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Dilepton Signal fromGiBUU Transport Model
Janus Weil
Frankfurt Institute for Advanced Studies
in collab. with: U. Mosel, H. van Hees, K. Gallmeister, S. Endres, M. Bleicher
Workshop onElectromagnetic Probes of Strongly Interacting Matter
ECT* Trento, May 20, 2013
J. Weil Dilepton Signal from GiBUU Transport Model
Introduction
HADES has measured various dileptonspectra in the few-GeV regime (1-4 GeV):
elementary reactions (pp, dp, pNb)heavy-ion collisions (CC, ArKCl, AuAu)
We need models (e.g. transport)to interpret & understand them!
What do we want to learn?⇒ in-medium spectral functions(in particular for the ρ meson)
heaviest system so far: Ar+KCl at 1.76 GeV(ρ . 3ρ0, T ∼ 80MeV)
What is the current status?
J. Weil Dilepton Signal from GiBUU Transport Model
Ar + KCl @ 1.76: status (aka the “∆ puzzle”)
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
dilepton mass mee [GeV]
GiBUU(vacuum SF)
datatotal
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
NN Brems.D13(1520)S31(1620)
ππ
J. Weil Dilepton Signal from GiBUU Transport Model
Questions
Is a ’vacuum’ cocktail sufficient to describethe ArKCl spectrum?
Is there hope to see any modifications of the ρ spec. func.?
answers currently depend on which model you believe in ...
biggest discrepancy: ∆ Dalitz channel
⇒ we need to check very carefully if we understand thecocktail with all its contributions
separating vacuum cocktail from medium modificationsrequires two steps:
1 fix vacuum cocktail & model input via elementary collisionsonly!
2 only afterwards: check if the same cocktail can describeheavy-ion collisions (or if medium-mod. are required)
J. Weil Dilepton Signal from GiBUU Transport Model
The GiBUU Transport Model
hadronic transport model (microscopic, non-equilibrium)unified framework for various types of reactions(γA, eA, νA, pA, πA, AA) and observablesBUU equ.: space-time evolution of phase-space density F(via gradient expansion from Kadanoff-Baym)
∂(p0−H)∂pµ
∂F (x ,p)∂xµ −
∂(p0−H)∂xµ
∂F (x ,p)∂pµ = C (x , p)
Hamiltonian H:hadronic mean fields, Coulomb, “off-shell potential”
collision term C (x , p): decays and collisionslow energy: resonance model, high energy: string fragment.
O. Buss et al., Phys. Rep. 512 (2012),http://gibuu.physik.uni-giessen.de
J. Weil Dilepton Signal from GiBUU Transport Model
Modeling collisions in the few-GeV regime
baryon-baryon collisions at low energies:resonance models vs. string fragmentation
HADES energy range is clearly in the resonance regime!
we need one consistent model for the whole energy range!
J. Weil Dilepton Signal from GiBUU Transport Model
Resonance Model
assumption: inel. NN cross section is dominated byproduction and decay of baryonic resonancesNN → NR,∆R (R : ∆, 7 N∗ and 6 ∆∗ states)based on Teis RM [Z. Phys. A 356, 1997] with several extensionsall resonance parameters taken from Manley/Saleski PWAgood descr. of total NN cross sections up to
√s ≈ 3.5GeV
all π, η and ρ mesons produced via R decays (ω, φ: non-res.)
0
5
10
15
20
25
30
35
40
2 2.5 3 3.5 4
σin
el [
mb]
sqrt(s) [GeV]
pp → X
HADES
2 2.5 3 3.5 4 0
5
10
15
20
25
30
35
40
sqrt(s) [GeV]
np → X
datainel.N∆
NN*N∆*∆∆
∆N*∆∆*
NNπω/φ
BYK
J. Weil Dilepton Signal from GiBUU Transport Model
Dilepton sources
V → e+e− (with V = ρ, ω, φ) via strict VMD: Γee(m) ∝ m−3
P → γe+e− (with P = π0, η, η′) [Landsberg, Phys.Rep.128, 1985]ω → π0e+e− [Landsberg]∆ → Ne+e− [Krivoruchenko, Phys.Rev.D65, 2002],em. transition form factor from Ramalho/Pena [Phys.Rev.D85, 2012]
baryonic resonances N∗, ∆∗: two-step decay R → ρN → e+e−N⇒ dilepton contributions from all res. which have a ρ coupling(with an ’implicit’ FF: strict VMD)
Bremsstrahlung in soft-photon approximation
J. Weil Dilepton Signal from GiBUU Transport Model
Delta form factor
electromagnetic N-∆ transition form factor only constrainedby data in space-like region
experimentally unknown in time-like region
recent models: Wan/Iachello (red, IJMP A20, 2005),Ramalho/Pena (green, PRD85, 2012)
100
101
102
0 0.2 0.4 0.6 0.8 1 1.2 1.4
|GM
|2
mee [GeV]
3.029**2W/I 1.23W/I 1.43W/I 1.63W/I 1.83W/I 2.03R/P 1.23R/P 1.43R/P 1.63R/P 1.83R/P 2.03
J. Weil Dilepton Signal from GiBUU Transport Model
∆ production cross section
only exclusive ∆+ production constrained by data
resonance models (UrQMD/GiBUU) agree roughly oninclusive production
but: inclusive cross section much larger in HSD/FRITIOF
string models do not obey isospin relations!
