electromagnetic probes: messengers from the hot and dense

Electromagnetic probes:Messengers from the hot and dense fireball

Hendrik van Hees

Goethe University Frankfurt

November 5, 2014

Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, 2014 1 / 45

Outline

1 Electromagnetic probes and hadron resonancesEm. current correlation function and electromagnetic probesSources of dilepton emission in heavy-ion collisionsThermal (effective hadronic) QFT approachKinetic theory (transport) approach

2 Dileptons in pp, pn, pA, AA in pure transport (GiBUU with J. Weil)GiBUUDalitz decays of hadron resonancesBaryon-resonance model at SIS energiesDielectrons (SIS/HADES)

3 Dileptons at SPS and RHIC (with Ralf Rapp)

4 Conclusions


Em. current correlatorin-medium approaches

`+`− and γ rates


Em. current correlation function and electromagnetic Probes

photon and dilepton thermal emission rates given by sameelectromagnetic-current-correlation function (Jµ = ∑f Qf ψf γµ ψf )[MT85, Wel90, GK91]

Π<µν(q) =

∫d4xexp(iq · x)

⟨Jµ(0)Jν(x)

⟩T =−2fB(q ·u) ImΠ(ret)

µν (q)

q0dNγ

d4xd3~q=− α

2π2 gµν Im Π(ret)µν (q)

∣∣∣q0=|~q|

fB(q ·u)

dNe+e−

d4xd4q=−gµν α2

3q2π3 ImΠ(ret)µν (q)

∣∣∣q2=M2

e+e−fB(q ·u)

u: four-velocity of the fluid cell; p ·u = phb0 energy in “heat-bath frame”

to lowest order in α: e2Πµν ' Σ(γ)µν

vector-meson dominance model:

Σγµν =

Gρ


Sources of dilepton emission in heavy-ion collisions

1 initial hard processes: Drell Yan2 “core”⇔ emission from thermal source

1qT

dN(thermal)

dMdqT=∫

d4x∫

dy∫

MdϕdN(thermal)

d4xd4q

3 “corona”⇔ emission from “primordial” mesons (jet-quenching)4 after thermal freeze-out⇔ emission from “freeze-out” mesons

[CF74]

N(fo) =∫ d3q

q0

∫qµ dσ

µ fB(uµ qµ/T)Γmeson→`+`−

Γmeson[HR08, HR06]


Hadronic many-body theory

HMBT for vector mesons [Ko et al, Chanfray et al, Herrmann et al, Rapp et al, . . .]

ππ interactions and baryonic excitations

ρ ρ

π

π B , a , K ,...*1 1

π,...N, K,

ρ ρ

+corresponding vertex corrections⇔ gauge invarianceBaryon (resonances) important, even at RHIC with low net baryon densitynB−nB

reason: nB+nB relevant (CP inv. of strong interactions)


Rapp-Wambach model

pion cloud: dressing with baryon resonance excitations [RW00]

direct ρ-N/∆ interactions⇒ [RW00]

direct ρ-heavy-meson interactions [GR99]


Photoabsorption on nucleons and nuclei

important: fit of model parameters to dataparticle-data book: decay widths, branching rations,...photo-absorption on nucleons and nuclei [RW00]


Meson contributions to ρ-selfenergy

0.0 0.2 0.4 0.6 0.8 1.0 1.2

M [GeV]

−30

−20

−10

0

10

20

30

Re

Σρ/m

ρ [

Me

V]

−70

−60

−50

−40

−30

−20

−10

0

Im Σ

ρ/m

ρ [

Me

V]

a1

π’h

1K1

ω

f1

sum

T=150MeV

q=0.3GeV

ω

suma

1

K1

[GR99, RW00]


In-medium spectral functions and baryon effects

0

1

2

3

4

5

6

7

8

9

0 0.2 0.4 0.6 0.8 1 1.2 1.4

-Im

Dρ (

GeV

-2)

