Thermal Electromagnetic Radiation in Heavy-Ion Collisions Ralf Rapp Cyclotron Institute + Dept of Phys & Astro Texas A&M University College Station, USA 34 th International School of Nuclear Physics “Probing the Extremes of Matter with Heavy Ions”
Jan 09, 2016
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
• 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?
√s = M
e+e → hadrons
)T,q(fMqdxd
dN Bee023
2em
44 Im Πem(M,q;B,T)
Im em(M) in Vacuum
1.2 Phase Transition(s) in Lattice QCD
• cross-over(s) ↔ smooth EM emission rates across Tpc
• chiral restoration in “hadronic phase”? (low-mass dileptons!)
• hadron resonance gas
Tpc~155MeV
≈
/ q
q0
-
-
[Fodor et al ’10]
2.) Spectral Function + Emission Temperature
In-Medium + Dilepton Rates
Dilepton Mass Spectra + Slopes
Excitation Function + Elliptic Flow
3.) Chiral Symmetry Restoration
Chiral Condensate
Weinberg + QCD Sum Rules
Euclidean Correlators
4.) Conclusions
Outline
>
>
B*,a1,K1
...
N,,K…
2.1 Vector Mesons in Hadronic Matter
D(M,q;B ,T) = [M 2 - m2 - - B - M ] -1-Propagator:
[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 …]
= B,M=Selfenergies:
Constraints: decays: B,M→ N, scattering: N → N, A, …
B /0
0 0.1 0.7 2.6
SPS RHIC / LHC
2.2 Dilepton Rates: Hadronic - Lattice - Perturbative dRee /dM2 ~ ∫d3q f B(q0;T) Im em
• continuous rate through Tpc
• 3-fold “degeneracy” toward ~Tpc
[qq→ee]-[HTL]
[RR,Wambach et al ’99]
[Ding et al ’10]
dRee/d4q 1.4Tc (quenched) q=0
2.3 Dilepton Rates vs. Exp.: NA60 “Spectrometer”
• invariant-mass spectrum directly reflects thermal emission rate!
Acc.-corrected + Excess Spectra In-In(17.3GeV) [NA60 ‘09]
M[GeV]
• Evolve rates over fireball expansion:
[van Hees+RR ’08]
qd
dRq
qdM)(Vd
dMdN therm
FB
therm fo
40
3
0
2.4 Dilepton Thermometer: Slope Parameters
• Low mass: radiation from around T ~ Tpc ~ 150MeV
• Intermediate mass: T ~ 170 MeV and above
• Consistent with pT slopes incl. flow: Teff ~ T + M (flow)2
Invariant Rate vs. M-Spectra Transverse-Momentum Spectra
Tc=160MeVTc=190MeV
cont.
Au-Au min. bias
2.5 Low-Mass e+e Excitation Function: SPS - RHIC
• no apparent change of the emission source • consistent with “universal” medium effect around Tpc
• partition hadronic/QGP depends on EoS, total yield ~ invariant
QM12
Pb-Au(17.3GeV)
Pb-Au(8.8GeV)
2.6 Direct Photons at RHIC
• v2,dir comparable to pions!
• under-predicted by early QGP emission
← excess radiation
• Teffexcess = (220±25) MeV
• QGP radiation?• radial flow?
Spectra Elliptic Flow
[Holopainen et al ’11,…]
2.6.2 Thermal Photon Spectra + v2
• hadronic emission close to Tpc essential (continuous rate!)
• flow blue-shift: Teff ~ T √(1+)/(1)
e.g. =0.3: T ~ 220/1.35~ 160 MeV
• small slope + large v2 suggest main emission around Tpc
• confirmed with hydro evolution
thermal + prim.
[van Hees,Gale+RR ’11]
[He at al in prep.]
2.) Spectral Function + Emission Temperature
In-Medium + Dilepton Rates
Dilepton Mass Spectra + Slopes
Excitation Function + Elliptic Flow
3.) Chiral Symmetry Restoration
Chiral Condensate
Weinberg + QCD Sum Rules
Euclidean Correlators
4.) Conclusions
Outline
3.1 Chiral Condensate + -Meson Broadening
/ q
q0
-
-
effective hadronic theory
• h = mq h|qq|h > 0 contains quark core + pion cloud
= hcore + h
cloud ~ +
• matches spectral medium effects: resonances + pion cloud• resonances + chiral mixing drive -SF toward chiral restoration
>
>
-
3.2 Spectral Functions + Weinberg Sum Rules
• Quantify chiral symmetry breaking via observable spectral functions• Vector () - Axialvector (a1) spectral splitting
)(sdsI AVn
n 00002
31
210
21
222
|q)q(|αcI,|qq|mI
,fI,FrfI
sq
πA
[Weinberg ’67, Das et al ’67; Kapusta+Shuryak ‘93]
→(2n+1)
pQCD
pQCD
• Updated “fit”: [Hohler+RR ‘12]
+ a1 resonance, excited states (’+ a1’), universal continuum (pQCD!)
