HADES versus DLS:  HADES versus DLS:  no puzzle anymore ! no puzzle anymore !

EElenalena Bratkovskaya Bratkovskaya

22.10.2007 , Workshop ‚Bremsstrahlung in dilepton production‘22.10.2007 , Workshop ‚Bremsstrahlung in dilepton production‘GSI, DarmstadtGSI, Darmstadt

10 years of DLS puzzle10 years of DLS puzzle

DLS-puzzle (since 1997):DLS-puzzle (since 1997):

•new (1997) DLS datanew (1997) DLS data for C+C and for C+C and Ca+Ca at 1.04 A GeV are higher than Ca+Ca at 1.04 A GeV are higher than the the old (1995)old (1995) DLS data by ~ a factor of DLS data by ~ a factor of 5-7 at 0.15<M<0.5 GeV 5-7 at 0.15<M<0.5 GeV

•Transport models:Transport models: good description of good description of p+pp+p and and p+dp+d data data from 1 to 5 GeVfrom 1 to 5 GeV missing yield at 0.15 < M < 0.5 GeVmissing yield at 0.15 < M < 0.5 GeV for C+C and Ca+Ca at 1.04 A GeV for C+C and Ca+Ca at 1.04 A GeV ((similar results obtained by HSD ‘97 ,similar results obtained by HSD ‘97 ,UrQMD’98 and Tübingen QMD‘03)UrQMD’98 and Tübingen QMD‘03)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.010-4

10-3

10-2

10-1

100

101

DLS'95 DLS'97

40Ca+40Ca1.0 GeV

d/d

M/(

ApA

t)2/3 [b

/(G

eV/c

2 )]

M [GeV/c2]

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

10-3

10-2

10-1

100

101

102

103

Brems. pn Brems. N All

DLS Dalitz Dalitz Dalitz Dalitz

C+C, 1.0 A GeVHSD, free spectral functions

d/d

M [b

/(G

eV c

2 )]

M [GeV/c2]

10 years of waiting for HADES …10 years of waiting for HADES …

A decade of search for the solution of the DLS puzzleA decade of search for the solution of the DLS puzzle

Constraints on Constraints on , , by TAPS data: by TAPS data:HSD:HSD: good description of TAPS data good description of TAPS data on on , , multiplicities and m multiplicities and mTT-spectra -spectra =>=>, , dynamics under control !dynamics under control !

Other channels: Other channels: accounting for accounting for in-mediumin-medium effects effects (collisional broadening of vector meson (collisional broadening of vector meson spectral functions, dropping vector meson spectral functions, dropping vector meson masses) masses) does notdoes not provide enough provide enough enhancement at intermediate Menhancement at intermediate M contribution from N(1520) contribution from N(1520) (E.B.&C.M. Ko, PLB 445 (1999) 265)(E.B.&C.M. Ko, PLB 445 (1999) 265)

and and higher baryonic resonanceshigher baryonic resonances are small are small (cf. Gy. Wolf et al., PRC67 (2003) 044002)(cf. Gy. Wolf et al., PRC67 (2003) 044002)

Also:Also: accounting for accounting for anisotropies in e+e-anisotropies in e+e-emissionemission gives only a small effect gives only a small effect

0.5 1.0 1.5 2.0

10-4

10-3

10-2

10-1

100

101

TAPS HSD

Ebeam

[A GeV]

C+C

Mul

t inc

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

10-3

10-2

10-1

100

101

102

DLS HSD'98, free spectral functions HSD'98, in-medium spectral functions

C+C, 1.0 A GeV

d/d

M [b

/(G

eV c

2 )]

M [GeV/c2]

HSD‘98HSD‘98

DLS versus HADESDLS versus HADES

Experiment:Experiment: No contradiction No contradiction between DLS and between DLS and HADES !HADES !

What about theory ?What about theory ?

