What transport theories do Problems with the input of transport

Hades dilepton data - can transport reproduce the HI data? - does a medium modify the spectra? What can we learn from the present data (and what remains unknown)

Dilepton production in pp and AAa challenge for transport and experimentJ. Aichelin, E. Bratkovskaya, M. Thomère , S. Vogel and M.Bleicher

What transport theories can do and what they cannot do

Transport theories study the time evolution of heavy ion reactions by following the (curved) trajectories of nucleons created by their mutual potential interactions and including their Fermi motionand collisions

They can model:- when and where a collisions takes place ( ) for given σ tot- whether the collisions are allowed (Pauli blocking)- the angular distribution (if dσ/dΩ is known)- the density and temperature at which a collision occurs

They can predict all observables

r ·p

¾=¼

BUT THEY CANNOT PREDICT THE ELEMENTARY CROSS SECTIONS

These are input quantities: either theory or experiment

What transport theories can do and what they cannot do

They are used to investigate

- Reactions which exist only in a medium (ΔN -> K+NΛ)- Medium properties of particles (ρ , K- , K+ ) and their cross

sections- Nuclear matter properties (EOS, momentum dependence of NN

potential)- Collective phenomena like in plane and elliptic flow, (hyper)nuclei

prod.

As far as dileptons as concerned: beautiful data + established transport (which reproduce the whole strangeness sector of HADES)

So why it is challenging to calculate dilepton production?

In the past it turned out that different results from transport theories are usually a consequence of

different input quantities (different parametrizations of unknown cross sections etc).

The complicated transport itself is well under control.

Dilepton predictions in transport pose a couple of problems already in pp the dilepton spectra is a superposition channel separation is experimentally difficult most of the channels little known for energies of interest (and each channels translates differently to HI)

for np channel very few data pd data only of limited use but HI have neutrons (bremsstrahlung)

So the challenge is to explain a very complicated exit channel without having sufficient knowledge about the simple ones.

Input of the transport theories:

from the energy under control ( pp @ 1.25 GeV)

to the realm of speculations (pp @ 3.5 GeV)

For pp at 1.25 GeV the situation isunder control:

single π production dominatesσinel is well known

π data compatible with isobarmodel (all π’s produced via Δ)

NN ->Δ ->NNπ

This energy is the cleanest for forstudying the Δ channel.

Butphase space limits the production of highmass Δ

Thus neither sensitive to ΓΔ nor to theelectromagnetic decay width dΓ/dM

pp reactions at 1.25 GeV

IQMD

HSD

π yield in pn is known butBremsstrahlungmore important than ΔDalitz above M >0.15 Little guidance fromdata

More essential:Tagged pd is NOT the same as pnEasy to verify:

is not equal to

pn reactions at 1.25 GeV

Diff. pn and pn(d) not explored neither theor. nor exp.

HSD

IQMD

HSD

Kinematic limitpdpn

pp reactions at 2.2 GeV Going up in energy the complications increase

several channels contribute (M<0.6 GeV:Δ,η, bremsstrahlung) for most of them only limited experimental information available

Here I discuss the 2 dominant channels : Δ and η

Between 1.5-2 GeV: two π production starts to dominate origin of π’s and hence Δ production rather unknown most recent data: Celsius/WASA, theory: Oset group

PLB679 (09) 30PLB695 (11) 115NPA633(98) 519

Below T= 1.5dominantly ΔΔ

but also contributions from

N*

and

higher mass Δ

above T=1.5 GeVunknown land

10

η production I:

Excess energy in CC

No data for np

pnη non trivial (N* and direct) and not known(Using CC η TAPS data is of limited use:Fermi, absorpt.)

Excess energy distr . in CC

data

11

In momentum space the situation is even more complex (and more informative)At T=2.85 GeV η is produced by

30% in pp ppη accordingto 3 body phase space

70% in pp N*(1535)+pcollision in the decay of theN*(1535)

This is clearly visible in the momentum spectrum of η’s

At other energies repartition unknown

Phase space

Phase spaceandN*(1535) decay

Presently only IQMD includes this.Very important for HI: Resonance contribution differs from pp due to finite lifetime (reabsorption).

PRC69,064003

Hades Collaboration Meeting Cyprus, Nov 2007 12

η production III: No quantitative theory available (coupling to N*’s) Every transport theory has a different parameterization (2 or 3 body , different pn extrapolations)Different results (but in the error bars for the yield )

World data

σ(np η) = σ(pp η)BR=BR/10

σ(np η) = 2 σ(pp η)

pp reactions for T > 2.2 GeVrealm of speculations:- No theory available- No measurements of exclusive channels available

Not even right degrees of freedom are knownStill hadronic (n-dim phase space) or already string (longitudinal phase space)? Only 2 possibilities:

either- Fit pp - extrapolate to pn- including your imagination about resonance (string) production- then predict pA

orWait for better (Hades) datawhich may limit the almost absolute freedom.

