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

≈

qq

/ 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

qq

/ 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)