1. Thermal Dileptons from High to Low Energies
2/5/2018
Ralf Rapp
Cyclotron Institute +
Dept of Phys & Astro
Texas A&M University
College Station, USA
ISF Research Workshop on
Study of High-Density Matter with Hadron Beams
Weizmann Institute (Rehovot, Israel),

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 (EM conductivity)
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
2/5/2018
Outline
1.) Introduction
2.) Degrees of Freedom of the Medium
 Quark-to-Hadron Transition
3.) Chiral Symmetry Restoration
 QCD +Weinberg Sum Rules
 Other Multiplets
4.) Phenomenological Tool
 Fireball Temperature
 Fireball Lifetime (pA?)
5.) Conclusions

5. 2.1 In-Medium r-Meson Spectral Functions
Dr (M,q;mB,T) = 1 / [M2 – (mr(0))2 - Srpp - SrB - SrM ]
Hot + Dense Matter
[RR+Gale ’99]
Hot Meson Gas
rB/r0
0.1
0.7
2.6
mB =330MeV
[RR+Wambach ’99]
r-meson “melts” in hot/dense matter
baryon density rB more important than temperature

6. 2.2 Dilepton Rates and Degrees of Freedom dRee /dM2 ~ ∫d3q/q0 f B(q0;T) Im Pem /M2
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]

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

8. 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]

9. 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

10. 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

11. Outline 1.) Introduction 2.) Degrees of Freedom of the Medium
2/5/2018
Outline
1.) Introduction
2.) Degrees of Freedom of the Medium
 Quark-to-Hadron Transition
3.) Chiral Symmetry Restoration
 QCD +Weinberg Sum Rules
 Other Multiplets
4.) Phenomenological Tool: Excitation Functions
 Fireball Temperature
 Fireball Lifetime (pA?)
5.) Conclusions

12. 4.1 NA60 Dimuons at SPS (√s=17.3 GeV)
Integrate rates over thermal fireball:
Radiation Spectrum e+ e- r
Low mass:
r-meson melting,
fireball lifetime
High mass:
QGP thermometer
Tavg ~ 200 MeV
q q -

13. 4.2 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/NICA?

14. 4.3 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?

15. 4.4 Dileptons at HADES: Coarse Graining
Coarse-graining of hadronic transport to
→ extract thermodynamic variables
→ convolute with thermal dilepton rate
Temperature + Baryon Density Dilepton Yield vs. Nucleon Flow
[Huovinen et al. ’02,
Endres et al ’15,
Galatyuk et al ‘16]
Au-Au
(1.23AGeV)
build-up of collectivity  EM radiation  “thermal” fireball
fireball lifetime “only” tfb ~ 13 fm/c

16. 4.4.2 Dileptons at HADES: Spectra + Lifetimes
Coarse-Graining Results with in-Medium Spectral Functions
Fair consistency with mass spectra and lifetime systematics

17. 4.5 Lifetime from Dileptons vs. HBT Radii
Rlong qualitatively consistent,
quantitatively much smaller

18. 5.) 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)
Dilepton radiation as a precision tool to measure
- fireball lifetime (low mass), including pA
- early temperature (intermediate mass; no blue-shift)
Coarse-graining enables to extend thermal-radiation tool to lower energies

19. 5.3 Low-Mass Dileptons in p-Pb (5.02GeV)
Thermal radiation at ~10% of cocktail
follows excess-lifetime systematics

20. Outline 1.) Introduction 2.) Degrees of Freedom of the Medium
2/5/2018
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

21. 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!

22. 2.1 In-Medium Vector Mesons at RHIC + LHC
Anti-/baryon effects melt the r meson
w also melts, f more robust ↔ OZI

23. 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

24. 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]

25. 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]

26. [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]

27. 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

28. 4.3.2 Photon Puzzle!? Tslopeexcess ~240 MeV
blue-shift: Tslope ~ T √(1+b)/(1-b)
 T ~ 240/1.4 ~ 170 MeV

29. 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)

30. 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

31. 4.2 Low-Mass Dileptons: Chronometer
In-In Nch>30
first “explicit” measurement of interacting-fireball lifetime:
tFB ≈ (7±1) fm/c

32. 4.1 Prospects I: Spectral Shape at mB ~ 0
STAR Excess Dileptons
[STAR ‘14]
rather different spectral shapes compatible with data
QGP contribution?

33. 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)

34. 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

35. 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,…]

36. 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

37. 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

38. 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

39. 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]

40. 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.]

41. 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

42. 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

43. 3.3.2 Fireball vs. Viscous Hydro Evolution
[van Hees,
Gale+RR ’11]
[S.Chen
et al ‘13]
very similar!