→(2n) [ALEPH ’98,OPAL ‘99]
V/s A/s
3.2.2 Evaluation of Chiral Sum Rules in Vacuum
• vector-axialvector splitting quantitative observable of spontaneous chiral symmetry breaking • promising starting point to analyze chiral restoration
• pion decay constants
• chiral quark condensates 00002
31
210
21
222
|q)q(|αcI|qq|mI
fIFrfI
sq
πA
3.3 QCD Sum Rules at Finite Temperature
• and ’ melting compatible with chiral restoration
V/s
Percentage Deviation
T [GeV]
[Hohler +RR ‘12]
[Hatsuda+Lee’91, Asakawa+Ko ’93, Klingl et al ’97, Leupold et al ’98, Kämpfer et al ‘03, Ruppert et al ’05]
3.4 Vector Correlator in Thermal Lattice QCD
]T/q[)]T/(q[
)T;q,q(dq
)T;q,(2
212 0
00
0
0sinh
coshemem
• Euclidean Correlation fct.
)T,(G
)T,(G
V
V
free
Hadronic Many-Body [RR ‘02] Lattice (quenched) [Ding et al ‘10]
• “Parton-Hadron Duality” of lattice and in-medium hadronic?
4.) Conclusions
• Low-mass dilepton spectra in URHIC point at universal source
• -meson gradually melts into QGP continuum radiation
• prevalent emission temperature around Tpc~150MeV (slopes, v2)
• mechanisms underlying -melting ( cloud + resonances) find counterparts in hadronic -terms, which restore chiral symmetry
• quantitative studies relating -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: and a1 in Vacuum
• dispersion relation:
• lhs: hadronic spectral fct. • rhs: operator product expansion
[Shifman,Vainshtein+Zakharov ’79]2
2
20 Q
)Q(Π
sQ
)s(Ims
ds
• 4-quark + gluon condensate dominant
vector axialvector
4.5 QGP Barometer: Blue Shift vs. Temperature
• QGP-flow driven increase of Teff ~ T + M (flow)2 at RHIC
• high pt: high T wins over high-flow ’s → minimum (opposite to SPS!)
• saturates at “true” early temperature T0 (no flow)
SPS RHIC
4.3.2 Revisit Ingredients
• multi-strange hadrons at “Tc”
• v2bulk fully built up at hadronization
• chemical potentials for , K, …
• Hadron - QGP continuity!• conservative estimates…
Emission Rates Fireball Evolution
[van Hees et al ’11]
[Turbide et al ’04]
4.1.3 Mass Spectra as Thermometer
• Overall slope T~150-200MeV (true T, no blue shift!)
[NA60, CERN Courier Nov. 2009]
Emp. scatt. ampl. + T- approximationHadronic many-bodyChiral virial expansion
Thermometer
M[GeV]
4.1.2 Sensitivity to Spectral Function
• avg. (T~150MeV) ~ 370 MeV (T~Tc) ≈ 600 MeV → m
• driven by (anti-) baryons
In-Medium -Meson Width
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
• theo. slopes originally too soft
• increase fireball acceleration, e.g. a┴ = 0.085/fm → 0.1/fm
• insensitive to Tc=160-190MeV
Effective Slopes Teff
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 decays
[Chatterjee et al ‘07, Zhuang et al ‘09]
[He et al ‘12]
4.2 Low-Mass Dileptons: Chronometer
• first “explicit” measurement of interacting-fireball lifetime: FB ≈ (7±1) fm/c
In-In Nch>30
3.2 Axialvector in Nucl. Matter: Dynamical a1(1260)
+ + . . . =
Vacuum:
a1
resonance
InMedium: + + . . .
[Cabrera,Jido, Roca+RR ’09]
• in-medium + propagators• broadening of - scatt. Amplitude• pion decay constant in medium:
3.6 Strategies to Test For Chiral Restoration
Lat-QCD Euclidean correlators
eff. theory for VC + AV
spectral functs.
constrain Lagrangian(low T, N)
vac. data + elem. reacts.
(A→eeX, …)
EM data in heavy-ion coll.