M (GeV)

ρ(770)T=0

T=120 MeVT=150 MeVT=175 MeV

[GR99, RW00]

baryon effects importantlarge contribution to broadening of the peakresponsible for most of the strength at small M



0

5

10

15

20

0.2 0.4 0.6 0.8 1 1.2

-Im

Dω

(G

eV

-2)

M (GeV)

ω(782)T=0

T=120 MeVT=150 MeVT=175 MeV

[GR99, RW00]




0

5

10

15

20

0.8 0.9 1 1.1 1.2

-Im

Dφ (

GeV

-2)

M (GeV)

φ(1020)

T=0T=120 MeVT=150 MeVT=175 MeV

[GR99, RW00]



Intermediate masses: hadronic “4π contributions”

e.m. current-current correlator⇔ τ → 2nπ

0

0.02

0.04

0.06

0.08

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-Im

ΠV

,A/(

π M

2)

M2 (GeV

2)

V [τ→ 2n π ντ]

V [τ→ 2 π ντ]

ρ + cont.

2π (ρ)

4π (fit)

0

0.01

0.02

0.03

0.04

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-Im

ΠV

,A/(

π M

2)

M2 (GeV

2)

A [τ→ (2n+1) π ντ]

A [τ→ 3 π ντ]

a1 + cont.

3π (a1)

5π (fit)

“4π contributions”: π +ω,a1→ µ++µ−

leading-order virial expansion for “four-pion piece”additional strength through “chiral mixing”[HR08, HR06]


Dileptons from thermal QGP

in QGP phase: qq annihilationHTL improved electromagnetic current correlator

q

q

γ∗ γ∗−iΠem,QGP =

or em. current correlator from the lattice [DFK+11] (extrapolated to finite q)“quark-hadron duality” around Tc

[Rap13]


Dilepton rates: Hadron gas↔ QGP

in-medium hadron gas matches with QGPsimilar results also for γ rates“quark-hadron duality”?

[Rap13]


Kinetic theory (transport) approach

cross sections in collision terms: same physics as in QFT approachesFermi’s golden rule: S-matrix amplitudes⇔ |M 2

ji | ⇔ self-energy diagramsother way around: cut self-energy diagrams⇔ S-matrix amplitudes

⇔N/∆

p/n ρ

N/∆

p/n ρ

p/n π

⇔⇔ . . .

[FHK+11]


Dileptons in pp, pn, pA, AApure transport: GiBUU (with Janus Weil)


The GiBUU Model

Boltzmann-Uehling-Uhlenbeck (BUU) framework for hadronic transportreaction types: pA, πA, γA, eA, νA, AAopen-source modular Fortran 95/2003 codeversion control via Subversionpublicly available realeases: https://gibuu.hepforge.orgReview on hadronic transport (GiBUU): [BGG+12]

all calculations for dileptons: J. Weil


http://gibuu.physik.uni-giessen.de

Resonance Model

reactions dominated by resonance scattering: ab→ R→ cd

Breit-Wigner cross-section formula

σab→R→cd =2sR +1

(2sa +1)(2sb +1)4π

p2lab

sΓab→RΓR→cd

(s−m2R)

2 + sΓ2tot

applicable for low-energy nuclear reactions Ekin . 1.1 GeVexample: σπ−p→π−p [Teis (PhD thesis 1996), data: Baldini et al, Landolt-Bornstein 12 (1987)]

0.0 0.2 0.4 0.6 0.8 1.0 1.20

10

20

30

40

50

60

70

80

Daten

total

∆(1232)

N(1440)

N(1535)

plab (GeV/c)

σ (

mb)


GiBUU: Resonance Model

further cross sections


GiBUU: Extension to HADES energies

[WHM12, WM13]

keep same resonances (parameters from Manley analysis)

production channels in Teis: NN→ N∆, NN→ NN∗,N∆∗, NN→ ∆∆extension to NN→ ∆N∗,∆∆∗, NN→ NNπ , NN→ NNρ,NNω,NNπω,NNφ ,NN→ BYK (B = N,∆, Y = Λ,Σ)

