V. Greco

BNL , 29 April 2005BNL , 29 April 2005

ReCo Overview & ReCo Overview & ProspectivesProspectives

Overview:Overview: Early successes of Reco+Fragm.

pT spectra ( enh. B/M ratio, RAA , Rcp ) Elliptic Flow (“scaling”)

Developments I: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

baryon/mesonpattern

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

Relation to EOS-WG Topics

Result robustvs uncertainties

Hadrons at RHIC

suppression: evidence of jet quenching before fragmentation

Fragmentation p/ Jet quenching should affect bothFragmentation is not the dominant

mechanism of hadronization at pT < 4-6GeV !?

PHENIX, nucl-ex/0212014

PHENIX, nucl-ex/0304022

pionspions protonsprotons

Coalescence vs. Fragmentation

Coalescence:

partons are already there ph= n pT ,, n = 2 , 3$ to be close in phase space $

Even if eventually Fragmentation takes over …

Fragmentation: Leading parton pT ph= z pT

according to a probability Dh(z)

z < 1, energy needed to create quarks from vacuum

Parton spectrum

B M

H

Partonic Hydro behavior shifted at higher pT

Phase-Space Coalescence

)(δ)...,...(),()π2(

σ 111

3

3

i2 iTTnnH

n

iiiq

iiH

T

H ppppxxfpxfpd

dpgpd

dN

fq invariant parton distribution function thermal (mq=0.3 GeV, ms=0.47 GeV)

with radial flow (=0.5)+

quenched minijets (L/= 3.5, mq=0.01GeV, ms=0.175 GeV)

fH hadron Wigner function

2

21

2

21

22

21

2 )()()(2

π9mmppxxf pxM

x =p ~ 0.85 fm coalescence radius parameter

|Mqq->m|2 depends only on the phase space weighted by wave function; npQCD also encoded in the quark masses (gluon dressing), mq=0.3 GeV, ms=0.475 GeV.

TAMU implementation

5.0|| yET ~ 730 GeV

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

V ~ 900 fm-3

GeVfm-3

dS/dy ~ 4800

L/

T=170 MeV

P. Levai et al., NPA698(02)631

quenchedsoft hard

Locally v1, u1 … not small

Coalescence on bulk matter consistent with hydro, experiments, c

Coalescence Integral solved in a 3D geometry, with radial flow space-momentum correlation (important to fix bulk parton distribution)

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

ReCo dominates up to 4..6 GeV/c; fragmentation and energy loss takes over above.

Baryon/Meson ratio

DUKE

OREGON

TAMU

DUKE

Elliptic Flow

D. Molnar and S.A. Voloshin, PRL91 (03)

/3)(p3v)(pv

/2)(p2v)(pv

Tq2,TB2,

Tq2,TM2,

Enhancement of partonic vEnhancement of partonic v22Coalescence scalingCoalescence scaling

n

p

nT

2V1

Shape consistent with cascade(AMPT, MPC)

To be seen, breaking of the scaling !

Duke

v2,q from a fit to data v2 p, K, prediction

w.f. effect 5% B/M breaking p ~0.25 GeV)Large breaking if p >> (OSU, PRC68)

Effect of Resonances & wave function

K, , p … v2 not affected by resonances! coal. moved towards data

V.G., C.M. Ko, PRC 70 (03)

w.f. + resonance decay

K & p

*

from

Resonances IIK* from QGP decays into a K with a v2 ~ to K directly produced

HG resonances: hadron final stage, h-h rescattering scaling with n=4

K

7.0:)( TPr

HG2

QGP2

full2 ))(1()( vPrvPrv TT )( TPr )( TPr

Medium effects: m* shift v2 of decay product

C. Nonaka , PRC69, 31902 (2004)

r (pT ) is determined by experiments and related to width of particles and cross section in the hadronic medium.

No sensitive to resonance width(Final spectra weak dependence)

Can we learn more via the analisis of resonances v2?Can we see evidence of chiral symmetry restoration?

’s from

Polarized QGP?

Z.T. Liang, X.N. Wang, PRL94,102301(05)

Global transverse polarization in the direction orthogonal to the reactionplane

MECHANISM: qq collision carry an angular momentum that can be transferred to the spin due to spin-orbital coupling

3

1

3

12

2

00

q

q

P

P

dx

dpxpxL z

zy

2~~

Pq degree of quark polarization

Higher Fock StateCostituent quark picture is a good description of hadron PDFas Q2 < 1 GeV2 (higher Fock state are suppressed)Still contribution from higher terms may not be negligible

B. Muller, nucl-th0503003

...321 qqqqcgqqcqqcM Is v2 scaling preserved?

Spectra are also 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 quark

For narrow w.f. limitStandard higher twist w.f

Charmed elliptic flow

V2q from , p, K, L

Coalescence can predictv2D for v2c = 0

S. Kelly,QM04V2 of electrons

V.G. et al., PLB595 (04) 202

Flow mass effect

Charm in a sQGP

Do heavy Flavor Equilibrate (strongly interact)?

