1. Thermal Dileptons + Photons: Baseline Approach
6/27/2018
Ralf Rapp
Cyclotron Institute +
Dept of Phys & Astro
Texas A&M University
College Station, USA
RIKEN/BNL Workshop on
“Thermal Radiation” in Heavy-Ion Reactions
BNL (Upton, NY),

2. 1.) Intro: EM Spectral Function + Fate of Resonances
Im Pem(M) in Vacuum
Im Πem(M,q;mB,T)
Electromagnetic spectral function
- √s < 2 GeV : non-perturbative
- √s > 2 GeV : perturbative (“dual”)
Vector resonances “prototypes”
- representative for bulk hadrons:
neither Goldstone nor heavy flavor
Medium modifications of resonances
- QCD phase structure
- HICs: correlate (mN,T) ↔ spectral shape
e+e- → hadrons
√s = M

3. 1.2 Chiral Restoration in Lattice QCD
≈ qq / qq0
Tpcc ~155MeV
[Fodor
et al ’10]
compatible with hadron resonance gas (also for thermodynamics!)
chiral restoration in “hadronic phase”? (low-mass dileptons!)
cross-over ↔ smooth EM emission rates across Tpc

4. Outline 2.) Spectral Function in Medium
6/27/2018
Outline
2.) Spectral Function in Medium
 Effective Hadronic Theory in Medium
 QGP Emission and Lattice QCD
 Chiral Restoration
3.) Dilepton Spectra in Heavy-Ion Collisions
 Nature of Emission Source from SPS to RHIC
 Spectral Shapes and Temperatures
 Radial and Elliptic Collectivity
4.) Conclusions

5. 2.1 Baseline I: r Meson in Hadronic Matter
[Pisarski, Chanfray et al, Herrmann et al, Asakawa et al, RR et al, Koch et al, Steele et al, Post et al, Eletsky et al, Harada et al …]
r-Propagator:
Dr (M,q;mB ,T) = [M 2 - mr2 - Srpp - SrB - SrM ] -1
>
B*,a1,K1... Sp r r
Selfenergies:
Srpp =
SrB,rM = Sp
N,p,K…
Constraints: decays: B,M→ rN, rp, ... ; scattering: pN → rN, gA, …
rB /r0
0.1
0.7
2.6
SPS
RHIC / LHC

6. 2.2 Chiral Condensate + r-Meson Broadening
-Im PV / s
qq / qq0
effective hadronic theory
h = mq h|qq|h > 0 contains quark core + pion cloud
= Shcore + Shcloud ~
matches spectral medium effects: resonances + pion cloud
resonances + “chiral mixing” drive r-SF toward chiral restoration Sp
> -

7. 2.3 Baseline II: Perturbative + Lattice QGP Rates dRee /dM2 ~ ∫d3q f B(q0;T) Im Pem
rates smoothly match around Tpc:
- compatible with cross-over
- 3-fold “degeneracy” -
[qq→ee]
[HTL]
[Braaten et al ‘91]
[Ding et al ’10]
dRee/d4q 1.4Tc (quenched)
q=0
[RR,Wambach et al ’99]

8. 2.4 Vector Correlator in Thermal Lattice QCD
Euclidean Correlation fct.
Lattice (quenched) [Ding et al ‘10]
Hadronic Many-Body [RR ‘02]
“Parton-Hadron Duality” of finite-T lattice + in-medium hadronic?

9. 2.5 Criteria for Chiral Restoration
Vector (r) – Axialvector (a1) degenerate
[Weinberg ’67,
Das et al ’67,
Kapusta+
Shuryak ‘94]
pQCD
QCD sum rules:
medium modifications ↔ vanishing of condensates
Degeneracy with thermal lattice-QCD
Approach to perturbative rate (QGP)
→ Talk by Hohler

10. Outline 2.) Spectral Function in Medium
6/27/2018
Outline
2.) Spectral Function in Medium
 Effective Hadronic Theory in Medium
 QGP Emission and Lattice QCD
 Chiral Restoration
3.) Dilepton Spectra in Heavy-Ion Collisions
 Nature of Emission Source from SPS to RHIC
 Spectral Shapes and Temperatures
 Radial and Elliptic Collectivity
4.) Conclusions

11. 3.1 Thermal Dilepton + Photon Emission Rates
6/27/2018 e+ e- γ
Im Πem(M,q;mB,T)
Im Πem(q0=q;mB,T)
determined by the same spectral function
finite photon rate ↔ divergent dilepton rate for M → 0
low mass:
r -meson
dominated
ImPem ~ [ImDr + ImDw /10 + ImDf /5]

12. 3.2 SPS I: Dielectrons with CERES/NA45
Evolve rates over fireball expansion:
Pb-Au(17.3GeV)
Pb-Au(8.8GeV)
Excess Spectra
established large enhancement
consistent with a “r-melting” around Tpc
large effects at lower beam energy: baryons!
M→0: photon point!

