1. What can we extract from Thermal EM Radiation in Heavy-Ion Collisions?
7/4/2018
Ralf Rapp
Cyclotron Institute +
Dept of Phys & Astro
Texas A&M University
College Station, USA
International School on Nuclear Physics, 38th Course
Erice (Sicily, Italy),

2. 1.) Intro: EM Spectral Function to Probe Fireball
Thermal Dilepton Rate
Im Πem(M,q;mB,T)
e+e- → hadrons r
Im Pem(M) / M2
Hadronic Resonances
- change in degrees of freedom?
- restoration of chiral symmetry?
Continuum
- temperature?
Low-q0,q limit: transport coefficient (charge)?
Total yields: fireball lifetime?
e+ e-
e e-
M [GeV]

3. 1.2 30 Years of Dileptons in Heavy-Ion Collisions
<Nch>=120
Robust understanding across QCD phase diagram:
QGP + hadronic radiation with melting r resonance

4. Outline 1.) Introduction 2.) Degrees of Freedom of the Medium
7/4/2018
Outline
1.) Introduction
2.) Degrees of Freedom of the Medium
 Quark-to-Hadron Transition
3.) Chiral Symmery Restoration
 QCD +Weinberg Sum Rules
 Other Multiplets
4.) Transport Properties
 Electric Conductivity
5.) Phenomenological Tool
 Fireball Lifetime + Temperature (Excitation Fct.)
 Fireball in pA?
6.) Conclusions

5. 2.) Dilepton Rates and Degrees of Freedom dRee /dM2 ~ ∫d3q f B(q0;T) Im Pem
r-meson resonance “melts”
spectral function merges into
QGP description
Direct evidence for transition
hadrons → quarks + gluons -
[qq→ee]
[HTL]
[Ding et al ’10]
dRee/d4q 1.4Tc (quenched) q=0
[RR,Wambach et al ’99]

6. Outline 1.) Introduction 2.) Degrees of Freedom of the Medium
7/4/2018
Outline
1.) Introduction
2.) Degrees of Freedom of the Medium
 Quark-to-Hadron Transition
3.) Chiral Symmery Restoration
 QCD +Weinberg Sum Rules
 Other Multiplets
4.) Transport Properties
 Electric Conductivity
5.) Phenomenological Tool
 Fireball Lifetime + Temperature (Excitation Fct.)
 Fireball in pA?
6.) Conclusions

7. 3.1 QCD + Weinberg Sum Rules
[Hatsuda+Lee’91,
Asakawa+Ko ’93,
Leupold et al ’98, …] r a1
Dr = rV -rA
[Weinberg ’67, Das et al ’67;
Kapusta+Shuryak ‘94]
accurately satisfied in vacuum
In Medium:
condensates from hadron resonance gas,
constrained by lattice-QCD
T [GeV]

8. 3.1.2 QCD + Weinberg Sum Rules in Medium
→ Search for solution for axial-vector spectral function
[Hohler +RR ‘13]
quantitatively compatible with (approach to) chiral restoration
strong constraints by combining SRs
Chiral mass splitting “burns off”, resonances melt

9. 3.2 Lattice-QCD Results for N(940)-N*(1535)
Euclidean Correlator Ratios Exponential Mass Extraction
“Nucleon”
“N*(1535)”
R = ∫(G+-G-)/(G++G-)
[Aarts et al ‘15]
also indicates MN*(T) → MN (T) ≈ MNvac
see also talk by R.-A. Tripolt

10. Outline 1.) Introduction 2.) Degrees of Freedom of the Medium
7/4/2018
Outline
1.) Introduction
2.) Degrees of Freedom of the Medium
 Quark-to-Hadron Transition
3.) Chiral Symmery Restoration
 QCD +Weinberg Sum Rules
 Other Multiplets
4.) Transport Properties
 Electric Conductivity
5.) Phenomenological Tool
 Fireball Lifetime + Temperature (Excitation Fct.)
 Fireball in pA?
6.) Conclusions

11. 4.) Electric Conductivity
Similar behavior for different transport? h/s ~ (2pT) DsHF ~ sEM/T
Probes soft limit of EM spectral function
sEM(T) = - e2 limq0→0 [ ∂/∂q0 Im PEM(q0,q=0;T) ]
Need density-squared contributions
Non-trivial for vertex corrections
(usually evaluated with vacuum propagators)
Start out with pion gas: dress pions in r-cloud + vertex corrections
[Atchison+RR in prog.]

12. 4.2 Low-Energy Limit of Spectral Function
Pion Gas Perturbative QGP
T=150MeV
ar = 0.7
ar = 1.2
ar = 2.7
q0 [MeV]
[Moore+Robert ‘06]
conductivity peak strongly smeared out
suggestive for strongly coupled system

13. 4.3 Conductivity: Comparison to other Approaches
in-med. p gas →
[Greif et al ‘16]
in-medium pion gas well above SYM limit
interactions with anti-/baryons likely to reduce it

14. Outline 1.) Introduction 2.) Degrees of Freedom of the Medium
7/4/2018
Outline
1.) Introduction
2.) Degrees of Freedom of the Medium
 Quark-to-Hadron Transition
3.) Chiral Symmery Restoration
 QCD +Weinberg Sum Rules
 Other Mutiplets
4.) Transport Properties
 Electric Conductivity
5.) Phenomenological Tool
 Fireball Lifetime + Temperature (Excitation Fct.)
 Fireball in pA?
6.) Conclusions

15. 5.1 Fireball Lifetime
Excitation Function of Low-Mass Dilepton Excess Yield
1000
[RR+van Hees ‘14]
[STAR ‘15]
Low-mass excess tracks lifetime well (medium effects!)
Tool for critical point search?