Dileptons from transport modelsDileptons from transport models

• HSD HSD

• UrQMD 1.3 (1998) UrQMD 1.3 (1998)

UrQMD 2.2 (2007) (Frankfurt)UrQMD 2.2 (2007) (Frankfurt)

• RQMD (Tübingen)RQMD (Tübingen)

• IQMD (Nantes)IQMD (Nantes)

• BRoBUU (Rossendorf)BRoBUU (Rossendorf)

HSDHSD – – HHadron-adron-SString-tring-DDynamics transport approachynamics transport approach

•for each particle species for each particle species ii ( (i i = = NN, , RR, , YY, , , , , K, …) the phase-space density , K, …) the phase-space density ffi i followsfollows the the transport equations transport equations

with collision termswith collision terms IIcoll coll describing:describing: elastic and inelastic elastic and inelastic hadronic reactions: hadronic reactions:

baryon-baryon, meson-baryon, meson-mesonbaryon-baryon, meson-baryon, meson-meson formation and decay of formation and decay of baryonic and mesonicbaryonic and mesonic resonancesresonances stringstring formation and decay formation and decay ((for inclusive particle production:for inclusive particle production:

BB BB X , mB X , mB X, X =many particles)X, X =many particles)

• implementation of implementation of detailed balance detailed balance on the level of 1on the level of 122

and 2and 22 reactions (+ 22 reactions (+ 2n n multi-particle reactionsmulti-particle reactions in HSD) in HSD)

•off-shell dynamicsoff-shell dynamics for short-lived states for short-lived states

Basic concept of HSD Basic concept of HSD

),...,f,f(fI,t)p,r(fHHt M21colliprrp

BB BB B´B´, BB B´B´, BB B´BB´B´m´m

mB mB m´B´, mB m´B´, mB B´B´Baryons: Baryons:

B=(p, n, B=(p, n, , ,

N(1440), N(1535), ...)N(1440), N(1535), ...)

Mesons: Mesons:

m=(m=(, , , ,

Dilepton channels in HSDDilepton channels in HSD

•All particles decaying to dileptons are All particles decaying to dileptons are first produced in BB, mB or mm collisionsfirst produced in BB, mB or mm collisions

•‚‚Factorization‘ of diagram Factorization‘ of diagram in the in the transport approach:transport approach:

•The dilepton spectra are calculated The dilepton spectra are calculated perturbatively perturbatively with the with the time integration methodtime integration method..

N N

N

N

R

e+

*e-

=

e-

N N

N R

N

R

e+

*

Time integration method for dileptons Time integration method for dileptons

tt00 ttabsabs

timetime FF

F – F – final time of computation in the codefinal time of computation in the codett00 – production time – production timettabsabs – absorption (or hadronic decay) time – absorption (or hadronic decay) time

ee--

e+e+

ee--

e+e+

‚‚Reality‘:Reality‘:

‚‚Virtual‘ – time integ. method:Virtual‘ – time integ. method:

only only ONE e+e- pairONE e+e- pair with probability ~with probability ~Br(Br(->e+e-)=4.5->e+e-)=4.5 . .1010-5-5

Calculate probability P(t) to Calculate probability P(t) to emitemit anan e+e- pair e+e- pair at at each time teach time t and integrate P(t) over time!and integrate P(t) over time!: t: t0 0 < t < t< t < tabsabs

: t: t00 <t < <t < infinityinfinity

The time integration method for dileptons in HSD The time integration method for dileptons in HSD

ee--

e+e+Dilepton emission rate:Dilepton emission rate:

N(t)]Δt)[N(tΔt

1

dt

dNΔt,dt:ynumericall

dtN(t)dtN(t)N(t)dt

eN)(t)eeN(ρ

Γ

cτ),eeBr(ρN

γτ

1(t)

dt

)eedN(ρ

F

F

τ

τ

00

γτ

t

0

totρ

FF

ΔM

1e(M)Br

ΔM

1

c)γ(

Δt(M)Γ

dM

dN c)γ(

τΓτ

time

eeρ FtoteeρeeρF

Dilepton invariant mass spectra:Dilepton invariant mass spectra:

0 < t < 0 < t < FF

timetimett00=0=0

FF < t < < t < infinityinfinity

NN bremsstrahlung - SPANN bremsstrahlung - SPA

Soft-Photon-ApproximationSoft-Photon-Approximation (SPA): (SPA):

N N -> N N eN N -> N N e++ee--

-->e>e++ee--

Phase-space corrected Phase-space corrected soft-photon cross section:soft-photon cross section:

elastNNσ

1

qdMd

qM,s,dσ

qdMd

)qM,dP(s,

SPA implementation in HSD: SPA implementation in HSD:

ee++ee- - production in production in elastic NN collisionelastic NN collision with probability: with probability:

elasticelastic

NNNN

‚‚quasi- elastic‘ quasi- elastic‘ N N -> N NN N -> N N

‚‚off-shell‘ correction factoroff-shell‘ correction factor

NN bremsstrahlung: OBE-modelNN bremsstrahlung: OBE-model

OBE-model:OBE-model: N N -> N N e N N -> N N e++ee--

‚‚pre‘pre‘ ‚‚post‘post‘

‚‚post‘post‘‚‚pre‘pre‘

+ gauge terms+ gauge terms

charged meson charged meson

exchangeexchange contact terms (from formfactors)contact terms (from formfactors)

The strategy to The strategy to restore gauge restore gauge invarianceinvariance is is

model dependent!model dependent!

