Heavy-Quark Diffusion

in the Primordial Quark-Gluon Liquid

Vector Mesons in Medium

and Dileptons in Heavy-Ion Collisions

Ralf Rapp Cyclotron Institute + Physics Department

Texas A&M University College Station, USA

Strong Interaction SeminarTU München, 26.10.09

1.) Intro-I: Probing Strongly Interacting Matter

• Electromagnetic Probes: penetrating: EM >> Rnuc

• Equilibrium: EM spectral function Im EM(q0,q;B,T)

Information via EM Spectral Function: • degrees of freedom (parton vs. hadron)• transport properties (EM conductivity, susceptibility)• relation to order parameters (chiral symmetry)• measure of temperature

1.2) Intro-IIa: Low-Mass Dileptons at CERN-SPS

CERES/NA45 [2000]

mee [GeV]

• strong excess around M ≈ 0.5GeV (and M > 1GeV ) • little excess in region

NA60 [2005]

1.2) Intro-IIb: Low-Mass Dileptons SIS + RHIC

HADES [2008]

• awaiting larger system sizes …

PHENIX [2008]

mee [GeV]

• very large low-mass excess• awaiting HBD results (run-10) …

1.) Introduction

2.) Chiral Symmetry + Vector Mesons EM Emission and Vector Mesons Chiral Symmetry Breaking and a1 Meson in Medium

3.) Dilepton Spectra in A-A and -A Thermal Emission and NA60 (SPS) Photoproduction and CLAS (JLab)

4.) Conclusions

Outline

2.1 Thermal Electromagnetic Emission

Tiqx )](j),x(j[)x(exdi)q(Π 0emem0

4em

EM Current-Current Correlation Function:

e+

e-

γ

)T(fMqd

dR Bee23

2em

4

)T(fqd

dRq B

2em

30

Im Πem(M,q)

Im Πem(q0=q)

Thermal Dilepton and Photon Production Rates:

Imem ~ [ImD+ ImD/10 + ImD/5]Low Mass: -mesondominated

But: “Higgs” Mechanism in Strong Interactions:qq attraction “Bose” condensate fills QCD vacuum

Spontaneous Chiral Symmetry Breaking

2.2 Chiral Symmetry + QCD Vacuum

)m( d,u 0QCD L : isospin + “chiral” (left/right-handed) invariant

350000 fm|qqqq||qq| LRRL

>

>

>

>qLqR

qL-qR

--

Profound Consequences:• effective quark-mass: ↔ mass generation

• massless Goldstone bosons 0,± , pion pole-strength f= 93MeV

• “chiral partners” split, M ≈ 0.5GeV:

00 |qq|m*q

JP=0± 1± 1/2±

• Weinberg Sum Rule(s)

2.3 Hadron Spectra + Chiral Symm. Breaking

Axial-/Vector Correlators

)Im(Ims

dsf IA

IV

112

pQCD cont.

“Data”: lattice [Bowman et al ‘02] Theory: Instanton Model [Diakonov+Petrov; Shuryak ‘85]

Constituent Quark Mass

• chiral breaking: |q2| ≤ 1 GeV2

• Gellmann Oakes Renner:

m2 f

2 = mq ‹0|qq|0›-

2.4 Sum Rules and Order Parameters

)Im(ImsdsI IA

IV

nn

11

210

21

222 0

31 q)q(αcI,I,fI,FrfI sπAππ

[Weinberg ’67, Das et al ’67, Kapusta+Shuryak ‘93]

• QCD-SRs

[Hatsuda+Lee ’91, Asakawa+Ko ’92, Klingl et al ’97, Leupold et al ’98, Kämpfer et al ‘03, Ruppert et al ’05, Kwon et al ‘08]

Promising synergy of lQCD and effective models

• Weinberg-SRs: moments VectorAxialvector

sQ

)s(Ims

dsQ

)Q(Π

20

2

2

...

Q

)qq(C

Q

GQ)()Q( ss

s 6

2

4

22

2

2

22

3ln1

81

>>

B*,a1,K1

...

N,,K…

2.5 -Meson in Medium: Hadronic Interactions

D(M,q;B ,T) = [M 2 - m2 - - B - M ] -1-Propagator:

[Chanfray et al, Herrmann et al, RR et al, Koch et al, Klingl et al, Mosel et al, Eletsky et al, Oset et al, Sasaki et al …]

= B,M=Selfenergies:

Constraints: decays: B,M→ N, scattering: N → N, A, …

B /0

0 0.1 0.7 2.6

[RR,Wambach et al ’99]

Meson “Melting” Switch off Baryons

2.6 Axialvector in Medium: Dynamical a1(1260)

+ + . . . =

Vacuum:

a1

resonance

InMedium: + + . . .

