D RAA correlation

datadata

The same problem (even worse!) for radiative energy loss: S. Wicks et al., nucl-th/07010631(QM06), N. Armesto et al., PLB637(2006)362

A() 2()Asakawa

J/

Spectral function in lQCD & ResonancesSpectral function in lQCD & Resonances

VGTVT

qg

Q TS

QQQQQ SSSS 0

q-c “Im T”q-c “Im T” dominated by meson and diquark channel

lQCD

pQCD

Opposite T-dependence of Opposite T-dependence of

Fric

tion

coef

ficie

nt

V(r) - lQCD

Impact of Hadronization for heavy quarksImpact of Hadronization for heavy quarksHQ scattering in QGPHQ scattering in QGP

Langevin simulationin Hydro bulk

HadronizationHadronization

Coalescence + Fragmentation

sQGP2

,2

,, )(

p

fD

p

pf

t

f bcbcbc

BDbcbcMqbcBDBD DfffC

Pd

Nd,,,,,3

,3c,bc,b D,B

, D from resonantscattering according to lQCD V(r)

Van Hees-Mannarelli-Greco-Rapp, PRL100 (2008)

Improved RAA - V2 correlation

• toward a better agreement with data thanks to

a T dependence of the scattering opposite to pQCD

• coalescence can be viewed as coalescence can be viewed as a manifestation of T-matrix interaction a manifestation of T-matrix interaction

in the hadronization processin the hadronization process

Impact of hadronizationImpact of hadronization

Regeneration is revealed in : - pt spectra - elliptic flow

Implication for Quarkonium

Till now we have mainly looked at only J/Y yield, but thanks to coalescence there is a common c-quark collective dynamics with D meson …

Greco, Ko, Rapp PLB595(2004)

Jcoal.

No feed-downNo direct contr.

Suppression only

v2 from v2D :measure of

Ncoal/NINI

Coalecence only

pT- Quarkoniafrom regeneration

are consistent with Open heavy flavor!?

The open issue with the Mach-ConeThe open issue with the Mach-Cone

with G. Torrieri, J. Noronha, M. Gyulassy

A first look at the problem in the coalescence A first look at the problem in the coalescence modelmodel

away

near

Medium Cone Jet

(medium excitation)

High pHigh pTT Parton Parton Lower p Lower pTT “Mach “Mach Cone”?Cone”?

Properties of the cone:Properties of the cone:

angle does not depend on pt

ratio of B/M similar to the bulk one at the same pt

Peaks at the same angle for Baryon and Mesons

Afaniasev, PRL101 (2008)

cSv

cos 1 rad

Range of pRange of pTT is that where is that where

coalescence has manifested coalescence has manifested

its features its features ……

We used the Montecarlo simulations

At such pT coalescence is expected to play a role …Can it affect the peak structure?!

UL=UT=0.3 is the collective velocity in the wave generated by the jet

The double peak is not so easily produced in HydroThe double peak is not so easily produced in HydroHydro simulationHydro simulationLinearized hydro + AdS CFTLinearized hydro + AdS CFT

Quark distribution function before space integrationQuark distribution function before space integration

B.Betz,JPG35

Pure E depos.

Pure p depos.

Results for mesons

Mesons at 2 GeV show a dN/d with 2 peaks even if they come from quarks at 1 GeV that have only 1 peak

The position of the peaks is independent on pT like in experiments

Meson

pd

dN

/

p

Quark

pT

V.G., Torrieri, Noronha,Gyulassy, NPA830(2009)

Meson vs Baryon Meson vs Baryon One may expect a difference between baryon and meson!In the experiment is not observed a difference

But indeed coalescence generates a similar shapefor both angle and width

Why one should expect the same angle? and especiallyThe same depths of the peaks

Angle and depth of the signallook very similar.

Why the peak shows up?Why the peak shows up?The peak is created by the locality od coalescence. The two branches of the wavedoes not talk. Coalescence enhances the peak at each side and then summing up a dip appears.a dip appears.

Meson

Why baryons=mesons?Why baryons=mesons?Correlation should increase, but at pT/3

angular correlations is weaker -> exact compensation and meson/baryon Mach shape are similar.

Why two peaks? Why similar shape for Baryon and Meson?Why two peaks? Why similar shape for Baryon and Meson?

p

quark

meson

)2/()( 2TqTM pfpf

Considering only one side

Considering only one side

)3/()( 3TqTB pfpf

Take home messagesTake home messages (please!)

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

dense medium decrease the role of the vacuum massive quarks close in phase space

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

Universal elliptic flow (dynamical quarks “visible”): carried by quarks enhanced by coalescence consistent with/s =0.1 ?!

R.J. Fries, V. Greco, P. Sorensen - Ann. Rev. Part. Sci. 58, 177 (2008)

Result are robust against, uncertainty in resonance production,Result are robust against, uncertainty in resonance production,wave function, higher Fock states, energy conservationwave function, higher Fock states, energy conservation

It’s not a question of twiggling parameters to get a better fit to It’s not a question of twiggling parameters to get a better fit to the data, the data,

but there is a physical mechanism that generates relations but there is a physical mechanism that generates relations between between

RRAA AA (R(RCpCp) - v) - v22 for light and for light and heavy quarksheavy quarks + baryon/meson + baryon/meson

branches branches hard hard to get without a coalescence model to get without a coalescence model

More Recent PerspectivesMore Recent Perspectives

Mach-Cone like peaksMach-Cone like peaks: Hard to get but again coalescence can only help …

and this is another consistency

Role inRole in/s determination:/s determination: Transport Theory can entail a consistency between