Kaptari&Kämpfer, NPA 764 (2006) 338Kaptari&Kämpfer, NPA 764 (2006) 338

Bremsstrahlung – a new view on an ‚old‘ storyBremsstrahlung – a new view on an ‚old‘ story

2007 (era of HADES):2007 (era of HADES): The DLS puzzle is solved by The DLS puzzle is solved by accounting for a larger pn bremsstrahlung !!!accounting for a larger pn bremsstrahlung !!!

0.0 0.1 0.2 0.3 0.4 0.510-4

10-3

10-2

10-1

100

101

0.0 0.1 0.2 0.3 0.4 0.510-4

10-3

10-2

10-1

100

101

Bremsstrahlung

SPA, in HSD'97 Schäfer et al.'94 Shyam&Mosel'03 Kaptari&Kämpfer'06

p+n, 1.04 GeV

d/d

M [b

/(G

eV/c

2 )]

Schäfer et al.'94 de Jong&Mosel'96 Shyam&Mosel'03 Kaptari&Kämpfer'06

M [GeV/c2]

p+p, 1.04 GeV

d/d

M [b

/(G

eV/c

2 )]

New OBE-model New OBE-model (Kaptari&Kämpfer, NPA 764 (2006) 338):(Kaptari&Kämpfer, NPA 764 (2006) 338):

• pn pn bremstrahlung is bremstrahlung is largerlarger by a factor of by a factor of 4 4 than it has been than it has been calculated before (and used in transport calculations)!calculated before (and used in transport calculations)!

• pp pp bremstrahlung is smaller than pn, however, bremstrahlung is smaller than pn, however, not zeronot zero; consistent ; consistent with the 1996 calculations from with the 1996 calculations from de Jong in a T-matrix approachde Jong in a T-matrix approach

HSD: Dileptons from p+p and p+d - DLSHSD: Dileptons from p+p and p+d - DLS

• bremsstrahlungbremsstrahlung is the dominant contribution in p+d is the dominant contribution in p+d for 0.15 < M < 0.55 GeV at ~1-1.5 A GeV for 0.15 < M < 0.55 GeV at ~1-1.5 A GeV

0.1 0.3 0.5 0.7 0.9 1.110

-4

10-3

10-2

10-1

100

101

0.1 0.3 0.5 0.7 0.9 1.110

-4

10-3

10-2

10-1

100

101

0.1 0.3 0.5 0.7 0.9 1.110

-4

10-3

10-2

10-1

100

101

0.1 0.3 0.5 0.7 0.9 1.110

-4

10-3

10-2

10-1

100

101

0.1 0.3 0.5 0.7 0.9 1.110

-4

10-3

10-2

10-1

100

101

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.510

-4

10-3

10-2

10-1

100

101

Dalitz Dalitz Dalitz Dalitz Brems. NN Brems. N All

p+d, 1.04 GeV

d/d

M [b

/(G

eV/c

2 )]

Dalitz Dalitz Dalitz Dalitz Brems. NN Brems. N All

p+d, 1.27 GeV

p+d, 1.61 GeV

d/d

M [b

/(G

eV/c

2 )]

0

p+d, 1.85 GeV

p+d, 2.09 GeV

d/d

M [b

/(G

eV/c

2 )]

M [GeV/c2]

p+d, 4.88 GeV

M [GeV/c2]

0.1 0.3 0.5 0.7 0.9 1.110

-4

10-3

10-2

10-1

100

101

0.1 0.3 0.5 0.7 0.9 1.110

-4

10-3

10-2

10-1

100

101

0.1 0.3 0.5 0.7 0.9 1.110

-4

10-3

10-2

10-1

100

101

0.1 0.3 0.5 0.7 0.9 1.110

-4

10-3

10-2

10-1

100

101

0.1 0.3 0.5 0.7 0.9 1.110

-4

10-3

10-2

10-1

100

101

0.1 0.3 0.5 0.7 0.9 1.110

-4

10-3

10-2

10-1

100

101

Dalitz Dalitz Dalitz Dalitz Brems. pp All

p+p, 1.04 GeV

d/d

M [b

/(G

eV/c

2 )]

