Light and Heavy Hadronic Modes in Medium

Ralf Rapp

Cyclotron Institute + Physics Department

Texas A&M University College Station, USA

Universität Bielefeld, 11.01.05

“Freeze-Out” Hadron Gas

QGP ?!

Au + Au

1. Motivation: Relativistic Heavy-Ion Collisions

Au + Au → X

e+

e-

Signatures of the QGP?

• Suppression of J/-Mesons

• Decays of -Mesons

• Photons …

J/

1.2 Current Status: Towards QGP Discovery

• So far: RHIC observables ↔ bulk properties of the produced matter:

- energy density ≈20GeVfm-3 ↔ jet quenching (high-pt) - thermalization + EoS ↔ hydrodynamics (v0,v2)

- partonic degrees of freedom ↔ coalescence (p/, v2-scal)

• Future: need to understand microscopic properties (phase transition, “QGP” !?):

- Deconfinement ↔ quarkonia (J/, , …) - Chiral Symmetry Restoration ↔ dileptons ( - temperature ↔ photons )

1. Introduction

2. Vacuum: Chiral Symmetry (Breaking)

3. (Light) Hadrons below Tc

3.1 Mesons: 0± (-), 1± (-a1) , Baryons: N, 3.2 Towards Chiral + Resonance Scheme

3.3 URHICs: Dileptons + Photons

4. Heavy-Quark Modes 4.1 Charmed Hadrons below Tc 4.2 Heavy-Quark Equilibration 4.3 Quarkonia in the QGP

4.4 URHICs: Suppression vs. Regeneration

5. Conclusions

Outline

2.) Chiral Symmetry in QCD: Vacuum

2

4

1aq Gq)m̂Agi(q QCDL SU(2)L× SU(2)R

invariant (mu,d≈0)

Spontaneous Breaking: strong qq attraction Bose Condensate fills QCD vacuum!

0 LRRL qqqqqq >

>

>

>qLqR

qL-qR

-[cf. Superconductor: ‹ee›≠0 Magnet ‹M›≠0 , … ]

-

Profound Consequences:• energy gap: ↔ mass generation!

• massless Goldstone bosons 0,±

• “chiral partners” split, M≈0.5GeV:

qqm*qqq 2

JP=0± 1± 1/2±

2.1 Light Hadrons: Vacuum

Tiqx jxjexdiq )0()()( 4

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

=1± (qq)

)Im(Im2AVs

dsf

)s(DIm)g/m()s(Im 22

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

(qqq)

2.2 “Melting” the Chiral Condensate

How?

Excite vacuum (hot+dense matter)

• quarks “percolate” / liberated Deconfinement • ‹qq› condensate “melts”, iral Symm. chiral partners degenerate Restoration(-, -a1, … medium effects → precursor!)

0 0.05 0.3 0.75 [GeVfm-3] 120, 0.50 150-160, 20 175, 50 T[MeV], had

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

-

1.0 T/Tc

m‹qq›-lattice QCD

3. Hadrons in Medium: Light Sector (u,d)

3.1.1 0± Mesons: and “”

3.1.2 1± : (770) and a1(1260)

3.2 Chiral + Resonance Scheme3.3 Baryons: (1232), N3.4 Comparison to Lattice3.5 URHICs: E.M. Probes (and Resonances)

3.1.1 Pion and Sigma in Medium

D=[k02-k

2-(k0,k)]-1

>

>= +N,

N-1,-1

• N prevalent, smeared at T>0

D → D at Tc Precursor in nuclei ?!A→()S-WaveA

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

>

>

B*,a1,K1...

N,,K…

Constraints:- B,M→N, - N,A,N→N- QCDSRs, lattice

3.1.2 (Axial-) Vector Mesons in Medium

D(M,q:B,T)=[M2-m2--B-M ]-1

(a) Hadronic Many-Body Theory

medmed DvD 2

]ff[vD MMMM,B

2

Propagator:

[Chanfray etal, Herrmann etal, RR etal, Koch etal, Weise etal, Post etal, Eletsky etal, Oset etal, …]

(b) Effective Field TheoryHLS with L≡(“VM”); vacuum: loop exp. OO(p/, m/, g)

In-Med.: T-dep. of bare m(0), g via matching to OPE, match<

+ RG-running to on-shell dropping -mass

[Harada, Yamawaki, Sasaki etal]

[RR+Gale ’99]

(i) -Mesons at SPS

• -meson “melts” in hot and dense matter

• baryon densityB more important than temperature

B/0 0 0.1 0.7 2.6

Hot+Dense Matter Hot Meson Gas

[RR+Wambach ’99]

[Eletsky etal ’01]

Model Comparison

[RR+Wambach ’99]

(ii) Vector Mesons at RHIC

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

e+e- Emission Rates: dRee/dM ~ f B Imem

Quark-Hadron Duality ?!

in-med HG ≈ in-med QGP !

[qq→ee][qq+O(s)]

--

(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 =

3.2 Towards a Chiral + Resonance SchemeOptions for resonance implementation:(i) generate dynamically from pion cloud [Kolomeitsev etal ‘03, …]

(ii) genuine resonances on quark level

→ representations of chiral group [DeTar+Kunihiro ‘89, Jido etal ’00, …]

e.g.

