1. EM Radiation + Heavy Flavor in Heavy-Ion Collisions
7/19/2018
Ralf Rapp
Cyclotron Institute +
Dept of Phys & Astro
Texas A&M University
College Station, USA
EMMI Workshop on
“Prospects + Challenges for Future Experiments in HICs”
GSI (Darmstadt, Germany),

2. 1.) Intro: EM Radiation + HQ Transport
e+e- → hadrons:
Im Pem(M) / M2
Heavy-Quark Potential
V [½GeV]
M [GeV]
r [½fm]
Im Πem(M,q;mB,T)
in-medium transport coefficients
Modifications of
light resonances:
transition to QGP?
Basic QCD force
in QGP +
at hadronization? Q e+ e- r
well-defined baselines

3. 2.1 EM Radiation and Chiral Phase Transition
≈ qq / qq0
Tpcc ~155MeV
[Fodor et al ’10]
[Gerber+Leutwyler ‘89,
Karsch,Redlich+Tawfik ‘05]
hadron resonance gas
chiral restoration in “hadronic phase”? (low-mass dileptons!)

4. 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

5. 2.3 QCD + Weinberg Sum Rules in Medium
[Hatsuda+Lee’91, Asakawa+Ko ’93,
Klingl et al ’97, Leupold et al ’98,
Kämpfer et al ‘03, Ruppert et al ’05]
[Weinberg ’67, Das et al ’67;
Kapusta+Shuryak ‘94]
T [GeV]
melting scenario quantitatively compatible with chiral restoration
microscopic calculation of in-medium axialvector to be done
[Hohler et al ‘12]
s [GeV2]
rV,A/s
Vacuum T=140MeV T=170MeV

6. 2.4 Dilepton Spectro-Thermo-Meter at SPS
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 higher
Consistent with pT slopes: Teff ~ T + M (bflow)2

7. 2.5 e+e- Excitation Function: SPS - RHIC
Pb-Au(8.8GeV)
Au-Au (20-200GeV)
QM12
Pb-Au(17.3GeV)
no apparent change of the excess emission source
suggests “universal” medium effect around Tpc
caveat: PHENIX central; FAIR,LHC?
[cf. also Bratkovskaya et al, Alam et al, Bleicher et al …]

8. 2.6.1 Direct Photons at RHIC Spectra Elliptic Flow
← excess radiation
total
[van Hees,
Gale+RR ’11]
Teffexcess = (220±25) MeV
flow blue-shift: Teff ~ T √(1+b)/(1-b) , b~0.3: T ~ 220/1.35 ~ 160 MeV
small slope + large v2 suggest main emission around Tpc

9. 2.6.2 Direct Photons at LHC Spectra Elliptic Flow
● ALICE
[van Hees et al in prep]
similar to RHIC results (not enough v2)
larger (non-pert.) photon emission rates around Tpc?
other explanations…?

10. 3.) Heavy Flavor in Medium
Large scale mQ >> T, LQCD , coupled to non-perturbative environment
Open Heavy Flavor:
Hadronization: mQ >> Tpc
- heavy flavor individually conserved through transition
- hadron formation with light-quark content of QGP
- (pre-) resonant Qq correlations above Tpc
Diffusion
- same interaction operative as in hadronization
- dominated by elastic scattering
→ friction + diffusion coefficients D c

11. 3.1 Heavy-Quark Transport and Spectral Function
p2 ~ mQ T >> k2 ~ T2  Brownian Motion: Q
Fokker Planck Eq.
thermalization rate diffusion coefficient
Scattering amplitude
(non-pert. driving kernel!)
Scattering rate (self-energy) → spectral function (propagator)

12. 3.2 Heavy Quarkonia in Medium
Field-theoretic potential approach
effective propagator: Coulomb + string
fit to lattice-QCD free energy
[Megias
et al ‘07]
In-Medium
Q-Q T-Matrix: - -
Q-Q propagator:

13. 3.3 Quarkonium Spectral Functions + Correlators
[Aarts et
al ‘07]
limiting cases:
assume V=U or F
[Satz et al ’01+’08, Mocsy+Petreczky ’05+’08, Wong ’06,
Cabrera,Riek+RR ’06+’10, Beraudo et al ’06, Lee et al ’09, …]

14. → ← - 3.4 Quarkonium Transport J/y + q,g c + c + X - D J/y c
Rate Equation for
J/y + q,g c + c + X
J/y D - c
reaction rate equilibrium limit
(y -width)
in-med properties: spectral function, encodes screening/dissociation
formation sensitive to HQ distributions
[cf. also
Andronic et al,
Zhuang et al,
Ferreiro et al, …]

15. 3.5 Back to Open Heavy Flavor-
heavy-light T-matrix → HQ transport
“Feshbach” resonances (hadronization!)
c-q
Thermalization Rate
gc [1/fm]
factor 3-4 faster than pert. QCD
marked 3-momentum dependence

16. 3.6 Charm + Bottom Transport at RHIC +LHC
Min Bias Pb-Pb 2.76TeV
B-meson (non-prompt J/y)
■ CMS preliminary
strangeness enhancement exhibits
HQ interactions
[He et al ’12]
[see also van Hees et al, Gossiaux et al, Uphoff et al,…]

17. 4.) Conclusions
Low-mass dileptons (+photons) probe the matter formed in
URHICs around Tpc (mass shape+slopes, excitation fct, photon-v2)
Theory studies combining chiral hadronic models + sum rules
Heavy flavors probe QGP diffusion + hadronization,
possibly dominated by same non-perturbative interaction
Self-consistent / unified approach to HQ + quarkonium transport
EM Radiation + Heavy-Flavor remain premier tools to study
non-perturbative properties of QCD matter at future HI facilities

18. Outline 2.) Spectral Function + Emission Temperature
7/19/2018
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

19. 3.4 Vector Correlator in Thermal Lattice QCD
Euclidean Correlation fct.
Lattice (quenched) [Ding et al ‘10]
Hadronic Many-Body [RR ‘02]
“Parton-Hadron Duality” of lattice and in-medium hadronic?

20. 4.2 Low-Mass e+e- at RHIC: PHENIX vs. STAR
PHENIX enhancement (central!) not accounted for by theory
STAR data ok with theory (charm?!)

21. 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

22. 2.3 Dilepton Rates vs. Exp.: NA60 “Spectrometer”
Evolve rates over fireball expansion:
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!

23. 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)

24. 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]

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. 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

27. 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

28. 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

29. 2.3.2 NA60 Mass Spectra: pt Dependence
Mmm [GeV]
more involved at pT>1.5GeV: Drell-Yan, primordial/freezeout r , …

30. 3.4.2 Back to Spectral Function
suggests approach to chiral restoration + deconfinement

31. 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]

32. 4.2 Low-Mass Dileptons: Chronometer
In-In Nch>30
first “explicit” measurement of interacting-fireball lifetime:
tFB ≈ (7±1) fm/c

33. 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]

34. 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]

35. 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 - -

36. 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”)

37. 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

38. 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

39. 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!

40. 3.5 Summary: Criteria for Chiral Restoration
Vector (r) – Axialvector (a1) degenerate
[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)

41. 2.2 Dilepton Rates: Hadronic - Lattice - Perturbative dRee /dM2 ~ ∫d3q f B(q0;T) Im Pem
continuous rate through Tpc
3-fold “degeneracy” toward ~Tpc -
[qq→ee]
[HTL]
[Ding et al ’10]
dRee/d4q 1.4Tc (quenched)
q=0
[RR,Wambach et al ’99]

42. 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