Dalitz Dalitz Dalitz Dalitz Brems. pp All

p+p, 1.27 GeV

p+p, 1.61 GeV

d/d

M [b

/(G

eV/c

2 )]

p+p, 1.85 GeV

p+p, 2.09 GeV

d/d

M [b

/(G

eV/c

2 )]

M [GeV/c2]

p+p, 4.88 GeV

M [GeV/c2]

HSD: Dileptons from A+A at 1 A GeV - DLSHSD: Dileptons from A+A at 1 A GeV - DLS

• bremsstrahlungbremsstrahlung and and -Dalitz are the dominant contributions -Dalitz are the dominant contributions in A+A for 0.15 < M < 0.55 GeV at 1 A GeV !in A+A for 0.15 < M < 0.55 GeV at 1 A GeV !

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

10-3

10-2

10-1

100

101

102

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

10-3

10-2

10-1

100

101

102

Brems. NN Brems. N All

DLS Dalitz Dalitz Dalitz Dalitz

C+C, 1.04 A GeVin-medium effects: CB+DM

d/d

M [b

/(G

eV c

2 )]

M [GeV/c2]

Brems. NN Brems. N All

DLS Dalitz Dalitz Dalitz Dalitz

C+C, 1.04 A GeVno medium effects

d/d

M [b

/(G

eV c

2 )]

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.010-3

10-2

10-1

100

101

102

103

104

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.010-3

10-2

10-1

100

101

102

103

104

Brems. NN Brems. N All

DLS Dalitz Dalitz Dalitz Dalitz

Ca+Ca, 1.04 A GeVin-medium effects: CB+DM

d/d

M [b

/(G

eV c

2 )]

M [GeV/c2]

Brems. NN Brems. N All

DLS Dalitz Dalitz Dalitz Dalitz

Ca+Ca, 1.04 A GeVno medium effects

d/d

M [b

/(G

eV c

2 )]

0.0 0.2 0.4 0.6 0.810-8

10-7

10-6

10-5

10-4

10-3

10-2

0.0 0.2 0.4 0.6 0.810-8

10-7

10-6

10-5

10-4

10-3

10-2

HADES

HSD: Dalitz Dalitz Dalitz Dalitz Brems. NN Brems. N All

C+C, 1.0 A GeVno medium effects

1/N

dN/d

M [

1/G

eV /c

2 ]

HSD: Dalitz Dalitz Dalitz Dalitz Brems. NN Brems. N All

M [GeV/c2]

HADES

C+C, 1.0 A GeVin-medium effects: CB+DM

1/N

dN/d

M [

1/G

eV /c

2 ]

Prelim

inar

y HADES d

ata

HSD: Dileptons from C+C at 1 and 2 A GeV - HADESHSD: Dileptons from C+C at 1 and 2 A GeV - HADES

• HADES data show exponentially decreasing mass spectra HADES data show exponentially decreasing mass spectra • Data are Data are better described by in-medium scenarios with collisional broadening better described by in-medium scenarios with collisional broadening • In-medium effects are more pronounced for In-medium effects are more pronounced for heavy systemsheavy systems such as Au+Au such as Au+Au

0.0 0.2 0.4 0.6 0.8 1.010-8

10-7

10-6

10-5

10-4

10-3

10-2

0.0 0.2 0.4 0.6 0.8 1.010-8

10-7

10-6

10-5

10-4

10-3

10-2

HADES

HSD: Dalitz Dalitz Dalitz Dalitz Brems. NN Brems. N All

C+C, 2.0 A GeVno medium effects

1/N

dN/d

M [

1/G

eV /c

2 ]

HSD: Dalitz Dalitz Dalitz Dalitz Brems. NN Brems. N All

M [GeV/c2]

HADES

C+C, 2.0 A GeVin-medium effects: CB+DM

1/N

dN/d

M [

1/G

eV /c

2 ]

HSD: Dilepton pHSD: Dilepton pTT and y spectra from C+C at 1 A GeV - HADES and y spectra from C+C at 1 A GeV - HADES

• HSD predictions for pHSD predictions for pTT and y spectra and y spectra are in are in good agreementgood agreement with the HADES data for all M-bins!with the HADES data for all M-bins!