Realistic bulk evol. (hydro,…)
Lat-QCD condensates + ord. par.
global analysis of M, pt, v2
test VC AV:chiral SRs
constrainVC + AV :
QCD SR
Chiral restoration?
Agreement with data?
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, , … at Tfo ~ 110MeV
• v2 saturates at Tch, good light-/strange-hadron phenomenology
[He et al ’11]
“Higgs” Mechanism in Strong Interactions:
• qq attraction condensate fills QCD vacuum!
Spontaneous Chiral Symmetry Breaking
2.1 Chiral Symmetry + QCD Vacuum
)m( d,u 0QCD L : flavor + “chiral” (left/right) invariant
350000 fm|qqqq||qq| LRRL
>
>
>
>qLqR
qL-qR
-
-
Profound Consequences:• effective quark mass: ↔ mass generation!
• near-massless Goldstone bosons 0,±
• “chiral partners” split: M ≈ 0.5GeV
00 |qq|m*q
JP=0± 1± 1/2±
2.3.2 NA60 Mass Spectra: pt Dependence
• more involved at pT>1.5GeV: Drell-Yan, primordial/freezeout , …
M [GeV]
4.4.3 Origin of the Low-Mass Excess in PHENIX?
• QGP radiation insufficient:
space-time , lattice QGP rate + resum. pert. rates too small
- “baked Alaska” ↔ small T - rapid quench+large domains ↔ central A-A - therm + DCC → e+ e ↔ M~0.3GeV, small pt
• 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]
[Z.Huang+X.N.Wang ’96 Kluger,Koch,Randrup ‘98]
2.2 EM Probes at SPS
• all calculated with the same e.m. spectral function!•thermal source: Ti≈210MeV, HG-dominated, -meson melting!
5.2 Intermediate-Mass Dileptons: Thermometer• use invariant continuum radiation (M>1GeV): no blue shift, Tslope = T !
• independent of partition HG vs QGP (dilepton rate continuous/dual)• initial temperature Ti ~ 190-220 MeV at CERN-SPS
Thermometer
4.7.2 Light Vector Mesons at RHIC + LHC
• baryon effects important even at B,tot= 0 : sensitive to Btot= + B (-N and -N interactions identical) • also melts, more robust ↔ OZI
-
5.3 Intermediate Mass Emission: “Chiral Mixing”
)q()q()()q( ,A
,VV
00 1
)q()q()()q( ,V
,AA
001 =
=
• low-energy pion interactions fixed by chiral symmetry
• mixing parameter
2
2
3
3
2 6224
fT)(f
)(kd
fk
k
[Dey, Eletsky +Ioffe ’90]
0
0 0
0
• 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
• modify fireball evolution: e.g. a┴ = 0.085/fm → 0.1/fm
• both large and small Tc compatible
with excess dilepton slopes
pions: Tch=175MeV a┴ =0.085/fm
pions: Tch=160MeV a┴ =0.1/fm
2.3.3 Spectrometer III: Before Acceptance Correction
• Discrimination power much reduced• can compensate spectral “deficit” by larger flow: lift pairs into acceptance
hadr. many-body + fireball
emp. ampl. + “hard” fireball
schem. broad./drop.+ HSD transportchiral virial
+ hydro
4.2 Improved Low-Mass QGP Emission
• LO pQCD spectral function: V(q0,q) = 6∕9 3M2/21+QHTL(q0)]
• 3-momentum augmented lattice-QCD rate (finite rate)
)q,q()T;q(fMqd
dRV
Bee0023
2em
4 6
4.1 Nuclear Photoproduction: Meson in Cold Matter
+ A → e+e X
[CLAS+GiBUU ‘08]
E≈1.5-3 GeV
e+
e
• extracted “in-med” -width ≈ 220 MeV
• Microscopic Approach:
Fe - Ti
N
product. amplitude in-med. spectral fct.+
M [GeV][Riek et al ’08, ‘10]
full calculationfix density 0.40
• -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
Tiqx )](j),x(j[)x(exdi)q(Π 0emem0
4em
EM Current-Current Correlation Function:
e+
e-
γ
)T(fMqd
dR Bee23
2em
4
)T(fqd
dRq B
2em
30
Im Πem(M,q)
Im Πem(q0=q)
Thermal Dilepton and Photon Production Rates:
Imem ~ [ImD+ ImD/10 + ImD/5]Low Mass: -mesondominated
3.5 Summary: Criteria for Chiral Restoration
• Vector () – Axialvector (a1) degenerate
)Im(ImsdsI AVn
n 2
102
1 0 q)q(αcI,I,fI sπ
[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)