Hadronic Matter andElectromagnetic Probes
Hendrik van Hees
Justus-Liebig Universität Gießen
September 1, 2009
Institut für
Theoretische Physik
JUSTUS-LIEBIG-
UNIVERSITÄT
GIESSEN
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 1 / 26
Outline
1 Electromagnetic probes in heavy-ion collisionsVector mesons and electromagnetic probesSources of dileptons
2 Comparison to NA60 dataInvariant-mass spectramT spectra and slope analysis
3 Conclusions and Outlook
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 2 / 26
Electromagnetic probes in heavy-ion collisions
γ, `±: no strong interactions
reflect whole “history” of collision:
from pre-equilibrium phasefrom thermalized mediumQGP and hot hadron gasfrom VM decays after thermalfreezeout
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
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 3 / 26
Vector Mesons and electromagnetic Probes
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
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)
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 5 / 26
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
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 6 / 26
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
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 7 / 26
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 ∝ τmed Γmeson→`+`−γdecay of mesons after fo: rate ∝ Γmeson→`+`−Γmeson
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 8 / 26
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”
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 9 / 26
Radiation from thermal sources: Meson t-channel exchange
motivation: qT spectra too soft compared to NA60 data
thermal contributions not included in models so far
ω
ρ
ρ
ℓ−
ℓ+
γ
π
π
also for π, a1
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 10 / 26
Excess spectra
Fireball with “standard” EoS-A (Tc = Tchem = 175 MeV)overall normalization ⇔ total fireball lifetimerelative normalization of thermal radiation fixed by rates
rates integrated over time, volume, ~q including NA60 acceptance
0
500
1000
1500
2000
0.2 0.4 0.6 0.8 1 1.2 1.4
dN
µµ/d
M (
cou
nts
)
M (GeV)
semicentral In-In
all qTTc=Tch=175 MeV
sum
DY
4π mix
FO + prim ρ
prim ρ
QGP+DD
in-med ρ
NA60
0
200
400
600
800
1000
1200
0.2 0.4 0.6 0.8 1 1.2 1.4
dN
µµ/d
M (
counts
)
M (GeV)
central In-In
all qT
Tc=Tch=175 MeV
sum
DY
4π mix
FO+prim ρ
prim ρ
QGP+DD
in-med ρ
NA60
good description of data
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 11 / 26
Excess spectra: IMR and multi-pion contributions
0
200
400
600
800
1000
1200
1 1.2 1.4
dN
µµ/d
M (
cou
nts
)
M (GeV)
semicentral In-Inall qT
Tc=Tch=175 MeVsum (4π vac)
4π vac
sum (4π mix)
4π mix
QGP
DD
NA60
“4π contributions” (π + ω, a1 → µ+ + µ−)slightly enhanced by VA mixing
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 12 / 26
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
Excess spectra: 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) Em Probes in RHICs September 1, 2009 14 / 26
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
Tc=Tch=175 MeV, at=0.1 c2/fm
+ω-t extotal
ω-t exωφ
DY4π mix
FO ρprim ρ
QGPin-med ρ
NA60
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 15 / 26
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)
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 16 / 26
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
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 19 / 26
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 freezeout ρ decays vs.thermal ρ’s larger
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 20 / 26
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-C, a⊥=0.1c2/fm
EoS-C, a⊥=0.1c2/fm + ω-t-ex (med ρ)
EoS-C, a⊥=0.1c2/fm + ω-t-ex (vac ρ)
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, a⊥
=0.1c2/fm
EoS-C, a⊥
=0.1c2/fm + DY
NA 60
NA 60 LMR
NA 60 IMR no DY
sensitivity to contributions from meson t-channel exchangehardens low-mass regionusing vacuum ρ in t-channel contribution: enhances slope in ρ region
sensitivity to Drell-Yan contribution
for IMR: describes effect seen in data (open vs. solid square data point)in LMR: too high around muon threshold ⇔due to uncertainties in extrapolation to low M?!?
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 21 / 26
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) Em Probes in RHICs September 1, 2009 22 / 26
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
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 23 / 26
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
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
/Nch
) d
2N
µµ/(
dM
dη
) (2
0 M
eV)-
1
M (GeV)
0.2 GeV
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)
0
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)
0.4 GeV
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)
0.8 GeV
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)
2.0 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)
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 25 / 26
Conclusions and Outlook
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!
Hendrik van Hees (JLU Gießen) Em Probes in RHICs September 1, 2009 26 / 26
Electromagnetic probes in heavy-ion collisionsVector mesons and electromagnetic probesSources of dileptons
Comparison to NA60 dataInvariant-mass spectramT spectra and slope analysis
Conclusions and Outlook