The Dilepton Probe in Heavy-Ion Collisionshees/publ/dubna09.pdfin-med r+w+f 4p mix QGP DY total total (no bar r) Pb(158 AGeV)+Au ´10-6 =335 p t >0.2GeV 2.1

The Dilepton Probein Heavy-Ion Collisions

Hendrik van Hees

Justus-Liebig Universität Gießen

September 11, 2009

Institut für

Theoretische Physik

JUSTUS-LIEBIG-

UNIVERSITÄT

GIESSEN

Hendrik van Hees (JLU Gießen) Dileptons in HICs September 11, 2009 1 / 22

Outline

1 Electromagnetic probes in heavy-ion collisionsElectromagnetic probes and vector mesonsChiral symmetry and dileptonsThermal sources of dileptonsNon-thermal sources of dileptons

2 Comparison to Heavy-Ion dataInvariant-mass spectraSensitivity to Tc and hadro-chemistryIMR: Parton- or hadron-dominated source?

3 Conclusions and Outlook


Electromagnetic probes in heavy-ion collisions

γ, `±: no strong interactions

reflect whole “history” of collision:

from pre-equilibrium phasefrom thermalized mediumQGP and hot/dense hadron gasfrom VM decays after thermalfreeze-out

ρ/ω γ∗ e−π, . . .

e+

γ

0 1 2 3 4 5

M [GeV/c]

J/

Drell−Yan

DD

Low− Intermediate− High−Mass Region> 10 fm > 1 fm < 0.1 fm

ψ ’

π0, η Dalitz decays

dN

/(d

y d

m)

ρ/ω

Φ

Ψ

Fig. by A. Drees


Electromagnetic probes and vector mesons

photon and dilepton thermal emission rates given by sameelectromagnetic-current-correlation function (Jµ =

∑f Qf ψ̄fγµψf )

[L. McLerran, T. Toimela 85, H. A. Weldon 90, C. Gale, J.I. Kapusta 91]

Π

Chiral symmetry

In vacuum: Spontaneous breaking of chiral symmetry

⇒ mass splitting of chiral partners

qq-excitations of the QCD vacuum

π

ρ ω

φ

(140)

(770) (782)

(1260)

(1020)

(1285)

(400-

1200)

a f

f

f

1 1

1

0

Energy (MeV)

P-S, V-A splitting

in the physical vacuum

(1420)

0 1 2 3

s [GeV2]

0

0.02

0.04

0.06

0.08

−Im

ΠV

,A/(

πs)

[d

im.−

less

]

V [τ −> 2nπ ντ]

A [τ −> (2n+1)π ντ]ρ(770) + cont. a

1(1260) + cont.


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 baryondensity nB−nB̄reason: nB+nB̄ relevant (CP inv. of strong interactions)


In-medium spectral functions and baryon effects

[R. Rapp, J. Wambach 99]

baryon effects important

large contribution to broadening of the peakresponsible for most of the strength at small M


Dilepton rates: Hadron gas ↔ QGP

in-medium hadron gas matcheswith QGP

similar results also for γ rates

“quark-hadron duality”!?

indirect evidence forchiral-symmetry restoration


Sources of dilepton emission in heavy-ion collisions

1 initial hard processes: Drell Yan2 “core” ⇔ emission from thermal source [McLerran, Toimela 1985]

1qT

dN (thermal)

dMdqT=∫

d4x∫

dy∫Mdϕ

dN (thermal)

d4xd4qAcc(M, qT , y)

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

[Cooper, Frye 1975]

N (fo) =∫

d3qq0

∫qµdσµfB(uµqµ/T )

Γmeson→`+`−Γmeson

Acc

additional factor γ = q0/M compared to thermal emissionphysical reason

thermal source rate ∝ τmedΓmeson→`+`−

γ

decay of mesons after fo: rate ∝ Γmeson→`+`−ΓmesonHendrik van Hees (JLU Gießen) Dileptons in HICs September 11, 2009 9 / 22

CERES/NA45 dielectron spectra

good agreement also for dielectron spectra in 158 GeV Pb-Auallows further check of low-mass tail from baryon effects down toM → 2me

0 0.2 0.4 0.6 0.8 1 1.2M

ee [GeV]

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

(dN

ee/d

M)

/ <

Nch>

[100 M

eV

/c2]-

1

CERES ’00

in-med ρ+ω+φ

4π mixQGP

DY

total

total (no bar ρ)

Pb(158 AGeV)+Au

×10−6

=335

pt>0.2GeV

2.10.2GeV

2.1

NA60 acceptance-corrected mass spectra

ZD: [K. Dusling, D. Teaney, I. Zahed 2007], RR: [J. Ruppert, T. Renk et al 2008], RH: [HvH, R. Rapp 2008]Hendrik van Hees (JLU Gießen) Dileptons in HICs September 11, 2009 11 / 22

Importance of baryon effects

Baryonic interactions important!

in-medium broadening

low-mass tail!

