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 AA a challenge for transport and experiment J. 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 motion and 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 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 ( 1.25 GeV) to the realm of speculations 3.5 GeV)

For pp at 1.25 GeV the situation is under control: single π production dominates σ inel is well known π data compatible with isobar model (all π’s produced via Δ) NN ->Δ ->NNπ This energy is the cleanest for for studying the Δ channel. But phase space limits the production of high mass Δ Thus neither sensitive to Γ Δ nor to the electromagnetic decay width dΓ/dM pp reactions at 1.25 GeV IQMD HSD

π yield in pn is known but Bremsstrahlung more important than Δ Dalitz above M >0.15 Little guidance from data More essential: Tagged pd is NOT the same as pn Easy 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 limit pd pn

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 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) 30 PLB695 (11) 115 NPA633(98) 519 Below T= 1.5 dominantly ΔΔ but also contributions from N * and higher mass Δ above T=1.5 GeV unknown land

10 η production I: Excess energy in CC No data for np pn  η 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 according to 3 body phase space 70% in pp  N * (1535)+p collision in the decay of the N * (1535) This is clearly visible in the momentum spectrum of η’s At other energies repartition unknown Phase space and N * (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 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 GeV realm of speculations: - No theory available - No measurements of exclusive channels available Not even right degrees of freedom are known Still 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 or Wait for better (Hades) data which may limit the almost absolute freedom. No solid information -> input of transport models can differ wildly and so do 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 the elementary reaction input We can profite from the fact that in ratios of cross sections 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 and then extract the physics from calculations at the same energy.

Same pn bremsstrahlung parametrization 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 HSD

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 HSD UrQMD

HSD IQMD At 2 GeV C+C same observation both approaches agree well with data however channel decomposition not identical Sum over different channels washes out the differences

What reveal the data about the medium?

Best access: R AA : HI results divided by scaled NN Complex task : we follow exactly the exp analysis Fermi motion difference p(d) and pn Ratio compatible with 1 for M <.45 ratio around 2 For.12 < M <.325 HSD

Ratio AA/NN >1 if E/N the same even 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 IQMDHSD

In medium enhancement surprising ? Not really !! Bremsstrahlung ~ number of pn collisions -> ratio >1 final π multiplicity ~ number of participants but 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+Au 1 AGeV Only 20 % of the produced Δ create a final state π but all produce dileptons Strong enhancement of the dilepton yield in AA

Spectral fct electrom. decay width identical Is this observation robust? against modifications of Γ Δ 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 function HSD: Monitz UrQMD: Bass

The different decay widths give different dilepton spectra for M Δ ≠ M Δ Pole HSD,IQMD,URQMD: Wolf param. different Γ Δ give similar spectra different dΓ/dM give different spectra Γ Δ 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 Krivoruchenko electromag. decay width yields similar results for ratio HSD and IQMD use different Δ widths. In medium enhancement also not very different In medium enhancement does does little depend on the explicit form of Γ Δ 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 Γ Δ 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 Γ Δ and dΓ/dM ?

Conclusions HADES dilepton data in AA reveal for the first time the the existence of the N -> Δ -> π -> Δ -> π -> Δ ->.. chain Results on dileptons of transport models only modestly sensitive to input quantities like Γ Δ 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