[WHM12, WM13]


GiBUU Extension to HADES energies

good description of total pp, pn (inelastic) cross section

dilepton sourcesDalitz decays: π0,η → γ`+`−; ω → π0`+`−, ∆→ N`+`−

ρ,ω,φ → `+`−: invariant mass `+`− spectra⇒spectral properties of vector mesonsfor details, see [WHM12]


Exclusive pion production: p+p (3.5 GeV) (SIS/HADES)

exclusive p+p→ p+n+π+

left: Mpπ+ spectrum; right: Mnπ+ spectrummodel 1: GiBUU; model 2: UrQMDchance to refine resonance models further!


GiBUU: “ρ meson” in pp

production through hadron resonancesNN→ NR→ NNρ , NN→ N∆→ NNπρ

“ρ”-line shape “modified” already in elementary hadronic reactionsdue to production mechanism via resonances


GiBUU: ∆ meson in VMD model

so far: ∆-Dalitz decay treated separately from other resonancesnow: treating ∆ as all other resonances via VMD modelmodel for em. transition form factor

10-6

10-5

10-4

10-3

10-2

10-1

100

1 1.2 1.4 1.6 1.8 2 2.2 2.4

Γ∆ [

Ge

V]

m∆ [GeV]

πN ManleyπN MonizπN Bass

(ρN)PManley + ρN

[WEH+14]




10-2

10-1

100

1 1.2 1.4 1.6 1.8 2 2.2 2.4

A∆ [

Ge

V-2

]

m∆ [GeV]

πN ManleyπN MonizπN Bass

Manley + ρN

[WEH+14]




10-3

10-2

10-1

100

101

0 0.1 0.2 0.3 0.4 0.5

dσ/d

mee

[µb/

GeV

]

dilepton mass mee [GeV]

p + p at 1.25 GeV

dataGiBUU total

π0 → e+e-γ∆ QED∆ VMD

N* VMDBrems. OBE




10-4

10-3

10-2

10-1

100

101

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

dσ/d

mee

[µb/

GeV

]


d + p at 1.25 GeV

dataGiBUU total

π0 → e+e-γη → e+e-γ

∆ QED∆ VMD

N* VMDBrems. OBE




10-4

10-3

10-2

10-1

100

101

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

dσ/d

mee

[µb/

GeV

]


p + p at 2.2 GeV

dataGiBUU total

ω → e+e-

ω → π0e+e-


∆ QED∆ VMD

N* VMD∆* VMD

Brems. OBE




10-3

10-2

10-1

100

101

0 0.2 0.4 0.6 0.8 1

dσ/d

mee

[µb/

GeV

]


p + p at 3.5 GeV

dataGiBUU total

ω → e+e-

φ → e+e-

ω → π0e+e-


∆ QED∆ VMD

N* VMD∆* VMD

Brems. OBE


GiBUU: p+Nb (3.5 GeV) (SIS/HADES)

with vacuum spectral functions:

10-1

100

101

102

103

0 0.2 0.4 0.6 0.8 1

dσ

/dm

ee [

µb/G

eV

]


p + Nb at 3.5 GeV

preliminary dataGiBUU total

ρ → e+e

-

ω → e+e

-

φ → e+e

-

ω → π0e

+e

-

π0 → e

+e

-γ

η → e+e

-γ

∆ → Ne+e

-



with medium modified spectral functions:p + Nb at 3.5 GeV

10-1

100

0.55 0.6 0.65 0.7 0.75 0.8 0.85

dσ

/dm

ee [

µb

/Ge

V]

prelim. datavacCB

CB+shiftshift

0.55 0.6 0.65 0.7 0.75 0.8 0.85


ρ

0.55 0.6 0.65 0.7 0.75 0.8 0.85

ω

no definite hint for medium modifications in p Nb



medium effects built in transport modelbinding effects, Fermi smearing, Pauli blockingfinal-state interactionsproduction from secondary collisions

sensitivity on medium effects of vector-meson spectral functions?p + Nb at 3.5 GeV

