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The Versatility of
Thermal Photons and Dileptons
Ralf Rapp Cyclotron Institute +
Department of Phys & Astro Texas A&M University College Station, USA
TPD WorkshopBNL (Upton, NY), 05.-07.12.11
1.) Introduction: Components of EM Probes HICs
• Thermal Emission Rate micro-physics: → Electro-Magnetic spectral function
• Space-Time Evolution of Fireball macro-physics (equation of state: (P))
→ temperature + flow fields
• Equation of State - governed by micro-physics
(deg. of freedom, interactions)
- drives the macro-physics
- encodes deconfinement + chiral restoration
e+
e-
γ
),T;q,M()T;q(fM
~qdxd
dNB
Bee emIm02441
)t,r(v,)t,r(T
2.) Transport Properties
EM Conductivity + Low-Energy Photons
3.) Spectral Properties
Vector Spectral Functions + the Fate of Resonances Dilepton Invariant-Mass Spectra
4.) Chiral Restoration Criteria: Axialvector, Lattice QCD, pert. QCD
QCD +Weinberg Sum Rules
5.) Fireball Properties
Lifetime, Temperature, Collectivity
6.) Conclusions
Outline
2.) Transport: Electric Conductivity
)q,q(Imqqe)q,q(Im
qqe 01000 0
00
20
00
2
emememlimlim
• hadronic theories (T~150MeV): - chiral pert. theory (pion gas): em / T ~ 0.11 e2
- hadronic many-body theory: em / T ~ 0.09 e2
[Fernandez-Fraile+ Gomez-Nicola ’07]
• lattice QCD (T ~ (1.5-3) Tc ): em /T ~ (0.26±0.02) e2
[Gupta ’04, Aarts et al ’07, Ding et al. ‘11]
• soft-photon limit of thermal emission rate em
303404
0 T)q(qdxd
dNq
• EM Susceptibility ( → charge fluctuations):
Q2 Q 2 = χem = Πem(q0=0,q→0)
2.2 Soft Photons at SPS: WA98
[Turbide,RR+Gale’04]
Thermal Radiation + pQCD Add→ Bremsstrahlung
em
30340
40 T)q(
qdxd
dNq
[Liu+RR’06]
2.) Transport Properties
EM Conductivity + Low-Energy Photons
3.) Spectral Properties
Vector Spectral Functions + the Fate of Resonances Dilepton Invariant-Mass Spectra
4.) Chiral Restoration Criteria: Axialvector, Lattice QCD, pert. QCD
QCD +Weinberg Sum Rules
5.) Fireball Properties
Lifetime, Temperature, Collectivity
6.) Conclusions
Outline
3.) EM Spectral Function I: Fate of Resonances
• Electromagn. spectral function - √s ≤ 1 GeV : non-perturbative - √s > 1.5 GeV : perturbative (“dual”)
• Vector resonances “prototypes” - representative for bulk hadrons: neither Goldstone nor heavy flavor
• Modifications of resonances ↔ phase structure: - hadron gas → Quark-Gluon Plasma - realization of transition?
√s = M
e+e → hadrons
)T,q(fMqdxd
dN Bee023
2em
44 Im Πem(M,q;B,T)
Im em(M) in Vacuum
3.2 Phase Transition(s) in Lattice QCD
• different “transition” temperatures?! • smooth transitions! (smooth e+e rate) • partial chiral restoration in “hadronic phase” ?! (low-mass dileptons!) • leading-order hadron gas
“Tcconf ” ~170MeV
“Tcchiral ”~150MeV
≈
/ q
q-
-
>>
B*,a1,K1
...
N,,K…
3.3Vector Mesons in Hadronic Matter
D(M,q;B ,T) = [M 2 - m2 - - B - M ] -1-Propagator:
[Chanfray et al, Herrmann et al, Asakawa et al, RR et al, Koch et al, Klingl et al, Post et al, Eletsky et al, Harada et al …]
= B,M=Selfenergies:
Constraints: decays: B,M→ N, scattering: N → N, A, …
B /0
0 0.1 0.7 2.6
SPS RHIC
3.4 “Smoothness” of Dilepton Rates across “Tc”
• smooth transition hadrons ↔ QGP?!• resonance melting + chiral mixing
• on-shell qq vs. annihil. in transport code
-
dRee /dM2 ~ ∫d3q f B(q0;T) Im em
3.5 Dilepton Rates vs. Exp.: NA60 “Spectrometer”
• invariant-mass spectrum directly reflects thermal emission rate!
Acc.-corrected + Excess Spectra In-In(158AGeV) [NA60 ‘09]
M[GeV]
Thermal Emission Rate
• Evolve rates over fireball expansion:
[van Hees+RR ’08]
qd
dRq
qdM)(Vd
dMdN therm
eeFB
thermee
fo
40
3
0
3.5.2 Sensitivity of NA60 to Spectral Function
• Significant differences in low-mass region• Overall slope T~150-200MeV (!)
