Electromagnetic Probes of the Medium

(Status of the Field)

Ralf Rapp Cyclotron Institute + Physics Department

Texas A&M University College Station, USA

INT Program (Week 8) on “Quantifying the Properties of Hot QCD Matter”

INT (Seattle), 12.-16.07.10

1.) Introduction: EM Probes + QCD Phase Diagram

• Electromag. Spectral Function - √s < 2 GeV : non-perturbative - √s ≥ 2 GeV : pertubative (dual)

• Phase structure tied to in-medium spectral functions - expect: hadron gas → QGP - realization of transition?

• Thermal dilepton emission rate (EM >> Rnucleus)

• thermal (M→0) → temperature,• EM conductivity + susceptibility

√s=M

)T,q(fMqd

dR Bee023

2em

4

Im Πem(M,q;B,T)

1.) Introduction

2.) Chiral Symmetry Spontaneous Chiral Symmetry Breaking Chiral Partners, Sum Rules

3.) Light Vector Mesons in Medium Lagrangian + Constraints Spectral Function in Hot/Dense Matter

4.) Dilepton Phenomenology Nuclear Photoproduction High-Energy Heavy-Ion Collisions

5.) Conclusions

Outline

2.) Chiral Symmetry Breaking + Hadron Spectrum

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

Quark Level: Const. Mass Observables: Hadron Spectrum

• Mq* ~ ‹0|qq|0›

• chiral breaking: |q2| ≤ 1 GeV 2

-

350000 fm|qqqq||qq| LRRLCondensates fill QCD vacuum:

• energy gap• massless Goldstone mode• “chiral partners” split (½ GeV)

JP=0± 1± 1/2± 3/2±

(1700)

N(1520)

(1232)

M

[GeV

]

• spectral distributions!

2.3 Q2-Dependence of Chiral Breaking

Axial-/Vector Mesons

pQCD cont.

F2-Structure Function (spacelike)

JLAB Data

≈ x

• average → Quark-Hadron Duality• lower onset-Q2 in nuclei?

[Niculescu et al ’00]

p

d• Weinberg Sum Rule(s)

)Im(Ims

dsf IA

IV

112

2.4 Sum Rules and Order Parameters

)Im(ImsdsI AVn

n 2

102

122

2 031 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]

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

1.) Introduction

2.) Chiral Symmetry Spontaneous Chiral Symmetry Breaking Chiral Partners, Sum Rules

3.) Light Vector Mesons in Medium Lagrangian + Constraints Spectral Function in Hot/Dense Matter

4.) Dilepton Phenomenology Nuclear Photoproduction High-Energy Heavy-Ion Collisions

5.) Conclusions

Outline

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

[Chanfray et al, Herrmann et al, Urban et al, Weise et al, Oset et al, …]

• Pion Cloud

>>

R=, N(1520), a1, K1 ...

h=N, , K …

=• -Hadron Scattering

= +

[Haglin, Friman et al, RR et al, Post et al, …]

• constrain effective vertices: R→ h, scattering data (N→N, N/A)

• Vacuum: chiral Lagrangian +

→ P-wave phase shift, el.-mag. formfactor

• Hadronic Matter: effective Lagrangian for interactions with heat bath In-Medium -Propagator

3.2 -Meson in Vacuum and Hot/Dense Matter

3.3 Constraints from Nuclear Photo-Absorption -absorption cross section in-medium–spectral function

)q,M(DIm)qq(ImqA

)q( med

N

absA 04

0em0

0

NA

-ex

[Urban,Buballa, RR+Wambach ’98]

Nucleon Nuclei

• melting of 2.+3. resonances• quantitative determination of interaction vertex parameters

3.4 Spectral Function in Nuclear Matter

In-med. -cloud +N→B* resonances

N→B* resonances (low-density approx.)