10-1

100

0.55 0.6 0.65 0.7 0.75 0.8 0.85

dσ

/dm

ee [

µb

/Ge

V]

prelim. datavacCB

CB+shiftshift

0.55 0.6 0.65 0.7 0.75 0.8 0.85


ρ

0.55 0.6 0.65 0.7 0.75 0.8 0.85

ω


GiBUU: Ar+KCl (1.76AGeV) (SIS/HADES)


GiBUU (NEW!): Au+Au (1.23 AGeV) (SIS/HADES)

10-8

10-7

10-6

10-5

10-4

10-3

0 0.2 0.4 0.6 0.8 1

1/N

π0 d

N/d

mee


Au + Au @ 1.23 GeV

acceptance from [email protected]

0.1 GeV < plep < 1.1 GeV

θee > 9°

GiBUU totalRes VMD

ππω → e

+e

-

φ → e+e

-

ω → π0e

+e

-

π0 → e

+e

-γ

η → e+e

-γ

∆ QED∆ VMD

pn Brems.pp Brems.πN Brems.

caveat: pp/np acceptance filter with single-e cut, pt < 100 MeVcorrect filter urgently needed!comparison to preliminary HADES data [Gal14]⇒ room for medium modifications(data points not shown here on request of the HADES collaboration)


GiBUU (NEW!): π+p (566 MeV) (SIS/HADES)

10-2

10-1

100

101

102

103

104

0 0.1 0.2 0.3 0.4 0.5 0.6

dσ/d

mee

[µb/

GeV

]


π- + p, Ekin = 0.566 GeV

GiBUU totalπ0 → e+e-γη → e+e-γ

πN Brems.N* VMD

D13(1520)S11(1535)

∆ QED∆ VMD

∆* VMD


GiBUU (NEW!): π+p (566 MeV) (SIS/HADES)

10-1

100

101

102

103

0 0.1 0.2 0.3 0.4 0.5

dσ/d

p T [µ

b/G

eV]

0 0.1 0.2 0.3 0.4 0.5

transverse momentum pT [GeV]

10-1

100

101

102

103

0 0.1 0.2 0.3 0.4 0.5

dσ/d

p T [µ

b/G

eV]

10-2

10-1

100

101

102

-4 -2 0 2 4 6

dσ/d

y [µ

b]

m < 140 MeV

-4 -2 0 2 4 6

rapidity y

140 MeV < m < 280 MeV

-4 -2 0 2 4 6

10-2

10-1

100

101

102

dσ/d

y [µ

b]

280 MeV < m

GiBUU totalN* VMD∆* VMD


πN Brems.∆ QED∆ VMD


GiBUU (NEW!): π+C (566 MeV) (SIS/HADES)

10-2

10-1

100

101

102

103

104

0 0.1 0.2 0.3 0.4 0.5 0.6

dσ/d

mee

[µb/

GeV

]


π- + C, Ekin = 0.566 GeV


πN Brems.pn Brems.

N* VMDD13(1520)S11(1535)

∆ QED∆ VMD

∆* VMD


GiBUU (NEW!): π+C (566 MeV) at (SIS/HADES)

10-1

100

101

102

103

104

0.1 0.2 0.3 0.4 0.5 0.6

dσ/d

p T [µ

b/G

eV]

0.1 0.2 0.3 0.4 0.5 0.6

transverse momentum pT [GeV]

10-1

100

101

102

103

104

0.1 0.2 0.3 0.4 0.5 0.6

dσ/d

p T [µ

b/G

eV]

10-2

10-1

100

101

102

103

-4 -2 0 2 4 6

dσ/d

y [µ

b]

m < 140 MeV

-4 -2 0 2 4 6

rapidity y

140 MeV < m < 280 MeV

-4 -2 0 2 4 610-2

10-1

100

101

102

103

dσ/d

y [µ

b]

280 MeV < m


πN Brems.pn Brems.