13. 3.3 SPS II: Precision with m+m- at NA60
Acc.-corrected Excess Spectra
In-In(17.3GeV)
[NA60 ‘09]
vs Theoretical Input Rates r
cont.
Mmm [GeV]
[van Hees+RR ’08]
broadened r spectral function quantitatively confirmed
invariant-mass spectrum directly reflects thermal emission rate!
mass slope reveals emission temperature around Tpcc ~ 150 MeV

14. 3.4 Low-Mass e+e- Excitation Function at RHIC
PHENIX
STAR
QM12
tension between PHENIX and STAR (central Au-Au)
non-central Au-Au consistent with “universal” source around Tpc
partition hadronic/QGP depends on EoS
→ Talks by Wang, Vujanovic, Linnyk

15. 3.4.2 Hadronic vs. QGP Emission at RHIC
(Tc=180MeV)
(Tpc=170MeV)
smaller Tpc + lattice EoS enhance QGP + deplete hadronic yield
corroborates prevalent emission source around Tpc

16. 3.5 Direct Photons at RHIC Spectra Elliptic Flow
← excess radiation
Teffexcess = (220±25) MeV “moderate”
~  T √(1+b)/(1-b)  suggests T < 200 MeV
large v2 also suggests “later” emission (aka ~Tpc)

17. 3.5.2 Thermal Photon Spectra + v2
+ prim. g
(Tc=180MeV)
[van Hees,Gale+RR ’11]
M → 0 limit of dilepton rates (continuous across Tc!)
flow blue-shift, e.g. b=0.3: T ~ 220MeV / 1.35 ~ 160 MeV
confirms bulk emission around Tpc
compatible with hydro evolution if bulk-v2 saturates at Tpc
[He at al in prep.]
→ Talks by Skokov, Tuchin, Dusling

18. 3.6 Elliptic Flow of Dileptons at RHIC
maximum structure due to
late r decays
[He et al in prep.]
[Chatterjee et al ‘07, Zhuang et al ‘09]

19. 4.) Conclusions
Low-mass dileptons at SPS+RHIC point at universal source,
avg. emission temperatures T ~ 150MeV ~ Tpcc (slopes, v2)
r-meson smoothly melts into QGP continuum radiation
Mechanisms underlying r-melting (p cloud + resonances) find
counterparts in hadronic S-terms, restoring chiral symmetry
Quantitative studies relating r-SF to chiral order parameters with
QCD and Weinberg-type sum rules ongoing
Need conditions under which medium effects turn off
Future precise characterization of EM emission source at
RHIC, LHC + CBM/NICA/SIS holds rich info on QCD phase
structure (spectral shape + disp. rel., source collectivity + lifetime)

20. 4.1 How to Turn off Medium Effects
pp collisions: cocktail - seems to work (but: no medium effect)
Peripheral collisions - challenging: dense hadronic phase persists
d-A collisions: forward vs. backward y (formation time effects?)
High(er) pT
- seems to work: NA60 m+m-
Elementary projectiles on cold nuclei
- seems to work: CLAS gA → e+e- X
(Gr ≈ 220 MeV)
full calculation
fix density 0.4r0
Fe - Ti

21. 2.3.2 NA60 Mass Spectra: pt Dependence
Mmm [GeV]
rather involved at pT>1.5GeV: Drell-Yan, primordial/freezeout r , …

22. 3.4.3 Hadronic vs. QGP Photons at RHIC
(Tc=180MeV)
(Tpc=170MeV)
smaller Tpc + lattice EoS enhance QGP + deplete hadronic yield
corroborates prevalent emission source around Tpc

23. 3.6 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)

24. 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

25. 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~ MeV (true T, no blue shift!)

26. 3.2 Spectral Functions + Weinberg Sum Rules
Quantify chiral symmetry breaking via observable spectral functions
Vector (r) - Axialvector (a1) spectral splitting
[Weinberg ’67, Das et al ’67;
Kapusta+Shuryak ‘93]
t→(2n+1)p
pQCD
Updated “fit”: [Hohler+RR ‘12]
r + a1 resonance, excited states (r’+ a1’), universal continuum (pQCD!)
t→(2n)p
[ALEPH ’98,OPAL ‘99]
rV/s
rA/s

27. 3.2.2 Evaluation of Chiral Sum Rules in Vacuum
pion decay
constants
chiral quark
condensates
vector-axialvector splitting quantitative observable of
spontaneous chiral symmetry breaking
promising starting point to analyze chiral restoration

28. 2.3 QCD Sum Rules: r and a1 in Vacuum
dispersion relation:
[Shifman,Vainshtein+Zakharov ’79]
lhs: hadronic spectral fct.
rhs: operator product expansion
4-quark + gluon condensate dominant
vector axialvector

29. 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]

30. 2.4 Dilepton Thermometer: Slope Parameters
Invariant Rate vs. M-Spectra Transverse-Momentum Spectra
cont.
Tc=160MeV
Tc=190MeV r
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

31. 4.3.2 Revisit Ingredients Emission Rates Fireball Evolution
Hadron - QGP continuity!
conservative estimates…
multi-strange hadrons at “Tc”
v2bulk fully built up at hadronization
chemical potentials for p, K, …
[Turbide et al ’04]
[van Hees et al ’11]

32. 5.1 Thermal Dileptons at LHC
charm comparable, accurate (in-medium) measurement critical
low-mass spectral shape in chiral restoration window

33. 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= MeV)
enrich with (low-) pt cuts

34. 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= MeV

35. 3.4.2 Back to Spectral Function
suggests approach to chiral restoration + deconfinement

36. 4.2 Improved Low-Mass QGP Emission
LO pQCD spectral function: rV(q0,q) = 6∕9 3M2/2p [1+QHTL(q0)]
augment lat-QCD rate with
finite 3-momentum (g rate)

37. 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?!)

