Christoph Hartnack and Jörg AichelinSubatech (Ecole de Mines, CNRS/IN2P3, Université),

Nantes, FranceIn collaboration with

Arnaud Le Fevre and Yvonne Leifels, GSI Darmstadt

Helmut Oeschler, CERN

Strangeness production at threshold

and its interaction with nuclear matter

HypertritonsA marriage of fire and ice

Cold matter

Hot matter

IQMD and nuclear matter

Hot matter: strangeness, medium, eos

Hypernuclei in a simplified model

Sophisticated model, comparison w. FOPI

Recent results of HypHI

Keywords: Marriage, Fire, Ice, Strangeness, Clusters

Strangeness

Spectator clustersA(1-2 AGeV)+A

-Semiclassical dynamical N-body model - with quantum features -based on 2- and 3-body interactions

-- Microscopic calculation of heavy ion collisions on an event-by-event-basis

- includes N, Δ, π with isospin d.o.f.

-- strange particles treated virtually

Isospin-Quantum Molecular Dynamics model

Allows for a « photo » of the high density phase and for a look inside …

Our tool: IQMD

Definition of the potentials

Bethe Weizsaecker –mass formula:

Volume term +Surface term +Coulomb term +symmetry term

(+pairing term not included)

2 and 3 body interactions

Λ:Only Skyrme *2/3

(nucl. eos) (asy- eos)

(no equilibrium required)

The static part ( our « eos »)

3 parameters, 2 ground state condit.

1 remaining d.o.f.: compression mod.

Artificial link between curverture at ground state and high density behaviour.

Compression modulus K>170 MeV

Problems of causality for high densities ρ> 5-7 ρ0

Caution when extrapolating to high densities

The eos in IQMDafter the convolution of the Skyrme type potentials supplemented by momentum dependent interactions (mdi) for infinite saturated nuclear matter at equilibrium

hard

soft

Heavy ion collisions at around 2 AGeV (lab)Only slightly above threshold.

Data from HADES compared to IQMDUp to now a success story for the strangeness sector

Which temperature has our ''hot matter''? Inside the reaction zone temperatures of about 90 MeV

Ar(1.8 GeV)+KCl

Subthreshold kaon production•Production of kaons at energies below the kinetic threshold for K production in elementary pp collisions

•Fermi momenta may contribute in energy

•Multistep processes can cumulate the energy needed for kaon production

•Importance of resonances (especially the ∆) for storing energy

•Short livetime of resonance favors early production at high densities

•Sensitivity to in-medium effects and nuclear equation of state

High density: medium effectsOptical potential: repulsive for K+, enhances its « mass »

Several parametrizations exist & are implemented

Use of Schaffner-Bielich RMF results as standard

Optical potential influences K+ propagation but changes also the production threshold : penalty at high density

Reduction of the total yield: counter-effect to eos.

Many combinations are possible -Many channels have to be implemented

•Each channel contains isospin subdivisions

•Only few channels (like pppLK+) are measured by the experiment (even incomplete infos)

•Significant incertainties from parametrization of unknown channels or isospin subdivisions

Let us skip a lot of analysis

Experimental results from KAOS@GSI confronted to IQMD

Kaon yields (and thus also hyperon yields) mainly depend on :- Nuclear equation of state (soft eos yields quite more kaons than a hard on)- Kaon-nucleon optical potential (reduces yield due to penalty on production) - Unknown production cross sections including resonances (especially NΔ)This has mostly been fixed .... however still incertainties are existing

K+

Lessons from K+:One needs to do full systematics for learning something eqs. of state: rather soft KN potentials: indications in the range 20-40 MeV rescattering is important for spectra yields strongly influenced by unknown cross sections still observables to be explained (anisotropy v2(pT) …)

-> Let us now attack the hyperons They are strongly related to kaon production since the BB → NΛK channels are dominating since they cost less energy

Recent analysis of FOPI data indicate interesting physics

Thus the KN-potential effects the hyperons…

All incertainties to K+ yields apply also to the hyperons (and thus tΛ ).

Absolute yields not really conclusive, but spectra quite comparable.

For hypertritons tΛ we will use the ratio tΛ/Λ instead of absolute yields.

Simplified fragmentation modelThe particles propagate very long time under the influence of

the given potentials (2/3 Skyrme for hyperons).

Finally we look for particles remaining nearby in phase space.

Coalescence parameter defined by the range of the interaction.

Yields similar yields than the refined SACA calculations (used later) but allows for much higher statistics.

Different phase space regions

• Hyperons are produced preferentially at midrapidity but the formation of fragments can better be done in the spectator matter.

ProjectileTarget

ProjectileTarget

Importance of Λ rescattering

• Rescattering changes rapidity distribution of hyperons• This effects the overlap of hyperons and spectator matter • Strong influence on the yields of the hypertritons

Larger hypernuclei

Λt

n-Λ p-Λ

Λd

Λ4He

Λ5He

Λ6He

Soft EOSwith m.d.i.no Kaon pot.