10-1
100
101
2 2.5 3 3.5 4 4.5 5 5.5
σpp [m
b]
sqrt(s) [GeV]
pp → ∆+X production
∆+X (Res)
∆+p (Res)
∆+X (Py)
∆+p (Py)
∆+X (Fr)
∆+p (Fr)
HSD inclHSD excl
UrQMD inclUrQMD excl
∆+p data
2 2.5 3 3.5 4 4.5 5 5.5
sqrt(s) [GeV]
pp → ∆++
X production
∆++
X (Res)∆
++n (Res)
∆++
X (Py)∆
++n (Py)
∆++
X (Fr)∆
++n (Fr)
2 2.5 3 3.5 4 4.5 5 5.5-0.5
0
0.5
1
1.5
2
2.5
3
3.5
sqrt(s) [GeV]
isospin ratio ∆++
/∆+
incl. (Res)excl. (Res)
incl. (Py)excl. (Py)incl. (Fr)
excl. (Fr)
lesson: don’t trust string fragmentation models at low energies!J. Weil Dilepton Signal from GiBUU Transport Model
p+p at 3.5 GeV
Pythia + Iachello FF
10-3
10-2
10-1
100
101
0 0.2 0.4 0.6 0.8 1
dσ
/dm
ee [
µb
/Ge
V]
dilepton mass mee [GeV]
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
10-3
10-2
10-1
100
101
0 0.2 0.4 0.6 0.8 1
dσ
/dp
T [
µb/G
eV
]
0 0.2 0.4 0.6 0.8 1
transverse momentum pT [GeV]
0 0.2 0.4 0.6 0.8 1
10-3
10-2
10-1
100
101
0 0.2 0.4 0.6 0.8 1
dσ
/dp
T [
µb/G
eV
]
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
10-4
10-3
10-2
10-1
100
0 0.5 1 1.5 2
dσ
/dy [
µb]
m < 150 MeV
0 0.5 1 1.5 2
rapidity y
150 MeV < m < 470 MeV
0 0.5 1 1.5 2
470 MeV < m < 700 MeV
0 0.5 1 1.5 2
10-4
10-3
10-2
10-1
100
dσ
/dy [
µb]
700 MeV < m
Resonance Model + Ramalho FF
10-3
10-2
10-1
100
101
0 0.2 0.4 0.6 0.8 1d
σ/d
mee [
µb
/Ge
V]
dilepton mass mee [GeV]
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
10-3
10-2
10-1
100
101
0 0.2 0.4 0.6 0.8 1
dσ
/dp
T [
µb/G
eV
]
0 0.2 0.4 0.6 0.8 1
transverse momentum pT [GeV]
0 0.2 0.4 0.6 0.8 1
10-3
10-2
10-1
100
101
0 0.2 0.4 0.6 0.8 1
dσ
/dp
T [
µb/G
eV
]
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
10-4
10-3
10-2
10-1
100
0 0.5 1 1.5 2
dσ
/dy [
µb]
m < 150 MeV
0 0.5 1 1.5 2
rapidity y
150 MeV < m < 470 MeV
0 0.5 1 1.5 2
470 MeV < m < 700 MeV
0 0.5 1 1.5 2
10-4
10-3
10-2
10-1
100
dσ
/dy [
µb]
700 MeV < m
J. Weil Dilepton Signal from GiBUU Transport Model
Resonance contributions in p+p @ 3.5
10-3
10-2
10-1
100
0 0.2 0.4 0.6 0.8 1
dσ
/dm
ee [
µb/G
eV
]
dilepton mass mee [GeV]
ρ → e+e
-
D13(1520)S11(1535)S11(1650)F15(1680)P13(1720)
all Res.S31(1620)D33(1700)F35(1905)
in the resonance model approach we get large contributionsfrom several N∗ and ∆∗ resonances
πN spectra confirm significant resonance contr. (A. Dybczak)
J. Weil Dilepton Signal from GiBUU Transport Model
other elementary collisions
10-3
10-2
10-1
100
101
0 0.1 0.2 0.3 0.4 0.5
dσ
/dm
ee [
µb
/Ge
V]
dilepton mass mee [GeV]
p + p at 1.25 GeV
dataGiBUU total
π0 → e
+e
-γ
∆ → Ne+e
-
ρ → e+e
-
D13(1520)
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
/dm
ee [
µb
/Ge
V]
dilepton mass mee [GeV]
p + p at 2.2 GeV
dataGiBUU total
ρ → e+e
-
ω → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
D13(1520)P13(1720)
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
/dm
ee [
µb/G
eV
]
dilepton mass mee [GeV]
d + p at 1.25 GeV
dataGiBUU total
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
pn Brems.ρ → e
+e
-
D13(1520)S11(1535)
p+p at 1.25 and 2.2 GeV rather well described
large underestimation in d+p
OBE models can help to understand isospin effects(Shyam/Mosel, PRC82, 2010)
J. Weil Dilepton Signal from GiBUU Transport Model
’light’ nuclear systems