In-med -cloud + N → N(1520)

Constraints:N , A N →N PWA

• strong broadening + small upward mass-shift• empirical constraints important quantitatively

N=0

N=0

N=0.50

[Urban et al ’98]

[Post et al ’02]

[Cabrera et al ’02]

3.5 Spectral Function in Heavy-Ion Collisions

• -meson “melts” in hot /dense matter• medium effects dominated by baryons

B /0

0 0.1 0.7 2.6

Hot+Dense Matter

[RR+Gale ’99]

Hot Meson Gas

[RR+Wambach ’99]

1.) Introduction

2.) Resonances + Chiral Symmetry Spontaneous Chiral Symmetry Breaking Chiral Partners

3.) Light Vector Mesons in Medium Lagrangian + Constraints Spectral Function in Hot/Dense Matter

4.) Dilepton Phenomenology Nuclear Photoproduction High-Energy Heavy-Ion Collisions

5.) Conclusions

Outline

4.1 Nuclear Photoproduction: Meson in Cold Matter

+ A → e+e X

[CLAS+GiBUU ‘08]

E≈1.5-3 GeV

e+

e

• extracted “in-med” -width ≈ 220 MeV

• Microscopic Approach:

Fe - Ti

N

product. amplitude in-med. spectral fct.+

M [GeV][Riek et al ’08, ‘10]

full calculationfix density 0.40

• -broadening reduced at high 3-momentum; need low momentum cut!

4.2 Thermal Dilepton Emission

Rate:e+

e-)T,q(f

Mqdxd

dN Bee023

2em

44

Im Πem(M,q;B,T)

Imem ~ [Im D+ Im D/10 + Im D/5]

M ≤ 1 GeV: non-perturbative M > 1.5 GeV: perturbativeIm em ~ Nc ∑(eq)2

√s=M

e+

e-

e+

e-

q

q

-

ee→had / ee→ ~ Im em(M)

“Hadronic Spectrometer” (T ≤ Tc) “QGP Thermometer” (T > Tc)

4.2.2 Dilepton Rates: Hadronic vs. QGP dRee /dM2 ~ ∫d3q f B(q0;T) Im em

• Hadronic and QGP rates tend to “degenerate” toward ~Tc

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

[qq→ee]-[HTL] F2-Structure Function

p

d

JLAB Data

[RR,Wambach et al ’99]

4.2.3 Dileptons in Heavy-Ion Collisions: Spectrometer

• thermal radiation dominant• invariant-mass spectrum directly reflects thermal emission rate!

+ Spectra at CERN-SPS In-In(158AGeV) [NA60 ‘09]

M[GeV]

Thermal Emission Rate

• Evolve rates over fireball expansion:

[van Hees+RR ’08]

qd

dRqqd

)(VddM

dN thermee

FB

thermee

fo

40

3

2 20

• “4“ states dominate free EM correlator above M ≈ 1.1GeV

• lower estimate: use vacuum 4 correlator

• more realistic: O(T2) medium effect → “chiral V-A mixing”:

with

4.2.4 Intermediate-Mass Region

)q()q()()q( AVV001

21)T( c

[Eletsky+Ioffe ‘90]

42

53

[van Hees+RR ‘06]

4.2.4.2 Intermediate-Mass Dileptons: Thermometer• QGP or Hadron Gas (HG) radition? • vary critical temperature Tc in fireball evolution

• partition QGP vs. HG depends on Tc

(spectral shape robust: dilepton rate “dual” around Tc! )

• Initial temperature Ti ~ 190-220 MeV at CERN-SPS

green: Tc=190MeVred: Tc=175MeV (default)blue: Tc=160MeV

qq →

→ (e.g. a1 → )

-

4.2.5 Dimuon pt-Spectra and Slopes: Barometer

• modify fireball evolution: e.g. a┴ = 0.085/fm → 0.1/fm

• both large and small Tc compatible

with excess dilepton slopes

pions: Tch=175MeV a┴ =0.085/fm

pions: Tch=160MeV a┴ =0.1/fm

M[GeV]

4.2.6 Conclusions from Dilepton “Excess” Spectra

• thermal source (T~120-200MeV)

• M<1GeV: in-medium meson - no significant mass shift - avg. (T~150MeV) ~ 350-400 MeV

(T~Tc) ≈ 600 MeV → m

- driven by baryons

• M>1GeV: radiation around Tc

• fireball lifetime “measurement”: FB ~ (6.5±1) fm/c (semicentral In-In)

[van Hees+RR ‘06, Dusling et al ’06, Ruppert et al ’07, Bratkovskaya et al ‘08]

• currently fails at RHIC

4.2.6 Origin of the Low-Mass Excess in PHENIX?

- small Teff slope - why not in semi-central?- generic space-time argument:

maximal emission around Tmax ≈ M / 5.5 (for Im em =const)

Low mass (M<1GeV): Tmax < 200MeV

• Soft QGP Radiation?