Prelim

inar

y HADES d

ata

0.0 0.2 0.4 0.6 0.8 1.010-10

10-9

10-8

10-7

10-60.0 0.2 0.4 0.6 0.8 1.0

10-8

10-7

10-6

10-5

10-40.0 0.2 0.4 0.6 0.8 1.0

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-21/

N

dN/d

p T1/

N

dN/d

p T1/

N

dN/d

p T

M>0.55 GeV/c2

pT

0.15<M<0.55 GeV/c2

Dalitz Dalitz Dalitz Dalitz Brems. pn Brems. N All

M<0.15 GeV/c2

C+C, 1.0 A GeV, HADES acc.

-0.5 0.0 0.5 1.0 1.5

10-8

10-7

10-6

10-5

10-4

10-3

-0.5 0.0 0.5 1.0 1.5

10-8

10-7

10-6

10-5

10-4

10-3

-0.5 0.0 0.5 1.0 1.5

10-8

10-7

10-6

10-5

10-4

10-3

M>0.15 GeV/c2

y

M<0.15 GeV/c2

C+C, 1.0 A GeV, HADES acc.

Dalitz Dalitz Dalitz Dalitz Brems. pn Brems. N All

1/N

dN/d

y1/

N

dN/d

y

all M

1/N

dN/d

y

HSD: Dilepton pHSD: Dilepton pTT and y spectra from C+C at 2 A GeV - HADES and y spectra from C+C at 2 A GeV - HADES

• HSD predictions for pHSD predictions for pTT and y spectra and y spectra are in are in good agreementgood agreement with the HADES data for all M-bins!with the HADES data for all M-bins!

M<0.15 GeV/cM<0.15 GeV/c22 M>0.55 GeV/cM>0.55 GeV/c220.15<M<0.55 GeV/c0.15<M<0.55 GeV/c22

Prelim

inar

y HADES d

ata

Bremsstrahlung in UrQMD 1.3 (1998)Bremsstrahlung in UrQMD 1.3 (1998)Ernst et al, PRC58 (1998) 447Ernst et al, PRC58 (1998) 447

0.0 0.2 0.4 0.6 0.8 1.0 1.210-3

10-2

10-1

100

Kaptari'06 1.0 2.1 4.9

Bremsstrahlung pn

UrQMD'97 1.0 2.1 4.9

M [GeV/c2]

d/d

M [b

/(G

eV/c

2 )]

Bremsstrahlung-UrQMD’98 Bremsstrahlung-UrQMD’98 smaller than bremsstrahlung-Kaptari’06 smaller than bremsstrahlung-Kaptari’06 by a factor of 3-6by a factor of 3-6

SPA:SPA:

SPA implementation in UrQMD (1998): SPA implementation in UrQMD (1998): ee++ee- - production in production in elastic NN collisionselastic NN collisions (similar to HSD) (similar to HSD)

Dileptons from pp and pd - UrQMD 1.3Dileptons from pp and pd - UrQMD 1.3Ernst et al, PRC58 (1998) 447Ernst et al, PRC58 (1998) 447

• „„old“old“ bremsstrahlung: missing yield bremsstrahlung: missing yield for p+d at 0.15 < M < 0.55 GeV for p+d at 0.15 < M < 0.55 GeV at ~1-1.5 A GeV at ~1-1.5 A GeV

Dileptons from A+A - UrQMD 1.3Dileptons from A+A - UrQMD 1.3

Ernst et al, PRC58 Ernst et al, PRC58 (1998) 447(1998) 447

• „„old“old“ bremsstrahlung: missing yield bremsstrahlung: missing yield for for A+A at 0.15 < M < 0.55 GeV at 1 A GeV A+A at 0.15 < M < 0.55 GeV at 1 A GeV (consistent with HSD with „old SPA“)(consistent with HSD with „old SPA“)

Dileptons from A+A - UrQMD 2.2 (2007)Dileptons from A+A - UrQMD 2.2 (2007)

D. Schumacher, S. Vogel, M. Bleicher, D. Schumacher, S. Vogel, M. Bleicher, Acta Phys.Hung.Acta Phys.Hung. A27A27 (2006) (2006) 451451

NO bremsstrahlung in UrQMD 2.2NO bremsstrahlung in UrQMD 2.2

Dileptons from pp and pd - RQMD (Tübingen)Dileptons from pp and pd - RQMD (Tübingen)

C. Fuchs et al.C. Fuchs et al., , Phys. Rev. C67 025202(2003)Phys. Rev. C67 025202(2003)

• NONO bremsstrahlung: missing yield bremsstrahlung: missing yield for p+d at for p+d at 0.15 < M < 0.55 GeV at ~1-1.5 A GeV 0.15 < M < 0.55 GeV at ~1-1.5 A GeV

Dileptons from A+A - RQMD (Tübingen)Dileptons from A+A - RQMD (Tübingen)

C. Fuchs et al.C. Fuchs et al., , Phys. Rev. C67 025202(2003)Phys. Rev. C67 025202(2003)

• NO bremsstrahlung in RQMDNO bremsstrahlung in RQMD

• too strong too strong Dalitz contribution Dalitz contribution (since no time integration?) (since no time integration?)