• in-medium + propagators• substantial broadening of - scattering amplitude• consequences for chiral restoration to be elaborated

[Cabrera,Jido,Roca+RR ’09 in preparation]

3.) Dilepton Spectra in A-A and -A

Thermal Dilepton Emission Rate:e+

e-

)T,q(fMqdxd

dN Bee023

2em

44

Im Πem(M,q;B,T)

Thermal Sources: Relevance:

- Quark-Gluon Plasma: high mass + temp. qq → e+e , … M > 1.5 GeV, T >Tc

- Hot + Dense Hadron Gas: M ≤ 1 GeV → e+e , … T ≤ Tc

-

q

q

_

e+

e

e+

e

Im Πem ~ Im D

3.1 Dilepton Rates: Hadronic vs. QGP

dRee /dM2 ~ ∫d3q f B(q0;T) Im em

• Hard-Thermal-Loop [Braaten et al ’90]

enhanced over Born rate

• Hadronic and QGP rates “degenerate” around ~Tc

• Quark-Hadron Duality at all M ?! ( degenerate axialvector SF!)

[qq→ee] [HTL]

-

3.2 Dilepton “Excess” Spectra at SPS

• “average” (T~150MeV) ~ 350-400 MeV

(T~Tc) ≈ 600 MeV → m

• fireball lifetime: FB ~ (6.5±1) fm/c[van Hees+RR ‘06, Dusling et al ’06, Ruppert et al ’07, Bratkovskaya et al ‘08]

)y,M(Acc),T;q,M(qxdd

dNq

qMd)(Vd

dMdN

iFB

fo

44

therm

0

3therm

0

Thermal Emission Spectrum:

3.2.2 NA60 Data vs. In-Medium Dimuon Rates

• acceptance-corrected data directly reflect thermal rates!

M[GeV] [RR,Wambach et al ’99]

[van Hees+RR ’07]

3.2.3 NA60 Dimuons: Sensitivity to QGP and Tc

• vary critical and chemical-freezeout temperature (Tfo ~ 130 MeV fix)

• overall shape of spectra robust: “duality” of dilepton rate around “Tc”!

• yields slightly larger for large Tc (hadronic volume!), || < 1fm/c

• intermediate mass (M>1GeV): QGP vs. hadronic depends on Tc

Intermediate Mass Region“EoS-B” “EoS-C”

3.3 Low-Mass Dileptons at RHIC: PHENIX

• Successful approach at SPS fails at RHIC

3.4Meson in Cold Nuclear Matter

+ A → e+e X e+

e

Nuclear Photo-Production:

[CLAS/JLab ‘08]

[Riek et al ’08]Theoretical Approach:

Mee[GeV]

Fe - Ti

N ≈ 0.5 0

N

elementary production amplitude

in-medium spectral function+

M [GeV]

E=1.5-3 GeV

4.) Conclusions

• Electromagnetic Probes - study matter properties in nuclear reactions - low mass: in-medium vector mesons

• Chiral Symmetry Breaking (Restoration) - chiral partners: - a1 (degeneracy at Tc)

• Thermal Dilepton Rates - melting toward Tc (quark-hadron duality?)

• Dilepton Spectra - quantitative agreement at SPS - ok at TJNAF (-A) - failure at RHIC thus far

4.5 EM Probes in Central Pb-Au/Pb at SPS

• updated fireball (aT=0.045→0.085/fm)• very low-mass di-electrons ↔ (low-energy) photons

[Srivastava et al ’05, Liu+RR ‘06]

Di-Electrons [CERES/NA45] Photons [WA98]

[van Hees+RR ‘07]

4.8 Axialvector in Medium: Explicit a1(1260)

>

> >

>

N(1520)…

,N(1900)…

a1 + + . . .

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

)DImg

mDIm

g

m(

s

dsf a

a

a1

1

1

2

4

2

42

N-1

2.5Cold Nuclear Matter: Photo-Production

Fe -Ti N ≈ 0.5 0

+ A → e+e X

E=1.5-3 GeV

[Riek et al ’08]

[CLAS/JLab +GiBUU ’08]

2.3.2 Acceptance-Corrected NA60 Spectra

• more involved at pT>1.5GeV: Drell-Yan, primordial/freezeout , …M [GeV] M [GeV]

X.) Example for Comprehensive Analysis: NA60

thermal medium radiating from around Tc with melted ,

well-bound J/ with large collectivity

DileptonsCharmonium

FlowCharmonium

Production

2.4 Spectral Function at Lower Collision Energies

• largest sensitivity for M ≤ 0.4 GeV soft modes!

• Critical point: -L mixing (q≠0) with m→ 0, but: → e+e signal (too) weak