[CERN Courier Nov. 2009]
Emp. scatt. ampl. + T- approximationHadronic many-bodyChiral virial expansion
M[GeV]
3.5.3 Sensitivity to Spectral Function II
• avg. (T~150MeV) ~ 350-400 MeV
(T~Tc) ≈ 600 MeV → m
• driven by baryons
• Breit-Wigner shape insufficient: Im ~ - q0 vac (1+ B/0)
3.6 Low-Mass e+e at RHIC: PHENIX vs. STAR
• “large” enhancement not accounted for by theory • QGP radiation not an option…
• (very) low-mass region overpredicted?! (SPS?!)
2.) Transport Properties
EM Conductivity + Low-Energy Photons
3.) Spectral Properties
Vector Spectral Functions + the Fate of Resonances Dilepton Invariant-Mass Spectra
4.) Chiral Restoration Criteria: Axialvector, Lattice QCD, pert. QCD
QCD +Weinberg Sum Rules
5.) Fireball Properties
Lifetime, Temperature, Collectivity
6.) Conclusions
Outline
4.) Criteria for Chiral Restoration
• Vector () – Axialvector (a1) degenerate
)Im(ImsdsI AVn
n 2
102
1 0 q)q(αcI,I,fI sπ
[Weinberg ’67, Das et al ’67]
pQCD
• QCD sum rules:
medium modifications ↔ vanishing of condensates
• Agreement with thermal lattice-QCD
• Approach to perturbative rate (QGP)
4.1 Axialvector in Medium: Dynamical a1(1260)
+ + . . . =
Vacuum:
a1
resonance
InMedium: + + . . .
[Cabrera,Jido, Roca+RR ’09]
• in-medium + propagators• broadening of - scatt. Amplitude• pion decay constant in medium:
n
nn
Q
c)Q(Π 2
2
nonpert. Wilson coeffs. (condensates)
0.2% 1%
4.2 QCD Sum Rules: (770) in Nuclear Matter
• dispersion relation:
• lhs: OPE (spacelike Q2): • rhs: hadronic model (s>0):
[Shifman,Vainshtein,+Zakharov ’79]
sQ
)s(Ims
dsQ
)Q(Π
20
2
2
[Hatsuda+Lee’91, Asakawa+Ko ’92, Klingl et al ’97, Leupold et al ’98, Kämpfer et al ‘03, Ruppert et al ’05]
)ss()(s
)s(DImg
m)s(Im
sdual
18
2
4
2q)q(• ~50% reduced in nuclear matter
◊ ← vacuum
4.3 Hadronic - Perturbative QGP - Lattice QCD dRee /dM2 ~ ∫d3q f B(q0;T) Im em
• Hadronic, pert. + lattice QCD tend to “degenerate” toward ~Tc
• Quark-Hadron Duality at all M ?! ( degenerate axialvector SF!)
[qq→ee]-[HTL]
[RR,Wambach et al ’99]
[Ding et al ’10]
dRee/d4q 1.4Tc (quenched) q=0
4.3.2 Euclidean Correlators: Lattice vs. Hadronic
]T/q[)]T/(q[
)T;q,q(dq
)T;q,( VV 221
2 0
00
0
0sinh
cosh • Euclidean Correlation fct.
)T,(G
)T,(G
V
V
free
Hadronic Many-Body [RR ‘02] Lattice (quenched) [Ding et al ‘10]
• “Parton-Hadron Duality” of lattice and in-medium hadronic?!
4.3.3 Back to Spectral Function
• suggests approach to chiral restoration + deconfinement
-Im
em
/(C
T q
0)
2.) Transport Properties
EM Conductivity + Low-Energy Photons
3.) Spectral Properties
Vector Spectral Functions + the Fate of Resonances Dilepton Invariant-Mass Spectra
4.) Chiral Restoration Criteria: Axialvector, Lattice QCD, pert. QCD
QCD +Weinberg Sum Rules
5.) Fireball Properties
Lifetime, Temperature, Collectivity
6.) Conclusions
Outline
5.1 Low-Mass Dileptons: Chronometer
• first “explicit” measurement of interacting-fireball lifetime: FB ≈ (6.5±1) fm/c
• search for critical slowing down!
In-In Nch>30
5.2 Intermediate-Mass Dileptons: Thermometer• use invariant continuum radiation (M>1GeV): no blue shift, Tslope = T !
• independent of partition HG vs QGP (dilepton rate continuous/dual)• initial temperature Ti ~ 190-220 MeV at CERN-SPS
Thermometer
5.3 Dimuon pt-Spectra and Slopes: Barometer
• theo. slopes originally too soft
• increase fireball acceleration, e.g. a┴ = 0.085/fm → 0.1/fm
• insensitive to Tc=160-190MeV
Effective Slopes Teff
5.4 Direct Photons at RHIC
• v2,dir as large as that of pions!?
• underpredcited by QGP-dominated emission
← excess radiation
• Teffexcess = (220±25) MeV
• QGP radiation?• radial flow?
Spectra Elliptic Flow
[Holopainen et al ’11,…]
5.4.1 Revisit Ingredients
• multi-strange hadrons at “Tc”
• v2bulk fully built up at hadronization
• chemical potentials for , K, …
• Hadron - QGP continuity!
Emission Rates Fireball Evolution
[van Hees et al ’11]
[Turbide et al ’04]
5.4.2 Thermal Photon Spectra + v2: PHENIX
• both spectral slope and v2 point at
blue-shifted hadronic source…• to be tested in full hydro
thermal + prim.
[van Hees,Gale+RR ’11]
6.) Conclusions: Potential of Thermal EM Radiation at RHIC
• Transport: conductivity, susceptibility (→ diffusion, /s)
• Spectrometer: “prototype” in-med. spectral function, hadron-to-quark transition
• Chiral Restoration: Weinberg + QCD sum rules, lattice QCD (B~0!) + perturbative limit
• Thermometer: int.-mass dileptons (heavy-flavor subtracted)
• Chronometer: search for anomalous fireball lifetimes
• Barometer: pt spectra (M=0-2GeV)
• Quality control: rates (constraints, continuity), medium evolution, consistency with SPS, …
• Needed: NA60-quality data
• RHIC premiere facility for soft EM probes of transition region
2.3.2 NA60 Mass Spectra: pt Dependence
• more involved at pT>1.5GeV: Drell-Yan, primordial/freezeout , …
M [GeV]
4.1.2 Mass-Temperature Emission Correlation• generic space-time argument:
Tmax ≈ M / 5.5
(for Im em =const)
23em44
33
0e /T/M
FBeeee )MT(
MIm
)T(Vqxdd
dNqxdd
qM
dMddN
55.T/Mee TdTdM
dN eT)(M,Im em
• thermal photons:
Tmax ≈ (q0/5) * (T/Teff)2
→ reduced by flow blue-shift! Teff ~ T * √(1+)/(1)
4.7.2 Light Vector Mesons at RHIC + LHC
• baryon effects important even at B,tot= 0 : sensitive to Btot= + B (-N and -N interactions identical) • also melts, more robust ↔ OZI
-
5.3 Intermediate Mass Emission: “Chiral Mixing”
)q()q()()q( ,A
,VV
00 1
)q()q()()q( ,V
,AA
001 =
=
• low-energy pion interactions fixed by chiral symmetry
• mixing parameter
2
2
3
3
2 6224
fT)(f
)(kd
fk
k
[Dey, Eletsky +Ioffe ’90]
0
0 0
0
• degeneracy with perturbative spectral fct. down to M~1GeV
• physical processes at M≥ 1GeV: a1 → e+e etc. (“4 annihilation”)
3.2 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
2.3.2 Acceptance-Corrected NA60 Spectra
• more involved at pT>1.5GeV: Drell-Yan, primordial/freezeout , …M [GeV] M [GeV]
4.4.3 Origin of the Low-Mass Excess in PHENIX?
• QGP radiation insufficient:
space-time , lattice QGP rate + resum. pert. rates too small
- “baked Alaska” ↔ small T - rapid quench+large domains ↔ central A-A - therm + DCC → e+ e ↔ M~0.3GeV, small pt
• must be of long-lived hadronic origin
• Disoriented Chiral Condensate (DCC)?
• Lumps of self-bound pion liquid?
• Challenge: consistency with hadronic data, NA60 spectra!
[Bjorken et al ’93, Rajagopal+Wilczek ’93]
[Z.Huang+X.N.Wang ’96 Kluger,Koch,Randrup ‘98]
2.2 EM Probes at SPS
• all calculated with the same e.m. spectral function!•thermal source: Ti≈210MeV, HG-dominated, -meson melting!
2.3.3 Spectrometer III: Before Acceptance Correction
• Discrimination power much reduced• can compensate spectral “deficit” by larger flow: lift pairs into acceptance
hadr. many-body + fireball
emp. ampl. + “hard” fireball
schem. broad./drop.+ HSD transportchiral virial
+ hydro
4.2 Improved Low-Mass QGP Emission
• LO pQCD spectral function: V(q0,q) = 6∕9 3M2/21+QHTL(q0)]
• 3-momentum augmented lattice-QCD rate (finite rate)
)q,q()T;q(fMqd
dRV
Bee0023
2em
4 6
4.4.1 Variations in QGP Radiation
• improvements in QGP rate insufficient
4.4.2 Variations in Fireball Properties
• variations in space-time evolution only significant in (late) hadronic phase
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!
1.2 Intro-II: EoS and Particle Content
• Hadron Resonance Gas until close to Tc
- but far from non-interacting: short-lived resonances R: a + b → R → a + b , R ≤ 1 fm/c
• Parton Quasi-Particles shortly above Tc
- but large interaction measure I(T) = -3P
both “phases” strongly coupled (hydro!):
- large interaction rates → large collisional widths
- resonance broadening → melting → quarks
- broad parton quasi-particles
- “Feshbach” resonances around Tc (coalescence!)
2.3.6 Hydrodynamics vs. Fireball Expansion
• very good agreement between original hydro [Dusling/Zahed] and fireball [Hees/Rapp]
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
