theory update on electromagnetic probes ii ralf rapp cyclotron institute + physics department texas...
TRANSCRIPT
Theory Update on
Electromagnetic Probes II
Ralf Rapp Cyclotron Institute + Physics Department
Texas A&M University College Station, USA
CATHIE/TECHQM WorkshopBNL (Upton, NY), 16.12.09
1.) Intro: 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.) Introduction
2.) EM Emission + Vector Mesons Thermal Rate and Conductivity Chiral Symmetry Breaking and a1 Meson in Medium
3.) Dilepton Spectra in A-A Thermal Emission at SPS The RHIC Problem
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
2.2 Electric Conductivity
)q,q(Imqq
e 020lim
32
0em00
2
em
• pion gas (chiral pert. theory)
em / T ~ 0.01 for T ~ 150-200 MeV
[Fernandez-Fraile+Gomez-Nicola ’07]
• quenched lattice QCD
em / T ~ 0.35 for T = (1.5-3) Tc
[Gupta ’04]
• soft-photon limit em30340230
)(T)q(
qdxd
dNq
• Weinberg Sum Rule(s)
2.3 Chiral Symmetry Breaking + Hadron Spectrum
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 f2 = mq ‹0|qq|0›-
350000 fm|qqqq||qq| LRRLCondensates fill QCD vacuum:
>>
B*,a1,K1
...
N,,K…
2.4 -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, Ruppert 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
2.4.2Meson in Cold Nuclear Matter: JLab
+ A → e+e X e+
e
Nuclear Photo-Production:
[CLAS/JLab ‘08]
[Riek et al ’08]Theoretical Approach:
Mee[GeV]
Fe - Ti
N
elementary production amplitude
in-medium spectral function+
M [GeV]
E=1.5-3 GeV
2.6 Axialvector in Medium: Dynamical a1(1260)
+ + . . . =
Vacuum:
a1
resonance
InMedium: + + . . .
• in-medium + propagators• broadening of - scattering amplitude
[Cabrera,Jido,Roca+RR ’09]
3.) Dilepton Spectra in A-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 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]
3.2.4 NA60 Dimuons: Sensitivity to QGP and Tc
• vary critical and chemical-freezeout temperature (Tfo ~ 130 MeV fix)
• spectral shape robust: “duality” of dilepton rate around “Tc”!
• intermediate mass (M>1GeV): QGP vs. hadronic depends on Tc
Intermediate Mass Region“EoS-B” “EoS-C”
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]
3.3 Low-Mass Dileptons at RHIC: PHENIX
• Successful approach at SPS fails at RHIC• Excess concentrated: - at low mass - in central collisions - at low pt (Teff ~ 100 MeV)
Inclusive Mass Spectrum Centrality Dependence of Excess
3.3.2 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]
3.3.3 Low-Mass Excess from DCC?
Dileptons from a DCC-DCC annihilation
[Witham+RR ‘08]
• too small• DCC-thermal to be evaluated …
3.3.4 Comparison of Thermal Emission Calculations
Chiral Reduction + Hydro Hadronic Many-Body + Fireball
• Decomposition at M=0.5(0.2)GeV: Hadronic LO-QGP NLO-QGP Dusling+Zahed 6 (6) 5.5 (2) 10 (25) RR+van Hees 20 (15) 4 (3) --
4.) Conclusions
• Electromagnetic Probes - versatile tool (spectral fcts., transport, temp., lifetime!)
• Chiral Symmetry Breaking (Restoration) - chiral partners: - a1 (degeneracy at Tc)
• Thermal Dilepton Rates - melting toward Tc : quark-hadron duality?!
hadron liquid?!
• Dilepton Spectra - quantitative agreement at SPS - failure at RHIC thus far (QGP not favored; DCC??)
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