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

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


+ω-t extotal

ω-t exωφ

DY4π mix

FO ρprim ρ

QGPin-med ρ

NA60


Sensitivity to Tc and hadro-chemistry

recent lattice QCD: Tc ' 190-200 MeV or Tc ' 150-160 MeV?thermal-model fits to hadron ratios: Tchem ' 150-160 MeV

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.2

0 1 2 3 4 5 6 7

T (

GeV

)

t (fm/c)

tfo=6.7 fm/c

EoS-A

EoS-B

EoS-C

0

0.02

0.04

0.06

0.08

0.1

0 1 2 3 4 5 6 7

µπ (

GeV

)t (fm/c)

tfo=6.7 fm/c

EoS-A

EoS-B

EoS-C

EoS-A: Tc = Tchem = 175 MeVEoS-B: Tc = Tchem = 160 MeVEoS-C: Tc = 190 MeV, Tchem = 160 MeV

Tc ≥ T ≥ Tchem: hadron gas in chemical equilibriumkeep fireball parameters the same (including life time)


EoS-B

0

500

1000

1500

2000

0.2 0.4 0.6 0.8 1 1.2 1.4

dN

µµ/d

M (

counts

)

M (GeV)

semicentral In-In

all qTTc=Tch=160 MeV

sum

DY

4π mix

FO + prim ρ

QGP+DD

in-med ρ

NA60

0

200

400

600

800

1000

0.2 0.4 0.6 0.8 1 1.2 1.4

dN

µµ/d

M (

counts

)

M (GeV)

semicentral In-In

qT1.0 GeV

Tc=Tch=160 MeV

sum

DY

4π mix

FO + prim ρ

QGP+DD

in-med ρ

NA60

103

104

105

106

107

108

0 0.5 1 1.5 2 2.5

1/q

T d

Nµ

µ/(

dq

T d

y)

(counts

)

mT-M (GeV)

semicentral In-In

0.4 GeV

EoS-C

0

500

1000

1500

2000

0.2 0.4 0.6 0.8 1 1.2 1.4

dN

µµ/d

M (

counts

)

M (GeV)

semicentral In-In

all qTTc=190 MeV

Tch=160 MeV

sum

DY

4π mix

FO + prim ρ

QGP+DD

in-med ρ

NA60

0

200

400

600

800

1000

0.2 0.4 0.6 0.8 1 1.2 1.4

dN

µµ/d

M (

counts

)

M (GeV)

semicentral In-In

qT1.0 GeV

Tc=190 MeV

Tch=160 MeV

sum

DY

4π mix

FO + prim ρ

QGP+DD

in-med ρ

NA60

103

104

105

106

107

108

0 0.5 1 1.5 2 2.5

1/q

T d

Nµ

µ/(

dq

T d

y)

(counts

)

mT-M (GeV)

semicentral In-In

0.4 GeV

Inverse-slope analysis

to extract Teff fit to1qT

dNdqT

=1mT

dNdmT

= C exp(−mTTeff

)fit of theoretical qT spectra: 1 GeV < qT < 1.8 GeV

100

150

200

250

300

0.2 0.4 0.6 0.8 1 1.2 1.4

Teff

(M

eV

)

M (GeV)

EoS-A

EoS-B

NA 60

NA 60 LMR

NA 60 IMR no DY 100

150

200

250

300

0.2 0.4 0.6 0.8 1 1.2 1.4

Teff

(M

eV

)

M (GeV)

EoS-A

EoS-C

NA 60

NA 60 LMR

NA 60 IMR no DY

standard fireball acceleration: too soft qT spectralower Tc in EoS-B and EoS-C helps (higher hadronic temperatures)NB: here, Drell Yan contribution taken out


Inverse-slope analysis

100

150

200

250

300

0.2 0.4 0.6 0.8 1 1.2 1.4

Teff

(M

eV

)

M (GeV)

EoS-B

EoS-B, a⊥

=0.1c2/fm

NA 60

NA 60 LMR

NA 60 IMR no DY 100

150

200

250

300

0.2 0.4 0.6 0.8 1 1.2 1.4

Teff

(M

eV

)

M (GeV)

EoS-C

EoS-C, a⊥

=0.1c2/fm

NA 60

NA 60 LMR

NA 60 IMR no DY

enhance fireball acceleration to a⊥ = 0.1c2/fmeffective at all stages of fireball evolution

agreement in IMR not spoiled ⇔ dominated from earlier stagesEoS-B harder ⇔ relative contribution of harder freeze-out ρ decaysvs. thermal ρ’s larger


