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 p+p@3.5

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