38. 4.2 Low-Mass Dileptons: Chronometer
In-In Nch>30
first “explicit” measurement of interacting-fireball lifetime:
tFB ≈ (6±1) fm/c

39. 3.2 Axialvector in Nucl. Matter: Dynamical a1(1260)p a1
resonance
Vacuum: = r Sr Sp p r Sr Sp In
Medium:
[Cabrera,Jido,
Roca+RR ’09]
in-medium p + r propagators
broadening of p-r scatt. Amplitude
pion decay constant in medium:

40. 3.6 Strategies to Test For Chiral Restoration
eff. theory for
VC + AV
spectral functs.
Lat-QCD Euclidean correlators
vac. data + elem. reacts. (gA→eeX, …)
constrain Lagrangian
(low T, rN)
constrainVC + AV : QCD SR
Lat-QCD condensates + c ord. par.
EM data in heavy-ion coll.
global analysis of M, pt, v2
test
VC - AV:
chiral SRs
Realistic bulk evol. (hydro,…)
Agreement with data?
Chiral restoration?

41. 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
p, K, p, L, … at Tfo ~ 110MeV
v2 saturates at Tch, good light-/strange-hadron phenomenology
[He et al ’11]

42. 2.1 Chiral Symmetry + QCD Vacuum
: flavor + “chiral” (left/right) invariant
“Higgs” Mechanism in Strong Interactions:
qq attraction  condensate fills QCD vacuum!
Spontaneous Chiral Symmetry Breaking
> qL qR - -
Profound Consequences:
effective quark mass:
↔ mass generation!
near-massless Goldstone bosons p0,±
“chiral partners” split: DM ≈ 0.5GeV
JP=0± ± /2±

43. 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)?
Lumps of self-bound pion liquid?
Challenge: consistency with hadronic data, NA60 spectra!
[Bjorken et al ’93, Rajagopal+Wilczek ’93]
- “baked Alaska” ↔ small T
- rapid quench+large domains ↔ central A-A
- ptherm + pDCC → e+ e- ↔ M~0.3GeV, small pt
[Z.Huang+X.N.Wang ’96
Kluger,Koch,Randrup ‘98]

44. 2.2 EM Probes at SPS
all calculated with the same e.m. spectral function!
thermal source: Ti≈210MeV, HG-dominated, r-meson melting!

45. 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 ~ MeV at CERN-SPS

46. 4.7.2 Light Vector Mesons at RHIC + LHC
baryon effects important even at rB,tot= 0 :
sensitive to rBtot= rB + rB (r-N and r-N interactions identical)
w also melts, f more robust ↔ OZI - -

47. 5.3 Intermediate Mass Emission: “Chiral Mixing”
[Dey, Eletsky +Ioffe ’90]
low-energy pion interactions fixed by chiral symmetry =
mixing parameter
degeneracy with perturbative
spectral fct. down to M~1GeV
physical processes at M≥ 1GeV:
pa1 → e+e- etc. (“4p annihilation”)

48. 3.2 Dimuon pt-Spectra and Slopes: Barometer
pions: Tch=175MeV
a┴ =0.085/fm
pions: Tch=160MeV
a┴ =0.1/fm
modify fireball evolution:
e.g. a┴ = 0.085/fm → 0.1/fm
both large and small Tc compatible
with excess dilepton slopes

49. 2.3.3 Spectrometer III: Before Acceptance Correction
emp. ampl. +
“hard” fireball
hadr. many-body
+ fireball
schem. broad./drop.
+ HSD transport
chiral virial
+ hydro
Discrimination power much reduced
can compensate spectral “deficit” by larger flow: lift pairs into acceptance

50. 4.1 Nuclear Photoproduction: r Meson in Cold Matter
g + A → e+e- X
extracted
“in-med” r-width
Gr ≈ 220 MeV e+ e-
Eg≈1.5-3 GeV g r
[CLAS ‘08]
Microscopic Approach:
Fe - Ti g N r
production amplitude
in-med. r spectral fct. +
M [GeV]
[Riek et al ’08, ‘10]
full calculation
fix density 0.4r0
r-broadening reduced at high 3-momentum; need low momentum cut!

51. 2.3.6 Hydrodynamics vs. Fireball Expansion
very good agreement
between original
hydro [Dusling/Zahed]
and fireball [Hees/Rapp]