Fokker-Plank approach on a hydro bulk evolution

Charm scatters with D hadronic (chiral restored) resonances in the QGP (Van Hees, Rapp, nucl-th/0412015 )

At high pT even light quarks don’t thermalize !

Isotropic cross section

Therm +flow

What happens at lower energy?

p+/ increase by 20%p/ decrease slight decrease

Without changing any coalescence parameter!

V. G., C. Ko, I.Vitev, nucl-th/0412043

Jet quenching from I. Vitev, PLB606, 303 (05)

Balance between fragmentation (w quenching) and coalescence

Uncertainties: amount of quenching,bulk properties (ET, b,..), p fragmentationfunction

Jet-like Correlation

ijijCwwwwW 143211234

20

220 //1cos

000 ,,,;, yyy

TjTijijjiiijjiji eeppfrrScprprC

Factorized Ansatz Factorized Ansatz • Gaussian correlations in azimuthal angle and rapidity y:

– S0=1 inside a Vc ( Vc ~const , Vc ~Npart )

– f0 =1 (weak pT dependence)

– C0 and 0 fixed to fit data

Correlation in the parton distribution

Different processes :F-F, SS-SS, F-SH, F-SS,SH-SH,SH-SS

Recombination enhancesRecombination enhancescorrelations in the parton phase, correlations in the parton phase, ( ~ amplification of elliptic flow)( ~ amplification of elliptic flow)

Source of correlation are jets: dumpenergy and partons into medium

ABAB YdY94.0

0

cone

Large correlationsfrom F-F, favoringbaryon triggers.

Lower associated yield when adding SS-SSwithout correlations(C0=0), especially for baryon triggers.

Mesons Baryons F-F and SS-SS withC0=0.08, Vc~Npart.

F-F and SS-SS withC0=0.08x100/Npart

(Vc~const.)

F-SH (- only)v=0.5

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 f0from R. Fries, HQ04

2/20

2 2/0

eNNQCYN BAABA

Numerical example

Constituent quark masses close in phase space hadronize to giveintermediate 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 ( @ pq > 0.75 GeV)

Result robust against uncertainty in resonance decay, wave function

(shape, presence of higher Fock state)

Need further investigationNeed further investigationEvolution with beam energy (breakdown point?) Jet-like Correlation Non Zero Rapidity

Connection to QCDConnection to QCD - Chiral Symmetry - Confinement Low pLow pTT

- Energy conservation - Entropy conservation - Particle conservation

What Can we say?

From Fragmentation to ReCo• Fragmentation: 1 parton has to hadronize (e+e-,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

R. Fries,HQ04At very low pT most hadrons are formed via coalescence (Voloshin, NPA715 (03))

(AA)

Bulk : Charge Fluctuations

kiik

ikii

i

ch

nncnqN

QD 2

2

4

Recombination with all the quark converted into baryon and meson

Neglecting: Correlations cik

Hadronic diffusion Gluons qqssdduu NNNNNNNQ

45

11

9

1

9

42

Close to the value used in V.G., PRC68 : Nq ~ 1100

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

Can we understand the results of fluctuations measurements?Are they compatible with a deconfined medium?

Entropy Conservation

Non-Relativistic/ no quantum effect

thN

NN

TNS log

2

5

2

5

1) g suppose mgm

gg NS 5.2 g

g

g Ng

gNS 8.0log

2

5

70% decrease

2) Our Coalescence (PRC68, 034904)

40804800 HADQGP SS16 % decrease

Volume expansion ( ~ 4 fm/c)

%18/ EE ZTT

ES log

1

But, the energy is not conserved !No factor 2 or more due to:- mass of the particle- off- equilibrium effect

Moreover entropy in the quark phaseMay be reduced by interactionC. Nonaka et al., nucl-th/0501028

What is the role of the mass?

Massive quarksmu ~ 0.3 GeVms ~ 0.5 GeV

What mass is it? It’s a thermal mass(zero component of vector self energy)

0.02 GeV

0.3 GeV

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)

Spectral function represents an effective way of treating off-shell effect due to the presence of the medium

Thermal masses and energy conservation

Thermal masses are related to EOS in a quasi-particle picture, but interactionis still important !

Self-consistent Dirac-Brueckner (DB)with a LQCD potential : hadronic resonances with chiral restored phaseM.Mannarelli and R.Rapp, work in progr.

Check Consistency with LQCD resonance spectral function

)(Re2/122 kmk Dp

0

0,)(Im2)( kk

4/)()(

)(,

22 k

kkA

p

LQCD V(r)

EOS

Spectralfunction

DB

Input of Coalescence

To be checked: properties of standard coalescence are preserved

Link to LQCD Energy Conservation ( Entropy , Resonances)

Confinement, or use of all Nquark is still pending

Recombination with thermal masses (from LQCD) Recombination with thermal masses (from LQCD)

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

Dynamical Coalescence

Quasi particle massive quarks interacting through LQCD potential

Investigation of Coalescence-Clusterization like in molecular dynamics

Does Coalescence work at low pT ?

Better enviroment for:

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 ..

Of Course our hope is to invalidate recombination! Right!

Heavy quark should be a better starting point for a decriptionIn term of q-q potential, more sophisticated model for J/, Y …

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

Summary