Light and Heavy Hadrons in Medium

Ralf Rapp

Cyclotron Inst. and Physics Dept.

Texas A&M University College Station, USA

Frankfurt am Main, 25.06.04

1.Introduction: Towards the Phase Transition

note: high-density CFL phase (CSC) characterized by “hadronic” excitations (“”, “”, …)

0 0.05 0.3 0.75 [GeVfm-3] 120 150-160 175 T [MeV] ½ 20 50 hadron

PT many-body degrees of freedom? QGP (2 ↔ 2) (3-body,...) (resonances?) consistent extrapolate pQCD

• Description of Chiral Symmetry Restoration / Decofinement requires nonperturbative approaches• Mean-field models (lin. -model, NJL) capture many aspects, but incomplete (limited d.o.f., only mass effects,…)

1. Introduction

2. Hadrons below Tc 2.1 Light Hadrons: Vacuum

2.2 Hadronic Many-Body Approach: u,d Sector - Mesons: 0± (-), 1± (-a1) , Baryons: - Consistency and Constraints (Nuclei, Lattice, …) - Towards a Chiral + Resonance Scheme - URHIC’s

2.3 Charmed Mesons

3. “Hadrons” at and above Tc

3.1 Continuity ?! 3.2 Heavy Quarks: Charmonium Regeneration 3.3 Light Quarks: Generalization of Coalescence

4. Conclusions

Outline

2.1 Light Hadrons: Vacuum

Tiqx jxjexdiq )0()()( 4

Correlation Function:Timelike (q2>0) : Im q0,q) → physical excitations

)Im(Im2AVs

dsf

)(Im)()(Im 22

sDg

ms

=1± (qq)

Chiral breaking: Q2 < (1.5-2 GeV)2 , J± < 5/2 (?!)

(qqq)

(ii) Light Sector in Vacuum II: Spacelike

Constituent Quark Mass

“Data”: lattice [Bowman etal ‘02]Curve: Instanton Model [Diakonov+ Petrov ’85, Shuryak]

p and d F2 Structure Functions Jlab Data

=2x/(1+√1+4M2x2/Q2) (Nachtmann Variable)

average → “Quark-Hadron Duality” [Niculescu etal. ’00]

2.2 Hadronic Many-Body Approach:

Light Sector (u,d)

2.2.1 0± Mesons: Pion and “Sigma”

2.2.2 1± : Rho and a1(1260)

2.2.3 Chiral + Resonance Scheme2.2.4 Baryons: (1232)2.2.5 Comparison to Lattice2.2.6 URHICs: E.M. Probes and Resonances

2.2.1 Pion and Sigma in MediumD=[k0

2-k2-(k0,k)]-1

>

>= +N,

N-1,-1

• finite N prevalent• “diluted” at T>0

“” → at Tc

Precursor in nuclei ?!A→()S-WaveA

URHICs: - fluct. (0,q→0) - M-spectra - (very) soft photons

(i) (770)

+>

>

B*,a1,K1...

N,,K…

Constraints:- branching ratios B,M→N, - N,Aabsorpt.,N→N- QCD sum rules

Significance of high B at low M Elab=20-40AGeV optimal?!

2.2.2 1± Mesons:

(ii) Vector Mesons at RHIC

baryon effects important even at B,tot=0 :sensitive to Btot=+B , more robust ↔ OZI -

(iii) Current Status of a1(1260)

>

> >

>

N(1520) …

,N(1900)…

a1 + + . . .

Exp: - HADES (A): a1→(+-) - URHICs (A-A) : a1→

]ImIm[1

1

1

2

4

2

42

aa

aD

g

mD

g

m

s

dsf

0 =

2.2.3 Towards a Chiral + Resonance SchemeOptions for resonance implementation:(i) generate dynamically from pion cloud [Lutz et al. ‘03, …]

(ii) genuine resonances on quark level → representations of chiral group [DeTar+Kunihiro ‘89, e.g. Jido etal ‘00, …]

N+

N(1535)-

a1 N(1520)-

N(1900)+ (1700)-

(?) (1920)+

S

P

S

S SS

P SS (a1)S

Importance of baryon spectroscopyto identify relevant decay modes!

2

3S

2

1S

2.2.4 In-Medium Baryons: (1232)

long history in nuclear physics ! ( A , A )

e.g. nuclear photoabsorption: M, up by 20MeV

little attention at finite temperature

-Propagator at finite B and T [van Hees + RR ’04]

in-medium vertex corrections incl. g’-cloud, (“induced interaction”)(1+ f - f N) thermal -gas

→N(1440), N(1520), (1600)

+ + + + ...

>

>>

> >>

>> NN-1 N-1

(i) Check: in Vacuum and in Nuclei

),(),()2(

4)( 03

3

0 qpqEGEfpd

qG NNpN

N

)(Re

)(Imtan)( 1

33 MG

MGM

232

2

),(3

2)( cmcm

NN kFkM

M

m

fM

→ ok !

(ii) (1232) in URHICs

broadening: Bose factor, →B repulsion: N-1, NN-1

not yet included: (N↔ ),( pEGmedN

2.2.5 Lattice Studies of Medium Effects

)2/sinh(

))2/1(cosh(),(Im),(

0

00

00 Tq

TqTqdqT

calculatedon lattice

more stable than below Tc?! (but: quenched)

MEM

1-

0-

extracted

[Laermann, Karsch ’04]

Comparison of Hadronic Models to LGT

)2/sinh(

))2/1(cosh(),(Im),(

0

00

00 Tq

TqTqdqT

calculate

integrate

More direct!

