Strangeness @ GSI Seen by transport models

1. Strangeness @ GSI Seen by transport models Christoph Hartnack & Jörg Aichelin Subatech Nantes Outline: • Comparison of transport models • K+&K- production and interaction of strange particles in matter • Comparision to data: yields, spectra, T, v2

2. Subthreshold kaon production • Production of kaons at energies below the kinetic threshold for K production in elementary pp collisions RARE! • Fermi momenta may contribute for obtaining the needed energy • Multistep processes can cumulate the energy needed for kaon production • Importance of resonances (especially the D) for storing energy • Short livetime of resonance favors early production at high densities • Sensitivity to in-medium effects and nuclear equation of state

3. Transport models: real vs virtual propagation • Real propagation: conserves event characteristics • Virtual propagation: allows for high stat. • UrQMD: real prop., creation of strangeness via resonances • IQMD, HSD, QMD, …: virtual propagation, direct production of strangeness in 2,3,4body collisions M. Bleicher et al.

4. Transport models: different ingredients E.E.Kolomeitsev et al. • Differences in unknown production cross sections • Differences in delta lifetimes, potentials etc Need of more experimental input for elementary reactions of B+B &M+B

5. … but still allowing conclusions • Hint on the existence of an optical KN potential Ch. Fuchs et al

6. In medium effects on kaons in IQMD • 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

7. K- production dominated by strangeness exchange Kaos data: F. Uhlig et al +BY +pY BB+pB+pY+BY +pB BB Direct channels BB, pB enhanced by K- potential, similar for exchange channels pY+BY. The K+ potential penalizes hyperon production and compensates in the dominant channels pY+BY.

8. Time-evolution & kaon production 0fm/c 4fm/c 8fm/c Central cell ’’T’’ 12fm/c 16fm/c 20fm/c K+: early, multistep induced product. when baryon density is highestK-: prod. later when pion density is highest, strangeness exchange

9. High density: high collision probability Rescattering heats the kaons: saturation of T (very high NC: downcooling source) Afterwards: potential push(more coll → later emitted → less push) K+ max prod at t=8fm/c

10. Spectra & temperatures of K+ IQMD (above, only with pot) and HSD (below) results are in good agreement with KaoS data

11. Spectra: slopes dominated by KN-rescattering Rescatteringpotential Collision number K+ K- K+ rescatter Strong enhancement of the slope from initial to final mom. Slight effects: enhancement (K+) or reduction (K-) High K+ rescattering less K- rescattering

12. Temperatures K+ and K- heated up by collisions with expanding nuclear medium. K- absorption acts as energy filter Finally the K+ get pushed out while the K- are drawn backwards by the KN potential KaoS A.Förster et al. PRC75(2007) 024906

13. Low energy K0: potential penalty Difference of spectra at low pcm due topotential penalty FOPI data KN POT NO POT FOPI can/could/might/should/hassee(n) the K+ N potential

14. Azimuthal distributions Azimuthal distributions are effected by rescattering, by optical potential and the emission time. 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+2v1 cos(f) + 2 v2cos(2f)) KaoS and FOPI see opposite signs of v2 for K+ and K- Ni+Ni 1.93 GeV, F. Uhlig et al, KaoS

15. Excitation function of v2 for K+ Rescattering and optical potentialcontribute to the v2 of kaons. The effects of the optical potential become dominant with respect to theeffect of rescatteringwhen 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. Data: KaoS

16. Time evolution for K+ & K- K+ K- Potential enhances v2 of kaons. The earlier the emission the stronger the effect The early K- show a squeeze which vanishes for the K- emitted lately

17. pT dependence of v2 for K+ & K- IQMD yields too strong v2 of K+ with KN potential IQMD has problems with the change of the sign of v2 of K-

18. FOPIs v1 & v2 for K+ and K- Potential acts different on K+&K- rescattering effect compensated? Indications on the existence of a KN-potential K- K+

19. The nuclear eos from Au/C ratios Data: Ch.Sturm et al. QMD: Ch. Fuchs IQMD supports this Ratio(K) at 0.8GeV: IQMD supports this KaoS data support soft eos soft hard

20. Soft eos from Apart scaling factor a Scaling of NK(Apart): NK=N0×(Apart)a The relation between the compression modulus and a is monotonously falling. KaoS data (Förster et al.) favor a value below 240 MeV, i.e. a soft eos. KaoS:Förster et al. soft hard PRL 96 (2006) 012302

21. Energy dependence of the system size systematics Soft eos confirmed System size Apart in Au+Au agrees with that

22. Conclusions on Kaon data • K+ yields: hints to KN potential, but uncertainties in input • Scaling of K+ yields with ASystem, Apart: soft eos • K- yield: dominance pY, BY, related to K+, uncert.in input • T(K+) dominated by rescattering, effected by emission time • T(K-) rescattering+absorption, emission time later • Difference of slopes: hints to KN potential • Low energy K0: strong sensitivity to KN potential • Polar distribution: dominated by rescattering • v2(K+) rescattering, KN potential pushes to more negative values • v2(K-) rescatt., emission time, KN pot.pushes towards more positive values • Difference of flow K+&K- reduces influence of resc.&enhances inf. KNpot • v1of K+&K- visible influence of KN potential