16. 5.2 Fireball Temperature Slope of Intermediate-Mass Excess Dileptons
unique ``early” temperature measurement (no blue-shift!)
Ts approaches Ti toward lower energies
first-order “plateau” at BES-II/CBM?

17. 5.3 Low-Mass Dileptons in p-Pb (5.02GeV)
Thermal radiation at ~10% of cocktail
follows excess-lifetime systematics
photons [Shen et al ‘15]

18. 6.) Conclusions
Explicit evidence for parton-hadron transition (r melting)
Progress in understanding mechanisms of chiral restoration
- evaporation of chiral mass r-a1 splitting (sum rules, MYM)
Electric conductivity suggests strongly coupled medium
Dilepton radiation as a precision tool to measure
- fireball lifetime (low mass), including pA
- early temperature (intermediate mass; no blue-shift)

19. 4.3 Comparison to Data: RHIC
Ideal Hydro Viscous Hydro
[van Hees et al, ‘11, ’14]
[Paquet et al ’16]
same rates + intial flow  similar results from various evolution models

20. 3.2 Massive Yang-Mills in Hot Pion Gas
Temperature progression of vector + axialvector spectral functions
supports “burning” of chiral-mass splitting
as mechanism for chiral restoration
[as found in sum rule analysis]

21. 4.1 Initial Flow + Thermal Photon-v2
Bulk-Flow Evolution
Direct-Photon v2
Ideal Hydro
0-20% Au-Au
initial radial flow: - accelerates bulk v2
- harder radiation spectra
(pheno.: coalescence, multi-strange f.o.)
much enhances thermal-photon v2
[He et al ’14]

22. [Holt,Hohler+RR in prep]
4.2 Thermal Photon Rates
Hadronic emission rate close to QGP-AMY
semi-QGP much more suppressed [Pisarski et al ‘14]
``Cocktail” of hadronic sources
(available in parameterized form)
Sizable new hadronic sources:
pr → gw , pw → gr , rw → gp
[Heffernan et al ‘15]
[Holt,Hohler+RR in prep]

23. 3.2 Massive Yang-Mills Approach in Vaccum
Gauge r + a1 into chiral pion lagrangian:
problems with vacuum phenomenology
→ global gauge?
Recent progress:
- full r propagator in a1 selfenergy
- vertex corrections to preserve
PCAC:
[Urban et al ‘02,
Rischke et al ‘10]
[Hohler +RR ‘14]
enables fit to t-decay data!
local-gauge approach viable
starting point for addressing
chiral restoration in medium

24. 4.3.2 Photon Puzzle!? Tslopeexcess ~240 MeV
blue-shift: Tslope ~ T √(1+b)/(1-b)
 T ~ 240/1.4 ~ 170 MeV

25. 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

26. 4.2 Low-Mass Dileptons: Chronometer
In-In Nch>30
first “explicit” measurement of interacting-fireball lifetime:
tFB ≈ (7±1) fm/c

27. 4.1 Prospects I: Spectral Shape at mB ~ 0
STAR Excess Dileptons
[STAR ‘14]
rather different spectral shapes compatible with data
QGP contribution?

28. 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)

29. 2.3 Low-Mass e+e- Excitation Function: 20-200 GeV
P. Huck et al. [STAR],
QM14
compatible with predictions from melting r meson
“universal” source around Tpc

30. 3.3.2 Effective Slopes of Thermal Photons
Thermal Fireball Viscous Hydro
[van Hees,Gale+RR ’11]
[S.Chen et al ‘13]
thermal slope can only arise from T ≤ Tc (constrained by
closely confirmed by hydro hadron data)
exotic mechanisms: glasma BE? Magnetic fields+ UA(1)?
[Liao at al ’12, Skokov et al ’12, F. Liu ’13,…]

31. 2.2 Transverse-Momentum Dependence
pT -Sliced Mass Spectra
mT -Slopes
x 100
spectral shape as function of pair-pT
entangled with transverse flow (barometer)

32. 3.1.2 Transverse-Momentum Spectra: Baro-meter
Effective Slope Parameters
SPS
RHIC
QGP HG
[Deng,Wang,
Xu+Zhuang ‘11]
qualitative change from SPS to RHIC: flowing QGP
true temperature “shines” at large mT

33. 2.2 Chiral Condensate + r-Meson Broadening
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
> - r

34. 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

35. 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]

36. 3.3.2 Fireball vs. Viscous Hydro Evolution
[van Hees,
Gale+RR ’11]
[S.Chen
et al ‘13]
very similar!

37. 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 - -

38. 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+GiBUU ‘08]
Microscopic Approach:
Fe - Ti g N r
product. 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!