Lots of rescattering for getting large hypernuclei

The hyperons have to « cool down » by collisions in order to really enter into larger fragmentsThis may take quite a long time and happens at low densitiesThat time motivated the freeze-out time of sophisticated model

Building hyperclusters: refined fragmentation model

• Use simulated annealing clusterisation algorithm (SACA, Aichelin et al, Puri et al, Le Fevre et al) succesfully working for fragmentation description applying the shown interactions (optionally pairing)

• Unfortunately very time consuming algorithm • Extension to inclusion of hyperons using Y-N

potentials (A. Le Fevre et al) V(Λ)=2/3VSkyrme(nuc)• Application of experimental detection constraints

from FOPI @ GSI• Preliminary results from A. Le Fevre, GSI,

using a freeze-out time of 20 fm/c • FOPI results are also still preliminary

2) Take randomly 1 nucleonout of one fragment

E=E1kin +E2

kin +V1+V2

3) Add it randomly to anotherfragment

E’=E1’kin +E2’

kin +V1’+V2’

If E’ < E take the new configurationIf E’ > E take the old with a probability depending on E’-ERepeat this procedure very many times... It leads automatically to the most bound configuration.

2 steps: 1) Pre-select good «candidates» for fragments according to proximity criteria: real space coalescence = Minimum Spanning Tree (MST) procedure.

Simulated Annealing Procedure: PLB301:328,1993; later called SACA.Our clusterisation algorithm

Arnaud Le Fèvre (GSI Helmholtzzentrum für Schwerionenforschung - Darmstadt) - FOPI Coll. Meeting 2012 - GSI

What the experiment does What the experiment does

Λ

np

Λt

detected decay :

3He + π-

pt/mFOPI Coll.Y. Zhang, Heidelberg

Ni+Ni @ 1.91 A.GeV

Preliminary

yLab

targetmid-rapidity

A

BExcess over combinatorial background only in region A

In one word : a tough task

Arnaud Le Fèvre (GSI Helmholtzzentrum für Schwerionenforschung - Darmstadt) - FOPI Coll. Meeting 2012 - GSI

Strong phase space constraintsStrong phase space constraints

Λ

np

ΛtHypertriton / Lambda ratiosPreliminary results of A Le Fevre, FOPI, GSI

FOPI B

Two different phase space regions

FOPI A

Sometimes we hit sometimes we miss... • Strong influence of rapidity

distribution, impact parameter etc

• Influences of rescattering and hyperon-nucleon potentials

• Preliminary FOPI data in

discussion, being re-analysed • Results of simplified

and sophisticated model are in the same range using same parameters.

• Triggered by the Λ spectra we modifyour rescattering cross section, some enhancement

A

B

FOPI B

HypHI results coming soon

IQMD gives the right magnitude of 3HΛ and 4HΛ yields and the right

relative ratio but too small yields

HypHI might see a large yield ofΛnn, which cannot be explained by IQMD, but there is still realm for discussion

(C. Rappolt et al, to be published)Vertex-recombination fromd π-, t π-, 3He π-, 4He π

IQMD+SACA : Li(2AGeV)+C

Conclusion• Kaons reveal interesting

properties of nuclear matter– Soft eos, optical potential

• Hyperons are related to kaon production– Yields related to effects on kaon yields– Spectra related to rescattering

• Hypertritons relate « hot » hyperons to « cold » fragmentation regions– Different initial phase space distributions– Crucial role of hyperon rescattering– In a good range but still a lot of things to explore

• Exciting times to come when FOPI and HypHI will publish definite results !

Hypertritons cinematically nearby the nucleons

• Rescattering already important for explaining hyperon flow • Resc. crucial for getting hyperons to the spectator matter

Last contact takes place at low densities

• Constituents of hypertritons may have seen high density phase • But the last interactions take place in the expansion phase

Kinematics of larger clusters

The hyperons align to the spectator matter : Large longitudinal component Small transversal component High flow : « The fragments go with the flow »

Novel Parametrisation

Anke parametrisation validated with ANKE data up to 25MeVbut decends to 0 while higher data advocate an asymptote of 12mb

Effect of parametrisation on transverse spectra quite small

Eos influences the kaon yields, but incertainties of cross sections larger than

eos effect

C+C

Au+AuσN∆Tsushima

σN∆=.75 σNN

However, the eoseffect vanishes for small A while

the cross section effect persists up to small A.

The solution: use ratios Au/CThis cancels many (also

exp.)uncertainties

RQMD: Ch. Fuchs

Data: KaoS @GSI

IQMD supports this(although IQMD and RQMD differ in absolute yields)

Different analysis yielding same conclusion :

The eos is soft !

ParticipantNumber and System Size

Spectra: slopes dominated by KN-rescattering

K+

K-

Rescattering potential

Strong enhancement of the slope from initial to final mom.

Slight effects: enhancement (K+) or reduction (K-)

K+ rescatter

Collision number

High K+ rescattering less K- rescattering

Normalized to pt > 450 MeV/cAbsolute normalization (b < 6 fm)Preliminary

HADES@GSI data 1.75 AGeV Ar + KCL

1.0 < α < 1.2KN-Potential is repulsive predicitons agree (almost) with exp

Wait for novel Au+Au @1.25 AGeV data

If the high energy part is dominated by rescattering