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
dσ
/dm
ee
dilepton mass mee [GeV]
C + C @ 1.0 GeV
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
NN Brems.D13(1520)S31(1620)
ππ
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0 0.2 0.4 0.6 0.8 1
1/N
π0 d
N/d
mee
dilepton mass mee [GeV]
C + C @ 2.0 GeV
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
NN Brems.D13(1520)S31(1620)
ππ
10-1
100
101
102
103
0 0.2 0.4 0.6 0.8 1 1.2
dσ
/dm
ee [
µb/G
eV
]
dilepton mass mee [GeV]
p + Nb @ 3.5 GeV
dataGiBUU total
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
D13(1520)S31(1620)F35(1905)
C+C is a light system, can be described roughly by asuperposition of NN collisions
2 GeV data well described, some discrepancies at 1 GeV
also p+Nb well reproduced, based on the good agreementwith [email protected]
J. Weil Dilepton Signal from GiBUU Transport Model
Ar + KCl @ 1.76 AGeV
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
dilepton mass mee [GeV]
GiBUU(vacuum SF)
datatotal
ρ → e+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
NN Brems.D13(1520)S31(1620)
ππ
]2 [MeV/ceeM
0 0.2 0.4 0.6
)ee
/dM
NN
)/(d
Nee
/dM
AA
) (d
N0
πAA
/N0
πNN
(N 0
1
2
3
4
5
6
7
8
(b)Ar+KCl 1.76A GeVC+C 1A GeV
C+C 2A GeV
Ar+KCl data shows excess over NN/CC (∼ factor 3)GiBUU with vac. SF misses data⇒ room for medium mod.
J. Weil Dilepton Signal from GiBUU Transport Model
Ar+KCl: off-shell transport
off-shell EOM for test particles[Cassing/Juchem (NPA 665, 2000),
Leupold (NPA 672, 2000)]:
~̇ri =1
1− Ci
1
2Ei
[2~pi +
∂
∂~piRe(Σi ) + χi
∂Γi
∂~pi
],
~̇pi = −1
1− Ci
1
2Ei
[∂
∂~riRe(Σi ) + χi
∂Γi
∂~ri
],
Ci =1
2Ei
[∂
∂EiRe(Σi ) + χi
∂Γi
∂Ei
],
χi =m2i − M
2
Γi,
dχi
dt= 0
test particles dynamicallychange their masses
some approximations required
only works ’close to mass shell’
10-8
10-7
10-6
10-5
10-4
10-3
0 0.2 0.4 0.6 0.8 1
dσ
/dm
ee [
mb
/Ge
V]
dilepton mass mee [GeV]
VM in-medium effects
datashift
CB+shiftvacCB
J. Weil Dilepton Signal from GiBUU Transport Model
pion-induced reactions
10-3
10-2
10-1
100
101
102
103
0 0.5 1 1.5 2
σee [
µb
]
Ekin [GeV]
π- p: dilepton excitation function
GiBUU totalρ → e
+e
-
ω → e+e
-
φ → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
D13(1520)S11(1535)F15(1680)F35(1905)
10-2
10-1
100
101
102
103
0 0.2 0.4 0.6 0.8 1
dσ
/dm
ee [
µb/G
eV
]
dilepton mass mee [GeV]
π- p at 540 MeV
GiBUU totalρ → e
+e
-
ω → e+e
-
ω → π0e
+e
-
π0 → e
+e
-γ
η → e+e
-γ
∆ → Ne+e
-
D13(1520)S11(1535)
biggest opportunity: directly determine dilepton contributionfrom N∗(1520), including form factor!
but: pion beam will actually not help to solve the “∆ puzzle”!
prev. calculations by Weidmann (PRC59, 1999) andEffenberger (PRC60, 1999)
J. Weil Dilepton Signal from GiBUU Transport Model
Conclusions
1 resonance-model approach provides good description of mostelementary dilepton data (as well as C+C)
2 contributions of N∗ and ∆∗ resonances are significant!
3 better constraints on resonance parameters needed(⇒ pion beam at GSI!)
4 future investigations of in-medium effects:
off-shell transport (GiBUU)coarse graining (UrQMD)
5 stop the black-boxing! we need open models!
J. Weil Dilepton Signal from GiBUU Transport Model