23em44

33

0e /T/M

FBeeee )MT(

MIm

)T(Vqxdd

dNqxdd

qM

dMddN

55em eT)(M, .T/Mee TIm

dTdMdN

- “baked Alaska” ↔ small T - rapid quench+large domains ↔ central A-A - therm + DCC → e+ e ↔ M~0.3GeV, small pt

• Disoriented Chiral Condensate (DCC)?[Bjorken et al ’93, Rajagopal+Wilczek ’93]

[Z.Huang+X.N.Wang ‘96]

4.3 Axialvector in Medium: Dynamical a1(1260)

+ + . . . =

Vacuum:

a1

resonance

InMedium: + + . . .

• in-medium + propagators• broadening of - scattering amplitude

[Cabrera et al. ’10]

5.) Conclusions• EM spectral function ↔ excitations of QCD vacuum - ideal tool to probe hot/dense matter

• Effective hadronic Lagrangian + many-body theory: - strong broadening in (baryonic) medium, suppresed at large momentum (CLAS!)

• Dileptons in heavy-ion collisions: - spectro-/thermo-/baro-meter (CERES, NA50,NA60!) - corroborate melting of toward expected Tc = 160-190 MeV

→ quark-hadron duality?! hadron liquid?!

• Sum rules + axialvector spectral function to tighten relations to (partial) chiral restoration

• Future experiments at RHIC-2, FAIR +LHC

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

• consistency of virtual+real photons (same em)

• very low-mass di-electrons ↔ (low-energy) photons[Srivastava et al ’05, Liu+RR ‘06]

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

[Turbide et al ’03,van Hees+RR ‘07]

3.5.3 Composition of Mass Spectra in qt-Bins

• high qt ≥ 1.5GeV:

- medium effects reduced - non-thermal sources take over

low qt

high qt

intermed. qt

3.5.2 Rho, Omega + Phi Freezeout from pt-Spectra

• sequential freezeout →→• consistent with mass spectra

• freezeout = fireball freezeout

• adjust and freezeout contribution to fit pt-spectra

5.2.5 NA60 Dimuons: pt-Slopes

• in-medium radiation “harder” than hadrons at freezeout?! (thermal radiation softer by Lorentz-1/• smaller Tch helps (larger Tfo)

• non-thermal sources (DY, …)?• additional transverse acceleration?• hadron spectra (pions)?

Tch=175MeVTch=160MeV

Tch=160MeVa┴ =0.1/fm

Tch=160MeVa┴ =0.085/fm

3.3 “Non-Thermal Dilepton Sources

→ relevant at M, qt ≥ 1.5 GeV (?)

• primordial qq annihilation (Drell-Yan): NN → e+eX

• mesons at thermal freeze-out (“blast-wave”):

- extra Lorentz- factor relative to thermal radiation - qt-spectra + yield fixed by fireball model

• primordial (“hard”) mesons: - schematic jet-quenching with abs fit to pions

-

• late decays: ,→ e+e , DD → e+eX, J/→e+e , …

_ f.o. + prim.

3.2.3 NA60 Excess Spectra vs. Theory

• Thermal source does very well • Low-mass enhancement very sensitive to medium effects• Intermediate-mass: total agrees, decomposition varies

[CERN Courier Nov. 2009]

2.2 Chiral + Resonance Scheme

N+

N(1535)-

a1 N(1520)-

N(1900)+ (1700)-

(?) (1920)+

S

P

S

S SS

P SS (a1)S

• add S-wave pion → chiral partner• P-wave pion → quark spin-flip • importance of baryon spectroscopy

2

3S

2

1S

3.1 Axial/Vector Mesons in Vacuum

Introduce a1 as gauge bosons into free + +a1 Lagrangian

2

21 g)(gintL

1202 )]M()m(M[)M(D )(

EM formfactor

scattering phase shift

2402 |)M(D|)m(|)M(F| )(

)M(DRe)M(DIm

)M(

1-tan

|F|2

-propagator: