Thermal Electromagnetic Radiation
in Heavy-Ion Collisions
Ralf Rapp
Cyclotron Institute +
Dept of Phys & Astro
Texas A&M University
College Station, USA
34th International School of Nuclear Physics
“Probing the Extremes of Matter with Heavy Ions”
Erice (Sicily, Italy), 20.09.12
1.) Intro: EM Spectral Function + Fate of Resonances
2
- em
3 2
dN ee
B

f
( q0 ,T ) Im Πem(M,q;mB,T)
4
4
d xd q  M
• Electromagn. spectral function
- √s < 2 GeV : non-perturbative
- √s > 2 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?
Im Pem(M) in Vacuum
e+e- → hadrons
√s = M
-  / qq
- 0
≈ qq
1.2 Phase Transition(s) in Lattice QCD
Tpcc ~155MeV
[Fodor
et al ’10]
• cross-over(s) ↔ smooth EM emission rates across Tpc
• chiral restoration in “hadronic phase”? (low-mass dileptons!)
• hadron resonance gas
Outline
2.) Spectral Function + Emission Temperature
 In-Medium r + Dilepton Rates
 Dilepton Mass Spectra + Slopes
 Excitation Function + Elliptic Flow
3.) Chiral Symmetry Restoration
 Chiral Condensate
 Weinberg + QCD Sum Rules
 Euclidean Correlators
4.) Conclusions
2.1 Vector Mesons in Hadronic Matter
[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 …]
Dr (M,q;mB ,T) = [M 2 - mr2 - Sr - SrB - SrM ] -1
Selfenergies: Sr =
r
S
S
SrB,rM =
r
>
B*,a1,K1...
>
r-Propagator:
N,,K…
Constraints: decays: B,M→ rN, r, ... ; scattering: N → rN, gA, …
SPS
RHIC / LHC
r B /r 0
0
0.1
0.7
2.6
2.2 Dilepton Rates: Hadronic - Lattice - Perturbative
dRee /dM2 ~ ∫d3q f B(q0;T) Im Pem
[qq→ee]
[HTL]
• continuous rate through Tpc
• 3-fold “degeneracy” toward ~Tpc
dRee/d4q 1.4Tc (quenched)
q=0
[Ding et al ’10]
[RR,Wambach et al ’99]
2.3 Dilepton Rates vs. Exp.: NA60 “Spectrometer”

therm
fo
3 dRtherm
dN mm
M
d
q
mm
• Evolve rates over fireball expansion:
  d VFB ( ) 
4
dM
q0
d
q
0
Acc.-corrected m+m- Excess Spectra
In-In(17.3GeV)
[NA60 ‘09]
[van Hees+RR ’08]
Mmm [GeV]
• invariant-mass spectrum directly reflects thermal emission rate!
2.4 Dilepton Thermometer: Slope Parameters
Invariant Rate vs. M-Spectra
cont.
r
Transverse-Momentum Spectra
Tc=160MeV
Tc=190MeV
• Low mass: radiation from around T ~ Tpcc ~ 150MeV
• Intermediate mass: T ~ 170 MeV and above
• Consistent with pT slopes incl. flow: Teff ~ T + M (bflow)2
2.5 Low-Mass e+e- Excitation Function: SPS - RHIC
Pb-Au(8.8GeV)
Au-Au min. bias
QM12
Pb-Au(17.3GeV)
• no apparent change of the emission source
• consistent with “universal” medium effect around Tpc
• partition hadronic/QGP depends on EoS, total yield ~ invariant
2.6 Direct Photons at RHIC
Spectra
Elliptic Flow
← excess radiation
• Teffexcess = (220±25) MeV
• QGP radiation?
• radial flow?
• v2g,dir comparable to pions!
• under-predicted by early QGP
emission [Holopainen et al ’11,…]
2.6.2 Thermal Photon Spectra + v2
thermal
+ prim. g
[van Hees,Gale+RR ’11]
• hadronic emission close to Tpc essential (continuous rate!)
• flow blue-shift: Teff ~ T √(1+b)/(1-b)
e.g. b=0.3: T ~ 220/1.35~ 160 MeV
• small slope + large v2 suggest main emission around Tpc
• confirmed with hydro evolution
[He at al in prep.]
Outline
2.) Spectral Function + Emission Temperature
 In-Medium r + Dilepton Rates
 Dilepton Mass Spectra + Slopes
 Excitation Function + Elliptic Flow
3.) Chiral Symmetry Restoration
 Chiral Condensate
 Weinberg + QCD Sum Rules
 Euclidean Correlators
4.) Conclusions
-  / qq
- 0
qq
3.1 Chiral Condensate + r-Meson Broadening
effective hadronic theory
• Sh = mq h|qq|h
> 0 contains quark core + pion cloud
+
Shcloud
~
+
>
S
>
=
Shcore
S
• matches spectral medium effects: resonances + pion cloud
• resonances + chiral mixing drive r-SF toward chiral restoration
3.2 Spectral Functions + Weinberg Sum Rules
• Quantify chiral symmetry breaking via observable spectral functions
• Vector (r) - Axialvector (a1) spectral splitting
In  -  ds sn ( rV - r A )

[Weinberg ’67, Das et al ’67;
Kapusta+Shuryak ‘93]
→(2n)
rV/s
I - 2  1 f2r2 - FA ,
I -1  fπ2 ,
3
I0  -2mq 0 | q q | 0 , I1  c αs 0 | (q q)2 | 0
[ALEPH ’98,OPAL ‘99]
→(2n+1)
rA/s
pQCD
pQCD
• Updated “fit”: [Hohler+RR ‘12]
r + a1 resonance, excited states (r’+ a1’), universal continuum (pQCD!)
3.2.2 Evaluation of Chiral Sum Rules in Vacuum
• pion decay
constants
I - 2  1 f2r2 - FA
3
• chiral quark
condensates
I0  -2mq 0 | q q | 0
I -1  fπ2
I1  c αs 0 | (q q)2 | 0
• vector-axialvector splitting quantitative observable of
spontaneous chiral symmetry breaking
• promising starting point to analyze chiral restoration
3.3 QCD Sum Rules at Finite Temperature
[Hatsuda+Lee’91, Asakawa+Ko ’93,
Klingl et al ’97, Leupold et al ’98,
Kämpfer et al ‘03, Ruppert et al ’05]
rV/s
T [GeV]
Percentage Deviation
• r and r’ melting
compatible with
chiral restoration
[Hohler +RR ‘12]
3.4 Vector Correlator in Thermal Lattice QCD

• Euclidean Correlation fct. P em ( ,q ;T )   dq0 rem ( q0 ,q ;T ) cosh [ q0( - 1 / 2T )]
0
Lattice (quenched)
[Ding et al ‘10]
2
sinh [ q0 / 2T ]
Hadronic Many-Body
[RR ‘02]
GV ( ,T )
GVfree( ,T )
• “Parton-Hadron Duality” of lattice and in-medium hadronic?
4.) Conclusions
• Low-mass dilepton spectra in URHIC point at universal source
• r-meson gradually melts into QGP continuum radiation
• prevalent emission temperature around Tpc~150MeV (slopes, v2)
• mechanisms underlying r-melting ( cloud + resonances) find
counterparts in hadronic S-terms, which restore chiral symmetry
• quantitative studies relating r-SF to chiral order parameters with
QCD and Weinberg-type sum rules
• Future precise characterization of EM emission source at
RHIC/LHC + CBM/NICA/SIS holds rich info on QCD phase
diagram (spectral shape, source collectivity + lifetime)
2.3 QCD Sum Rules: r and a1 in Vacuum
• dispersion relation:

2
Im
P
(
s
)
Π
(
Q
)
ds


 s Q2  s  Q2
0
• lhs: hadronic spectral fct.
[Shifman,Vainshtein+Zakharov ’79]
• rhs: operator product expansion
• 4-quark + gluon condensate dominant
vector
axialvector
4.5 QGP Barometer: Blue Shift vs. Temperature
SPS
RHIC
• QGP-flow driven increase of Teff ~ T + M (bflow)2 at RHIC
• high pt: high T wins over high-flow r’s → minimum (opposite to SPS!)
• saturates at “true” early temperature T0 (no flow)
4.3.2 Revisit Ingredients
Emission Rates
• Hadron - QGP continuity!
• conservative estimates…
[Turbide et al ’04]
Fireball Evolution
• multi-strange hadrons at “Tc”
• v2bulk fully built up at hadronization
• chemical potentials for , K, …
[van Hees et al ’11]
4.1.3 Mass Spectra as Thermometer
Emp. scatt. ampl.
+ T-r approximation
Hadronic many-body
Chiral virial expansion
Thermometer
[NA60, CERN Courier
Nov. 2009]
• Overall slope T~150-200MeV (true T, no blue shift!)
4.1.2 Sensitivity to Spectral Function
In-Medium r-Meson Width
Mmm [GeV]
• avg. Gr (T~150MeV) ~ 370 MeV  Gr (T~Tc) ≈ 600 MeV → mr
• driven by (anti-) baryons
5.1 Thermal Dileptons at LHC
• charm comparable, accurate (in-medium) measurement critical
• low-mass spectral shape in chiral restoration window
5.2 Chiral Restoration Window at LHC
• low-mass spectral shape in chiral restoration window:
~60% of thermal low-mass yield in “chiral transition region”
(T=125-180MeV)
• enrich with (low-) pt cuts
4.3 Dimuon pt-Spectra and Slopes: Barometer
Effective Slopes Teff
• theo. slopes originally too soft
• increase fireball acceleration,
e.g. a┴ = 0.085/fm → 0.1/fm
• insensitive to Tc=160-190MeV
3.4.2 Back to Spectral Function
• suggests approach to chiral restoration + deconfinement
4.2 Low-Mass e+e- at RHIC: PHENIX vs. STAR
• “large” enhancement not accounted
for by theory
• cannot be filled by QGP radiation…
• (very) low-mass region
overpredicted… (SPS?!)
4.4 Elliptic Flow of Dileptons at RHIC
• maximum structure due to
late r decays
[He et al ‘12]
[Chatterjee et al ‘07, Zhuang et al ‘09]
4.2 Low-Mass Dileptons: Chronometer
In-In Nch>30
• first “explicit” measurement of interacting-fireball lifetime:
FB ≈ (7±1) fm/c
3.2 Axialvector in Nucl. Matter: Dynamical a1(1260)

Vacuum:
In
Medium:
r

r
+
S
Sr
+
+
...
S
S
Sr
Sr
a1
= resonance
+ ...
[Cabrera,Jido,
Roca+RR ’09]
• in-medium  + r propagators
• broadening of -r scatt. Amplitude
• pion decay constant in medium:
3.6 Strategies to Test For Chiral Restoration
eff. theory for
VC + AV
spectral functs.
vac. data +
elem. reacts.
(gA→eeX, …)
constrain
Lagrangian
(low T, rN)
constrain
VC + AV :
QCD SR
EM data in
heavy-ion coll.
Realistic bulk
evol. (hydro,…)
global
analysis of
M, pt, v2
test
VC - AV:
chiral SRs
Agreement
with data?
Chiral
restoration?
Lat-QCD
Euclidean
correlators
Lat-QCD
condensates
+ c ord. par.
4.1 Quantitative Bulk-Medium Evolution
• initial conditions (compact, initial flow?)
• EoS: lattice (QGP, Tc~170MeV) + chemically frozen hadronic phase
• spectra + elliptic flow: multistrange at Tch ~ 160MeV
, K, p, L, … at Tfo ~ 110MeV
[He et al ’11]
• v2 saturates at Tch, good light-/strange-hadron phenomenology
2.1 Chiral Symmetry + QCD Vacuum
LQCD( mu ,d  0 )
: flavor + “chiral” (left/right) invariant
“Higgs” Mechanism in Strong Interactions:
q
L
• qq attraction  condensate fills QCD vacuum!
qR
0 | q q | 0  0 | qLqR  qRqL | 0  -5 fm -3
Spontaneous Chiral Symmetry Breaking
q- L
q-
R
Profound Consequences:
• effective quark mass:
↔ mass generation!
m*q  0 | q q | 0
• near-massless Goldstone bosons 0,±
• “chiral partners” split: DM ≈ 0.5GeV
JP=0±
1±
1/2±
2.3.2 NA60 Mass Spectra: pt Dependence
Mmm [GeV]
• more involved at pT>1.5GeV: Drell-Yan, primordial/freezeout r , …
4.4.3 Origin of the Low-Mass Excess in PHENIX?
• QGP radiation insufficient:
space-time , lattice QGP rate +
resum. pert. rates too small
• must be of long-lived hadronic origin
• Disoriented Chiral Condensate (DCC)? [Bjorken et al ’93, Rajagopal+Wilczek ’93]
[Z.Huang+X.N.Wang ’96
- “baked Alaska” ↔ small T
Kluger,Koch,Randrup ‘98]
- rapid quench+large domains ↔ central A-A
- therm + DCC → e+ e- ↔ M~0.3GeV, small pt
• Lumps of self-bound pion liquid?
• Challenge: consistency with hadronic data, NA60 spectra!
2.2 EM Probes at SPS
• all calculated with the same e.m. spectral function!
•thermal source: Ti≈210MeV, HG-dominated, r-meson melting!
5.2 Intermediate-Mass Dileptons: Thermometer
• use invariant continuum radiation (M>1GeV): no blue shift, Tslope = T !
Thermometer
• independent of partition HG vs QGP (dilepton rate continuous/dual)
• initial temperature Ti ~ 190-220 MeV at CERN-SPS
4.7.2 Light Vector Mesons at RHIC + LHC
• baryon effects important even at rB,tot= 0 :
sensitive to rBtot= rB + r-B (r-N and r-N interactions identical)
• w also melts, f more robust ↔ OZI
5.3 Intermediate Mass Emission: “Chiral Mixing”
[Dey, Eletsky +Ioffe ’90]
• low-energy pion interactions fixed by chiral symmetry
=
=
0
0
0
0
P Vm ( q )  (1-  )P V0,m ( q )   P A0,m ( q )
P Am ( q )  (1-  )P A0,m ( q )   P V0,m ( q )
• mixing parameter
3
2

d
k
4
T
  2
f ( wk )  2
3
f ( 2 ) 2wk
6 f
• 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
pions: Tch=175MeV
a┴ =0.085/fm
• modify fireball evolution:
e.g. a┴ = 0.085/fm → 0.1/fm
• both large and small Tc compatible
with excess dilepton slopes
pions: Tch=160MeV
a┴ =0.1/fm
2.3.3 Spectrometer III: Before Acceptance Correction
emp. ampl. +
“hard” fireball
hadr. many-body
+ fireball
chiral virial
+ hydro
schem. broad./drop.
+ HSD transport
• Discrimination power much reduced
• can compensate spectral “deficit” by larger flow: lift pairs into acceptance
4.2 Improved Low-Mass QGP Emission
2
dRee
em
B

f
( q0 ;T ) rV ( q0 ,q )
4
3 2
d q 6 M
• LO pQCD spectral function: rV(q0,q) = 6∕9 3M2/2 [1+QHTL(q0)]
• 3-momentum augmented lattice-QCD rate (finite g rate)
4.1 Nuclear Photoproduction: r Meson in Cold Matter
g + A → e+e- X
e+
g
r
• extracted
“in-med” r-width
Gr ≈ 220 MeV
Eg≈1.5-3 GeV
e-
[CLAS+GiBUU ‘08]
• Microscopic Approach:
product. amplitude
g
+
in-med. r spectral fct.
r
Fe - Ti
full calculation
fix density 0.4r0
N
[Riek et al ’08, ‘10]
M [GeV]
• r-broadening reduced at high 3-momentum; need low momentum cut!
2.3.6 Hydrodynamics vs. Fireball Expansion
• very good agreement
between original
hydro [Dusling/Zahed]
and fireball [Hees/Rapp]
2.1 Thermal Electromagnetic Emission
EM Current-Current Correlation Function:
m
m
Πem
( q )  -i  d 4 x eiqx  ( x0 )  [ jem
( x ), jem( 0 )]T
Thermal Dilepton and Photon Production Rates:
e+
e-
γ
Low Mass:
2
dRee
- em
B

f
( T ) Im Πem(M,q)
4
3 2
d q
 M
dRg
- em B
q0 3 
f ( T ) Im Πem(q0=q)
2
d q

ImPem ~ [ImDr + ImDw /10 + ImDf /5]
r -meson
dominated
3.5 Summary: Criteria for Chiral Restoration
• Vector (r) – Axialvector (a1) degenerate
In  -  ds s n (Im P V - Im P A )

[Weinberg ’67,
Das et al ’67]
I-1  fπ2 , I0  0 , I1  c αs (q q)2
• QCD sum rules:
medium modifications ↔ vanishing of condensates
• Agreement with thermal lattice-QCD
• Approach to perturbative rate (QGP)
pQCD