QNS and /s =0.1-0.2

Heavy Quark interaction in QGP:Heavy Quark interaction in QGP: RAA and v2(pT) explained only if coalescence is present

Consistency between D and J/Y spectra: one underlying c

Open IssuesOpen Issues

Role of Confinement - Vij(r,T) from lQCD (for heavy quarks)

- String Fragm.+ Coalescence+ Indipendent Fragmentation

Statistical Model (RR,Miao-Gao…) - Probability of resonance formation (entropy-energy)

Implementation coupled to Transport equations: - role in of correlation in v2 scaling - 2-3 particle jet correlation

Role of finite mass - 3D

Importance of 3D phase-space lowering pT

At low pT scaling can be largely brokenbut dumped by the shape of v2(pT)

Lower mass lead to larger breakingof the scaling due to coalescencebetween quark with large q=p1-p2

2 schematic cases

The observed scaling tells that the coalescingThe observed scaling tells that the coalescingquarks have small relative momentum!quarks have small relative momentum!

realistic shape

Exercise: Entropy of a gas with g d.o.f

Non-RelativisticNo quantistic

thN

NN

TNS log

2

5

2

5

1) g suppose mgm70% decrease

gg NS 5.2g

gg N

g

gNS 3.0log

2

5

3) Coalescence with (PRC68, 034904) - 16 % decrease

Gluon gas at equilibrium Pion gas out-of-equilibrium

Volume expansion needed to compensate the decrease is much larger than in coalecence model

ggg SNNS 7.08.12log2

5

2) Only qq m 28% decrease

N. Armesto et al., PLB637(2006)362S. Wicks et al., nucl-th/07010631(QM06)

lQCD resonant (bound) states persistlQCD resonant (bound) states persistfor QQ and qq -> Qq (D-like) resonant scatteringfor QQ and qq -> Qq (D-like) resonant scattering

lQCD resonant (bound) states persistlQCD resonant (bound) states persistfor QQ and qq -> Qq (D-like) resonant scatteringfor QQ and qq -> Qq (D-like) resonant scattering

RRAA AA , v, v22 of single e – Jet Quenching of single e – Jet Quenching

Radiative energy loss not sufficient

sQGP: non perturbative effect qq

Main Challenge is the in-medium quark interactionMain Challenge is the in-medium quark interaction

Effect of Effect of /s on the hadronic phase/s on the hadronic phase

Does the NJL chiral phase transition affect the elliptic flow of a fluid at fixed /s?

e-Print: arXiv:1001.2736 [hep-ph] - yesterday

Bulk : Charge Fluctuations

kiik

ikii

i

ch

nncnqN

QD 2

2

4

Recombination with all the quark converted into baryon and meson

Correlations cik

Neglecting: Hadronic diffusion Gluons

qqssdduu NNNNNNNQ 45

11

9

1

9

42

Close to the value used in Close to the value used in GKL, PRC68 : NGKL, PRC68 : Nqq ~ 1200 ~ 1200

ALCOR, PLB**: NALCOR, PLB**: Nq q ~~ 1300 1300

Statistical model Nhad at Tc & from recombination Nquark

C. Nonaka et al., nucl-th/0501028

Nhad = 507 (635)Nquark= 1125 (1377)

( ) nonet mesons +octet & decuplet baryons

)350(290

3702

2

COAL

EXP

Q

Q

STAR, PRC68 (2003) 44905

Same Side Correlation at intermediate Same Side Correlation at intermediate pptt

Away Side: quenching has di-jet structure

Same Side: hadrons correlated like in jet

framentation at the same pT where Reco manifest

itself . Is this compatible?

Trigger is a particle at

4 GeV < pTrig < 6 GeV

Associated is a particle at

2 GeV < pT < pTrig

trigger

Assoc.

quenched

φ

φ

)φ()φ(

)φ()φ(

)φ(

pp

AuAuAA

ddN

d

ddN

d

I

away

Same

Yield of correlated Hadrons respect to pp

CorrelationsCorrelations

Coalescence+FragmentationCoalescence+Fragmentation

reproduce the relative strength reproduce the relative strength

with baryon and meson triggerwith baryon and meson trigger

Any residual interaction in f(p)

lead correlation in the coalescing hadronsSimilar to effect on v2

to be seen the assumed Cto be seen the assumed Cabab is dynamical reproduceble at is dynamical reproduceble at RHICRHIC-> coupling to transport approach-> coupling to transport approach

Fries et al., PRL94 (2005)

Meson trigger Baryon trigger

2-parton correlation fromjet-bulk interaction

20/1cos

0 jiecCab

c0 and 0 fixed to fit data

pions protons

Miao et al., PRC76(07) - using the Bolzmann Collision approach

Baryon and Mesons spectra

Particles included-> agreement alsoOn yields

)()(

)()()(

xx

xxx

DD

DD

E791 beam: - hard cc production;- c recombine with d valence from - D enhancement

Braaten, Jia, Mehen: Phys. Rev. Lett. 89, 122002 (2002)

Quark-Antiquark Recombination in the Fragmentation Region K.P. Das & R.C. Hwa: Phys. Lett. B68, 459 (1977):

Sea quarks Recombination at XF = 0Rapp and Shuryak, Phys. Rev. D67, 074036 (2003)

Leading Particle EffectReservoir of partons modifies hadronization

Similarly for

at ISR/Fermilab (late ‘70)

In HIC the resorvoir is the thermal bulk!

)(

)(

ucD

dcD

)( ud

=0 from LO fragmentation

beam

A drawback: for themal distrbution there is exact compensation between the shift in pT of coalescence and the enhancement of correlation with pT