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

3.3 In-Medium Baryons: (1232) and N(939)

long history in nuclear physics ! ( A , A )

e.g. nuclear photoabsorption: M, up by 20-40MeV

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

in Nuclear Absorption

in Nuclei and Heavy-Ion Collisions

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

(1232) Spectral Fct. at RHIC Nucleon Spectral Fct. at RHIC

substantial broadening due to resonant N → B scattering

3.4 Lattice Studies of Medium Effects

)2/sinh(

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

0

00

00 Tq

TqTqdqT

calculatedon lattice

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)

3.5 Observables in URHICs

(i) Dileptons (ii) Photons

)T,q(fMqd

dR Bee023

2

4

1

Im Πem(M,q) ),( 0230 Tqfqd

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?

4. Heavy-Quark Modes

4.1 Charmed Mesons below Tc

4.2 Heavy-Quark Equilibration4.3 Charmonium in QGP4.4 URHICs: Suppression vs. Regeneration

4.1 Charmed Mesons in Hadronic Matter

reduced threshold for → DD J/ robust

’ fragile: ’→ DD decays

reldiss vf

kd

,

,3

31

)2(

[Grandchamp+RR ’03]

mD(T,B) expected to decrease

(Chiral Symmetry Restoration)

[Weise etal ’01]

2

2)(

p

fD

p

pf

t

f

1-D Fokker Planck Eq.

kpkwkdp ),(323 ),(

2

1 kpkwkdD

scatt. rate

diff. const.

TEtpp peetpf /2/)]([ 220

2

1),(

)1()( 22 teD

t

4.2 Heavy-Quark Thermalization in QGP ?

• Naively: 1 scatt. Q2≈ T2, (pt,therm)2≈ mcT Nscatt≈(pt,therm/Q)2 ≈5

• more quantitative: Boltzmann Eq. [Svetitsky ’88]

)](),()()([),( 3 pfkpwkpfkpwkdt

ftpf

t coll

e.g.: pQCD Xsections, T=500MeV, s=0.6(0.3)

=0.25 (0.06) fm-1 ↔ 4-15fm/c (very) slow!

Resonance cross section c + q → “D” → c + q ?!

4.2.1 Resonant Open-Charm Rescattering

h.c. c)v(

qG DDDcq 2

1L

• effective model with pseudo/scalar + axial/vector “D-mesons”

c + q → “D” → c + q

551 ,,,

“Light”-Quark Resonances

1.4Tc

[Asakawa+ Hatsuda ’03]

_ _

• chirally symmetric for light quarks

• heavy-quark symmetry j conserved to LO(1/mc)

• parameters: mD(0), GD

[van Hees+RR ’04]

4.2.2 Heavy-Quark Thermalization Times in QGP

• resonance scatt. isotropic• secondary open-charm ?! [50% for ])ccgg( 3

[van Hees+RR ’04]

pQCD

“D”

Charm Quarks Bottom vs. Charm

• bottom quarks “barely” thermalize at RHIC

4.2.3 Single-e± Spectra at RHIC: D → e+X

• dynamical origin of resonances? cc production? • onset of pQCD regime: pt>5-6GeV ? open bottom?

_ [Müller etal ’95, Molnar’04]

practically indistinguishable

PHENIX130AGeV e±

B

D

[Batsouli etal. ’02]

pt-Spectra: p-p vs Hydro Ellitpic Flow + Coalescence

jet- quench[Djordjevic etal ’04]

does charm equilibrate?

4.2 Charmonium in QGP• Lattice: c, J/ survive up to ~2Tc

• mass m≈ const ~ 2mc*

• width: reldiss

gqgq vTf

kd

,

,3

31 )(

)2(

[Datta etal ’03]

gluo-dissociation

“quasifree” diss.

[Bhanot+Peskin ‘84]

[Grandchamp+RR ‘01]

Cross Sections Dissociation Times

“jumps” at Tc sensitive to

rather direct link to lattice QCD!

*, ccc mN

4.3.1 Charmonium Regeneration vs. Suppression

• statistical coalescence at Tc: chem.+therm. equil.

• charmonia above Tc

formation in QGP: detailed balance!

)NN(d

dN eq

for thermalized c-quarks:

Equilibration close to Tc ?!

[PBM etal ’01, Gorenstein etal ’02, …]

[Thews etal ’01, Ko etal ’02 … Grandchamp+RR ’02]

J/ + g c + c + X←→ -

• QGP regeneration dominant• sensitive to: mc* , open-charm degeneracy, (Ncc)2 ↔ rapidity, √s, A

[Grandchamp +RR ’03]

4.3.2 Charmonium in A-A SPS RHIC

J/ Excitation Function

[Lumpkins, Grandchamp, van Hees, Sun +RR ’05]

4.3.3 Upsilon in A-A

RHIC LHC

• bottomonium suppression as unique QGP signature ?!• caveat: equil. number (very) sensitive to (mb)*, therm

5. 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

(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±15)MeV mean-field: MeVGmM VBB 55)(

2

3

2

3 )()(

(1232) Spectral Fct. at RHIC

(ii) (1232) in URHICs

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

not yet included: (N↔ ),( pEGmedN

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]

J/Width from Lattice QCD

E.M. Emission Rates

[RR+Wambach ’99]

3.1 Continuity?!

Light Hadron “Masses”

However: peak in susceptibilities at Tc

↔ m→ 0

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

qqchiral m

qq

m

2

2

TrFyxdeconf

QQeTrLTrLLL/)(22 ,

[Shuryak, Zahed, Brown ’04]

[Turbide,Gale+RR ’03]

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

• 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

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]