HADES - RQMD‘07HADES - RQMD‘07

DLS - RQMD‘03DLS - RQMD‘03

1 A GeV1 A GeV

Bremsstrahlung in IQMD (Nantes)Bremsstrahlung in IQMD (Nantes)M. Thomere, C. Hartnack, G. Wolf, J. Aichelin, PRC75 (2007) 064902M. Thomere, C. Hartnack, G. Wolf, J. Aichelin, PRC75 (2007) 064902

SPA implementation in IQMD (?): SPA implementation in IQMD (?): ee++ee- - production in production in each NN collisioneach NN collision (i.e. elastic and inelastic) !?(i.e. elastic and inelastic) !?

- differs from HSD and UrQMD’98 (only elastic NN collisions are counted!)- differs from HSD and UrQMD’98 (only elastic NN collisions are counted!)

HADES: C+C, 2 A GeVHADES: C+C, 2 A GeV

Bremsstrahlung in BRoBUU (Rossendorf)Bremsstrahlung in BRoBUU (Rossendorf)H.W. Barz, B. Kämpfer, Gy. Wolf, M. Zetenyi, nucl-th/0605036H.W. Barz, B. Kämpfer, Gy. Wolf, M. Zetenyi, nucl-th/0605036

SPA implementation in BRoBUU (?): SPA implementation in BRoBUU (?):

ee++ee- - production in production in each NN collisioneach NN collision (i.e. elastic and inelastic) !(i.e. elastic and inelastic) !

- similar to IQMD (Nantes)- similar to IQMD (Nantes)

Test in HSD:Test in HSD:bremsstrahlung production in NN collisions bremsstrahlung production in NN collisions

(only elastic vs. all)(only elastic vs. all)

0.0 0.2 0.4 0.6 0.8 1.010-8

10-7

10-6

10-5

10-4

10-3

10-2

Bremsstrahlung: HSD: elast. NN HSD-test: all NN Wolf: Nantes Wolf: Rossendorf

M [GeV/c2]

C+C, 2.0 A GeV, HADES

1/N

dN/d

M [

1/G

eV /c

2 ]

In HSD assume:In HSD assume: ee++ee- - productionproduction from „old“ SPA bremsstrahlung from „old“ SPA bremsstrahlung in each NN collisionin each NN collision (i.e. elastic and inelastic reactions)(i.e. elastic and inelastic reactions)=> => can reproduce the results by Gy. Wolfcan reproduce the results by Gy. Wolf et al., i.e. IQMD (Nantes) et al., i.e. IQMD (Nantes) and BRoBUU (Rossendorf) !and BRoBUU (Rossendorf) !

Summary: Bremsstrahlung in transport modelsSummary: Bremsstrahlung in transport models

Transport models give Transport models give similar resultssimilar results ONLYONLY with the same with the sameinitial input ! initial input !

=> => REQUESTS:REQUESTS:„„unification“ of the treatment of dilepton production in unification“ of the treatment of dilepton production in transport models:transport models: Similar cross sections for elementary channelsSimilar cross sections for elementary channels Time-integration method for dilepton production Time-integration method for dilepton production Off-shell treatment of broad resonancesOff-shell treatment of broad resonances

++Consistent microscopic calculations for eConsistent microscopic calculations for e++ee--

bremsstrahlung from NN and mN collisions!bremsstrahlung from NN and mN collisions!

We need:We need: clear separation of the individual contributions in a clear separation of the individual contributions in a form applicable in transport codes, e.g. many-dimensional matrix form applicable in transport codes, e.g. many-dimensional matrix (or parametrization) for (or parametrization) for dd/dMdydp/dMdydpT T (s,M,y,p(s,M,y,pT T ))

Summary Summary

HADES succeeded:HADES succeeded:the DLS puzzle is solved !the DLS puzzle is solved !

Outlook:Outlook: need new need new pppp and and pdpd data from HADES for a final check! data from HADES for a final check!