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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 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 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 limit
pdpn
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