No solid information -> input of transport models can differ wildly and sodo the results for pA and HI reactions.

HSD

Heavy Ion reactions

seen by the three transport approaches

To understand heavy ion reactions

we have to explore the uncertainties imposed by theelementary reaction input

We can profite from the fact that in ratios of crosssections for different systems most of the uncertainties drop out (determination of the EOS)

Problem: elementary data and HI data are not taken at the same energy

-> we have first to assure to reproduce the data andthen extract the physics from calculations at the same energy.

Same pn bremsstrahlungparametrization

HSD & IQMD: similar CC spectra at 1 AGeV (dilepton spectra was even predicted)- Input based on experiments and - HI dynamics (not trivial) controlled by many HI data analyzed by HSD and IQMD

Heavy Ions around 1 AGeV

HSD IQMD

IQMDHSD

No bremsstrahlung

All 3 well tested transport models

HSD, IQMD, UrQMD

agree on first glance with the data But a detailed look reveals differences:UrQMD:too few η, too many ρ, no bremsstrahlung

IQMD: too many ω (σ(np->ω)=5σ(pp->ω)

Heavy Ions around 2 AGeV

IQMD

HSDUrQMD

HSD

IQMDAt 2 GeV C+C same observation

both approaches agree well withdata

however

channel decomposition not identical

Sum over different channelswashes out the differences

What reveal the data about the medium?

Best access: RAA : HI results divided by scaled NN Complex task: we follow exactly the exp analysis

Fermi motion difference p(d) and pn

Ratio compatible with 1for M < .45

ratio around 2For .12 < M < .325

HSD

Ratio AA/NN >1 if E/N the sameeven for CC 2AGeV/ NN 1.25 GeV

Only when applying (exp) 1D –transformation transport results compatible with 1

ratio ArKCl/NN > CC/NN Results of different theories in between error bars

HSD

IQMD HSD

In medium enhancement surprising?

Not really !!

Bremsstrahlung ~ number of pn collisions -> ratio >1 final π multiplicity ~ number of participantsbut not ~ number of produced Δ

and each Δ can emit dileptons

enhancement increases with mass for Au+Au reactions ≈ 4!!

but little with energy.

Bremsstrahlung

Δ - Dalitz

Bass PhD thesis 1997: long N -> Δ -> π -> Δ -> π -> Δ ->…cycle

Au+Au1 AGeV

Only 20 % of the produced Δ create a final state π but allproduce dileptons

Strong enhancement of thedilepton yield in AA

Spectral fct electrom. decay width

identical

Is this observation robust?

against modifications of ΓΔ

against modification of dΓ/dM

The final dilepton spectra is given by:

But phase space suppresses the differences in HI reactions at SIS energies

Δ spectral functionHSD: MonitzUrQMD: Bass

The different decay widths give different dilepton spectra for MΔ ≠ MΔ Pole

HSD,IQMD,URQMD: Wolf param.

different ΓΔ give similar spectra

different dΓ/dM give different spectra

ΓΔ of spectral fct of decay width cancel

changes of the electromagn decay width are almost invisible in the total yield.

What’s about ratios?

… but Δ Dalitz is only one of the decay channels

HSD

HSD with Wolf and Krivoruchenkoelectromag. decay widthyields similar results for ratio

HSD and IQMD use differentΔ widths.

In medium enhancement also notvery different

In medium enhancement doesdoes little depend on the explicitform of ΓΔ and dΓ/dM

Present data do not allow for fixing the electrom. form factor

IQMD

HSD

At low energy Dileptons from Δ are a prominant channel but phase space limits the contribution of high mass Δ ->insensitive to Wolf/ Krivoruchenko, insensitive to ΓΔ

At higher energies: High mass Δ -> yield differs for Wolf/ Krivoruchenko but dileptons from Δ are not a prominant channel -> Influence of electrom. FF on the total yield is small.

So it will be difficult to use dileptons to nail down the Δ properties in detail

What HI tell us about ΓΔ and dΓ/dM ?

Conclusions

HADES dilepton data in AA reveal for the first time thethe existence of the N -> Δ -> π -> Δ -> π -> Δ ->.. chain

Results on dileptons of transport models only modestly sensitive to input quantities like ΓΔ and dΓ/dM.

To discover more from the data we need elementary cross sections for np -> η, ω, Δ, bremsstrahlung

We are in a very interesting energy domain: - transition from hadrons to quarks as degrees of freedom.- controlled study of vector mesons in matter