N* VMDD13(1520)S11(1535)

∆ QED∆ VMD

∆* VMD


Dileptons at SPS and RHICthermal fireball model (with Ralf Rapp)


M spectra (in pT slices)

NA60 experiment: dimuon measurement (In-In collisions at top SPS energy)

10-9

10-8

10-7

10-6

10-5

0.2 0.4 0.6 0.8 1 1.2 1.4

(1/N

ch)

d2N

µµ/(

dM

dη

) (2

0 M

eV)-1

M (GeV)

all qT

Tc=Tch=175 MeV, at=0.1 c2/fm

+ω-t extotal

ω-t exωφ

DY4π mix

FO ρprim ρ

QGPin-med ρ

NA60

[HR06, HR08]




10-9

10-8

10-7

10-6

10-5

0.2 0.4 0.6 0.8 1 1.2 1.4

(1/N

ch)

d2N

µµ/(

dM

dη

) (2

0 M

eV)-1

M (GeV)

0<qt<0.2 GeV


+ω-t extotal

ω-t exωφ

DY4π mix

FO ρprim ρ

QGPin-med ρ

NA60

[HR06, HR08]




10-9

10-8

10-7

10-6

10-5

0.2 0.4 0.6 0.8 1 1.2 1.4

(1/N

ch)

d2N

µµ/(

dM

dη

) (2

0 M

eV)-1

M (GeV)

0.2 GeV<qt<0.4 GeV


+ω-t extotal

ω-t exωφ

DY4π mix

FO ρprim ρ

QGPin-med ρ

NA60

[HR06, HR08]




10-9

10-8

10-7

10-6

10-5

0.2 0.4 0.6 0.8 1 1.2 1.4

(1/N

ch)

d2N

µµ/(

dM

dη

) (2

0 M

eV)-1

M (GeV)

0.4 GeV<qt<0.6 GeV


+ω-t extotal

ω-t exωφ

DY4π mix

FO ρprim ρ

QGPin-med ρ

NA60

[HR06, HR08]




10-9

10-8

10-7

10-6

10-5

0.2 0.4 0.6 0.8 1 1.2 1.4

(1/N

ch)

d2N

µµ/(

dM

dη

) (2

0 M

eV)-1

M (GeV)

0.6 GeV<qt<0.8 GeV


+ω-t extotal

ω-t exωφ

DY4π mix

FO ρprim ρ

QGPin-med ρ

NA60

[HR06, HR08]




10-9

10-8

10-7

10-6

10-5

0.2 0.4 0.6 0.8 1 1.2 1.4

(1/N

ch)

d2N

µµ/(

dM

dη

) (2

0 M

eV)-1

M (GeV)

0.8 GeV<qt<1.0 GeV


+ω-t extotal

ω-t exωφ

DY4π mix

FO ρprim ρ

QGPin-med ρ

NA60

[HR06, HR08]




10-9

10-8

10-7

10-6

10-5

0.2 0.4 0.6 0.8 1 1.2 1.4

(1/N

ch)

d2N

µµ/(

dM

dη

) (2

0 M

eV)-1

M (GeV)

1.0 GeV<qt<1.2 GeV


+ω-t extotal

ω-t exωφ

DY4π mix

FO ρprim ρ

QGPin-med ρ

NA60

[HR06, HR08]




10-9

10-8

10-7

10-6

10-5

0.2 0.4 0.6 0.8 1 1.2 1.4

(1/N

ch)

d2N

µµ/(

dM

dη

) (2

0 M

eV)-1

M (GeV)

2.0 GeV<qt<2.2 GeV


+ω-t extotal

ω-t exωφ

DY4π mix

FO ρprim ρ

QGPin-med ρ

NA60

[HR06, HR08]




10-9

10-8

10-7

10-6

10-5

0.2 0.4 0.6 0.8 1 1.2 1.4

(1/N

ch)

d2N

µµ/(

dM

dη

) (2

0 M

eV)-1

M (GeV)

2.2 GeV<qt<2.4 GeV


+ω-t extotal

ω-t exωφ

DY4π mix

FO ρprim ρ

QGPin-med ρ

NA60

[HR06, HR08]


Importance of baryon effects

baryonic interactions important!in-medium broadeninglow-mass tail!