Proof of principle, not yet meaningful (need unquenched)

2.2.6 Observables in URHICs

(i) Lepton Pairs (ii) Photons

),(1

023

2

4Tqf

Mqd

dR Bee

Im Πem(M,q) ),( 0230 Tqf

qd

dRq B

Im Πem(q0=q)

e+

e- γ

baryon density effects!

[Turbide,Gale+RR ’03]

• consistent with dileptons• Brems with soft at low q?

(iii) Resonance Spectroscopy I: +- Spectra

MTqf

qdd

xdMd

dN vacRR

),()2(

03

3

3

Sudden Breakup Emission Rate

[Broniowski+Florkowski ’03]-mass shift ~ -50MeV small “” contribution underestimates

[Shuryak+ Brown ’03]

),(Im2

)()2(

Im0

03

3

4qMD

q

Mqf

qdd

xdMd

dNR

RR

Broadening+“”+BE not enough?!

(iv) Resonance Spectroscopy II : +p Spectra

N

Qualitatively in line with data (eV , MeV)

[courtesy P. Fachini]

(1232) at RHIC

eV±10)MeV mean-field: MeVGmM VBB 55)(

2

3

2

3 )()(

2.3 Charm(onium) below Tc

reldiss

k vsTEfkd

,,

,3

31 )(

)2(Dissociation rate

J→ DD,D*D

QCD-SR Mes-Ex

CQM pQCD

Reduced DD threshold: mD(Tc)≈-140MeV (NJL) J/ robust ’ fragile: direct ’→ DD decays

[Grandchamp+RR ’03]

3. “Hadrons” at and Above Tc

3.1 Continuity ?!3.2 Charmonium in QGP3.3 Light Hadrons in QGP

3.1 Continuity?!

Light Hadron “Masses”

[Shuryak, Zahed, Brown ’04]

However: peak in susceptibilities at Tc

↔ m→ 0

Observables ? e+e-+, fluct, , J/

qqchiral m

qq

m

2

2

TrFyxdeconf

QQeTrLTrLLL/)(22 ,

E.M. Emission Rates

3.2 Charmonium in QGPD=[M2-m

2-]-1 , m≈const (QCD-SR, LGT)

reldiss

gqkgq vTf

kdm

,,

,3

31 )(

)2(/Im

gluo-dissociation,inefficient for m≈ 2 mc

*

“quasifree” diss.[Grandchamp+RR ’01]

)( eqNNd

dN

if c-quarks thermalize

include back-channel :

“jumps” across Tc sensitive to mc*

[Grandchamp +RR ’03]

Charmonia in URHIC’s SPS RHIC

J/ Excitation Function

3.3 Light Hadrons in QGP

• “Resonance” matter at 1-2Tc?! - EoS can be ok [Shuryak+Zahed’04]

• assess formation rates from inelastic reactions (as in charmonium case): q+q ↔ “”+X , etc.

• solve (coupled) rate equations

• accounts for energy conservation, no “sudden” approximation -formation more reliable

To be resolved:• quark masses are not “constituent”:

• role of gluons? (not really heavier than quarks…) , …

generalizescoalescence [Greco,Ko+RR, in progress]

thqq mm 0

4. Conclusions

• Hadronic Many-Body Theory can provide:

- valuable insights into hadron properties in medium - understanding of observables in nuclear reactions

• The physics is often in the width (exception: e.g. “”)

• Interpretations?

- many spectral properties appear to vary smoothly- connections to phase transition to be established- need nonperturbative symmetry-conserving approach, e.g. selfconsistent -derivable thermodyn. potential

Additional Slides

[PHENIX]preliminary

[PHENIX]preliminary

4.3 Charm I: Open Charm (Central A-A) (i) Yields • RHIC: -30% for =02: CGC [Tuchin], Color-Dipole [Raufeisen]

• LHC: CGC: Npart ; nonlin. DGLAP: enhanced! [Kolhinen]

(ii) pT-Spectra

dE/dx : Null Effect?! [Djordjevic]

v2(e±) : Thermalization?!

3.4 Hydro vs. Coalescence: The 2-6GeV Regime

v2: mass-dependent

But: p/(4GeV)≈0.3 [PHENIX]: 1±0.15

[Hirano,Nara]

Challenges: p/=1 + jet correlation , elliptic flow

[Fries,Hwa,Molnar]

)()(|)(|)2(

2333 bbaahh

h pfpfqqdpd

gpd

dNE

universal partonic v2(pT/n) / n soft-soft ≈ thermal ( pT » m )soft-hard: explicit thermal+jet (correlations!)

[Greco et al.]

[PHENIX] [STAR]

Direct Photons at SPS and RHIC

• large “pre-equilibrium” yield from parton cascade (no LPM)• thermal yields ~ consistent• QGP undersaturation small effect

• pQCD Cronin ~ π0

T0≈205MeV sufficient• new WA98 points: -Bremsstr. via soft ?

[Turbide etal]

• RHIC central: Ncc≈10-20,

• QCD lattice: J/’s to~2Tc

4.3 Charm II: CharmoniumRegeneration in QGP / at Tc

J/ + g c + c + X→←[PBM etal, Thews etal]

Npart

[Grandchamp]

sensitivity to mc *

-If c-quarks thermalize: )( eqNN

d

dN