Properties of nuclear matter from subtheshold strangeness production Christoph Hartnack, Helmut Oeschler, Jörg Aichelin Subatech Nantes and TH Darmstadt Outline: ● Subthreshold production, optical potential ● Spectra, temperatures and KN rescattering ● Azimuthal distribution and the KN potential ● Scaling laws and the nuclear equation of state ● Conclusion Calculations performed with IQMD, a semiclassical, microscopic N-body model with quantum features for the description of HICs on an event-by-event basis

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

Time-evolution & kaon production K + : early, multistep induced product. when baryon density is highest K - : prod. later when pion density is highest, strangeness exchange 0fm/c 4fm/c 8fm/c 12fm/c 16fm/c 20fm/c

In medium effects on kaons KN-Rescattering, absorption for K - Optical potential: repulsive for K +, attractive for K - Penalizes K + production at high densities but favors K - production at high densities Effects yields but also dynamics Parametrization from Schaffner-Bielich RMF results

Au-data: Foerster et al, KaoS Ni-data: Uhlig et al., KaoS KN pot No Pot Can we reveal the KN potential from K + yields? Visible difference between calculations with and without KN potential on a log-scale. KN-pot yields less kaons, but incertainties on  induced cross sections discourage a preliminary conclusion.

K - production dominated by strangeness exchange BB +B+B +Y+Y +BY Direct channels BB,  B enhanced by K - potential, similar for exchange channels  Y+BY. The K + potential penalizes hyperon production and compensates in the dominant channels  Y+BY. BB+  B+  Y+BY

Spectra: slopes dominated by KN-rescattering K+K+ 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

Temperatures of K + IQMD results with KN- rescattering are in good agreement with KaoS data K + heated up by coll. with expanding nucl.medium K - show systematically lower temperatures. Reason: less rescattering, diff. potentials? KaoS A.Förster et al. PRC75(2007)

Azimuthal distributions Azimuthal distributions are effected by rescattering and by the optical potential. While the rescattering acts in the same direction for K + and K - the optical potential gives opposite effects for K + and K - Azimuthal distribution fitted with a (1+v 1 cos(  ) + 2 v 2 cos(2  )) KaoS and FOPI see opposite signs of v 2 for K + and K - Ni+Ni 1.93 GeV, F. Uhlig et al, KaoS

Excitation function of v 2 for K + Rescattering and optical potential are needed to describe the v 2 of kaons. The effects of the optical potential become dominant with respect to the effect of rescattering when going down in beam energy. This is in agreement with calculations of Li&Ko who found a strong potential effect for Au+Au 1 GeV/A.

Comparison of v 1 (y 0 ) to FOPI data Preliminary data from FOPI (Kim et al. ) favor an optical potential less strong than implemented by us

The original idea of measuring the eos Eos describes the energy needed to compress nuclear matter A hard eos requires more energy for a given density than a soft one For a given density and a given available energy a soft eos leaves more thermal energy to the system than a hard eos R.Stock: This thermal energy could be measured by regarding pion production

At which density can we measure the eos? Different densities are reached for hard and soft eos. A soft eos yields higher densities than a hard eos. The differences in compressional energy and thus in thermal energy become less. The pion number is not sensitive enough. Pions come out late due to reabsorption in dense matter Kaons might be an interesting probe. However the effects of the optical potential and incertainties of the cross section do not allow a direct measure of the eos from kaon yields.

The solution: ratios Au/C Data: Ch.Sturm et al. RQMD: Ch. Fuchs Robust against changes of cross sections, optical potential, Delta lifetimes, etc. KaoS data support soft eos IQMD supports this Symbols: KaoS data Lines IQMD

Au: central versus peripheral Different cross sections and potential parameters may change the global yield. However, the parameter  for the increase of the kaon yield N with the number A of participating nucleons (raising with centrality) N(K)=N 0 A  depends on the eos. central peripheral A soft eos yields higher values than a hard eos.

Determination of the eos from  soft hard The relation between the compression modulus and  is monotonously falling. KaoS data (Förster et al.) favor a value below 200 MeV, i.e. a soft eos. C.H. et al. PRL 96 (2006) KaoS:Förster et al. Same for Au/C ratio

Another scaling systematics: system size 2 independent observables ( centrality scaling and system size scaling) confirm soft eos System size, Kaos Data A part in Au+Au from KaoS agrees with that Scaling with system size in inclusive A+A events

Kaons and density isomers Could reveal density isomers by a sudden rise in the excitation function of kaons - KaoS might measure it Density isomers yield up to factors of 10 in K + production A 2 nd minimum would yield a sudden factor of 10 in the kaon yield MeV C.H. et al. PRL 72 (1994) 3767 Effect related to subthreshold prod.

A density isomer would have needed the strong raise indicated by the arrows. IQMD calculations using a KN optical potential and a soft eos are consistent with KaoS data on Au+Au and C+C of Sturm et al. For higher densities/beam energies we need other particles produced below threshold KaoS DATA: no isomer up to 3  0

Conclusions Kaon spectra reveal strong rescattering of kaons with the surrounding nuclear matter Comparison of flow variables supports the existence of KN optical potential Scaling laws of the kaon production claim strongly for a soft equation of state The KaoS measurements (which can be continued by eos data) contradict the existence of density isomers at moderate densities

Effect of the potential: penalty reimbursed Kaons with did not undergo collisions: No KN potential : final=initial Initial distributions show a difference of calculations with KN-pot and without pot at all energies. This is due to the penalty paid at the production. In the final state the kaons regain the paid penalty and the curves of both calculations become rather close Only at small energies a lack remains stemming from those kaons which failed to be produced due to the penalty.

KN collisions change the spectra Most kaons underwent many collisions before leaving. They show a significant enhancement of the slope. At the time before the freeze out of the kaons (about fm/c) the nucleonic system is still hot and expanding. The kaons carry the temperature of that expansion phase. initial

Comparison to data for K - Less rescattering for the K - yield smaller temperature than for K +

Comparison of spectra for K +

Temperature: centrality dependence

Temperature and collisions

Maxwellian Demon

Au+Au 1.5 GeV azimuthal distribution For Au+Au at 1.5 GeV we needed both potential and rescattering to reproduce the results of Foerster et al.

Influence on v 2 (p T ) at midrapidity Again opposite effect on K + an K - useful for balancing the effect of rescattering FOPI and KaoS see opposite signs of v 2 for K + and K -

V 2 :p T dependence

Polar distributions

Polar distribution: rescattering and potential

Excitation function of K +

A observation which is robust versus effects of production cross sections, KN-potential,  -lifetime  N  Tsushima  N  =.75  NN

Going down in beam energy A soft eos yields   1.4 at E=0.8 AGeV, a hard eos yields   1.2 Limits for lower E: no asymptotic yield for peripheral collisions

System size dependence E inc A soft eos obtains higher kaon yields for heavy systems KaoS: PRC in preparation

A mixture of both N C =0 has a visible fraction to the yield, shows a taller rapidity distribution and strongly negative flow. For N C >2 a positive flow and a wider y-distribution is observed

The potential shifts to negative flow N C =0: initial shadowing boosted by potential to strong neg. flow N C >2: initial bias, enhanced by scattering, reduced by potential Initial vs final Pot vs. NoPot

Final flow a superposition of different flows Initial flow: bias for having collisions or not Final flow: visible shift from the potential

Rescattering enhances potential effect For N C =0 the initial flow is inverted Rescattering adds up more positive flow