10-9

10-8

10-7

10-6

0.2 0.4 0.6 0.8 1 1.2 1.4

(1/N

ch)

d2N

µµ/(

dM

dη

) (2

0 M

eV)-1

M (GeV)

all qT


full modelno baryons

NA60


Update: Using lattice equation of stateuse equation of state from lattice calculations (cross over!)use QGP rates adapted to recent lattice resultsIMR slope: true (average) temperature of source (no blue shift as in qT spectra!):T ' 205-230 MeV (above Tc ' 160 MeV!)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

Tc=170 MeV, Tch=160 MeV, EoS-L

all qT

Dim

uo

n Y

ield

dN

µµ/d

Mµ

µ [

(20

MeV

)-1]

Dimuon Invariant Mass Mµµ

(GeV/c2)

total4π mix

QGPNA60

compatible with coarse-grained UrQMD calculation (see Stephan Endres’s talk!)Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, 2014 37 / 45

RHIC beam-energy scan (STAR)

dielectron spectra Au+Au collisions (√

sNN = 200 GeV) at RHIC/STARsame model as before successful over wide range of beam energies [Rap13]

NB: together with CG UrQMD also at SIS energies! (see S. Endres’s talk)



dielectron spectra Au+Au collisions at RHICsame model as before successful over wide range of beam energies [Rap13]

NB: together with CG UrQMD also at SIS energies! (see S. Endres’s talk)



fireball model⇒ lifetime, dilepton excess, temperature as fct. of√

sNN

indications of phase transition???

0

5

10

15

20

25

0 50 100 150 2000

5

10

15

20

25

Nℓ+

ℓ−/

Nch·1

06

τ fb(

fm/

c)

√sNN (GeV)

0.3GeV < M < 0.7GeVHGvacHGmedQGPHGvac+QGPHGmed+QGPτfb

150

180

210

240

0 50 100 150 200

T(G

eV)

√sNN GeV

Fit range: 1.5GeV < M < 2.5GeV


ConclusionsGeneral ideas

em. probes⇔ in-medium em. current-correlation functioneffective QFT models for hadronic interactions and `+`− (and γ!) productionHTL improved or lattice QGP `+`− (and γ) ratesdual rates around Tc (compatible with χ symmetry restoration)medium modifications of ρ , ω , φ

importance of hadron-resonance interactionsbaryon resonances prevalent for medium effectsreliable input on resonance physics in elementary reactions crucial!need to fix masses, couplings, form factors (including em. transition FFs)

Application to dileptons in HICsthermal fireball, (ideal) hydrodynamics, (coarse-grained) transport, hybrid...equation of state⇔ compatibility with QFT/transport models!?!use of thermal-QFT spectral VM functionssuccessful description at HADES, SPS, and RHIC (STAR)consistent description of M and mT spectra!not too sensitive to details of medium evolutionbeam-energy scan at RHIC and FAIR⇒ signature of phase transition?sensitivity to equation of state?signature of cross-over vs. 1st order (or even critical endpoint)?effective slope of M spectra in higher IMR (1.5 GeV < M < MJ/ψ ) provides 〈T〉


Bibliography I

[BGG+12] O. Buss, et al., Transport-theoretical Description of Nuclear Reactions,Phys. Rept. 512 (2012) 1.http://dx.doi.org/10.1016/j.physrep.2011.12.001

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