IMR: QGP vs. multi-pion radiation

0

50

100

150

200

0.9 1 1.1 1.2 1.3 1.4

dN

µµ/d

M (

cou

nts

)

M (GeV)

semicentral In-In

all pT

QGP (EoS-A)QGP (EoS-B)QGP (EoS-C)

4π (EoS-A)4π (EoS-B)4π (EoS-C)

EoS-B: QGP dominates over multi-pion radiationopposite in EoS-A and EoS-Cmulti-pion radiation dominantly from high-density hadronic phase

reason :dNll/dMdT ∝ Im Πem(M,T ) exp(−M/T ) T−5.5

radiation maximal for T = Tmax = M/5.5hadronic and partonic radiation “dual” for T ∼ Tccompatible with chiral-symmetry restoration!inconclusive whether hadronic or partonic emission in IMR!Hendrik van Hees (JLU Gießen) Dileptons in HICs September 11, 2009 18 / 22

Hadron spectra

analysis of “cocktail”: hadron-mT spectra

comparison to fireball evolution

“sequential freeze-out” due to different coupling strength

103

104

105

106

107

0 0.5 1 1.5 2 2.5

(1/m

T)

dN

/dm

T (

a.u.)

mT-M (GeV)

ω (semicentral)

Tc=175 MeV, Tch=160 MeV

aT=0.1 c2/fm, tfo=5 fm

prim+fofo

primNA60 ω

103

104

105

106

107

0 0.5 1 1.5 2 2.5

(1/m

T)

dN

/dm

T (

a.u.)

mT-M (GeV)

φ (semicentral)

Tc=175 MeV, Tch=160 MeV

aT=0.1 c2/fm, tfo=4 fm

prim+fofo

primNA60 φ


M spectra (in pT slices)

EoS-A: Tc = Tch = 175 MeVtransverse acceleration: a⊥ = 0.1c2/fm

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


+ω-t extotal

ω-t exωφ

DY4π mix

FO ρprim ρ

QGPin-med ρ

NA60

10-9

10-8

10-7

10-6

10-5

0.2 0.4 0.6 0.8 1 1.2 1.4(1

/Nch

) d

2N

µµ/(

dM

dη

) (2

0 M

eV)-

1

M (GeV)

0.2 GeV



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



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



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



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)

1.2 GeV



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)

1.8 GeV

Conclusions and Outlook

dilepton spectra ⇔ in-medium em. current correlatormodel for dilepton sources

radiation from thermal sources: QGP, ρ, ω, φρ-decay after thermal freeze-outdecays of non-thermalized primordial ρ’sDrell-Yan annihilation, correlated DD̄ decays

invariant-mass spectra and medium effects

excess yield dominated by radiation from thermal sourcesbaryons essential for in-medium properties of vector mesonsmelting ρ with little mass shift robust signal! (independent of Tc)IMR well described by scenarios with radiation dominatedeither by QGP or multi-pion processes (depending on EoS)

Reason: mostly from thermal radiation around160 MeV ≤ T ≤ 190 MeV⇔ “parton-hadron” duality of rates⇔ compatible with chiral-symmetry restoration!

dimuons in In-In (NA60), Pb-Au (CERES/NA45), γ in Pb-Pb (WA98)



fireball/freeze-out dynamics ⇔ mT spectra and effective slopes“non-thermal sources” important for qT & 1 GeVlower Tc ⇒ higher hadronic temperatures ⇒ harder qT spectrato describe measured effective slopes a⊥ = 0.085c2/fm→ 0.1c2/fmoff-equilibrium effects (viscous hydro)?

Further developments

understand recent PHENIX results (large dilepton excess in LMR)understand “DLS puzzle” (exp. confirmed by HADES)NN (np!) bremsstrahlung!vector- should be complemented with axial-vector-spectral functions(a1 as chiral partner of ρ)constrained with lQCD via in-medium Weinberg chiral sum rulesdirect connection to chiral phase transition!


Electromagnetic probes in heavy-ion collisionsElectromagnetic probes and vector mesonsChiral symmetry and dileptonsThermal sources of dileptonsNon-thermal sources of dileptons

Comparison to Heavy-Ion dataInvariant-mass spectraSensitivity to Tc and hadro-chemistryIMR: Parton- or hadron-dominated source?


Documents

The Dilepton Probe in Heavy-Ion Collisionshees/publ/dubna09.pdfin-med r+w+f 4p mix QGP DY total total (no bar r) Pb(158 AGeV)+Au ´10-6 =335 p t >0.2GeV 2.1