1. Extending the Bertini Cascade Model to Kaons Dennis H. Wright (SLAC) Monte Carlo 2005 17-21 April 2005

2. Outline ● The Bertini cascade vs. LEP model ● Extending the Bertini model to kaons – cross sections – final state generation – intra-nuclear propagation ● Validation – quasi-elastic scattering – strangeness exchange ● Conclusions and Plans

3. Motivation ● Propagation of low and medium energy particles (0 – 5 GeV) is important for: – validating medium energy experiments now in progress – calorimetry in planned high energy experiments ● Traditionally, p, n and  have received most of the attention at these energies: – comprise most of the hadronic shower – treated by 3 Geant4 models ● Kaons, hyperons and anti-particles are of interest too – only one Geant4 model handles them – more accurate alternative required

4. Bertini Cascade vs. Low Energy Parameterized Model ● Low Energy Parameterized Model (LEP) – handles p, n, , K, hyperons, anti-particles – derived from GHEISHA and not especially suited for low energies – no intra-nuclear physics included – quantum numbers conserved on average over events ● Bertini Cascade Model – currently handles only p, n, , but straightforward to extend to kaons, hyperons – appropriate for E < 10 GeV, validated at ~1 GeV and below – intra-nuclear cascade included – quantum numbers conserved event-by-event

5. Extending the Bertini Cascade: Cross Sections (1) ● Model uses free-space cross sections for projectiles and cascade particles interacting within nucleus => parameterize existing data ● Large amount of (K +,p) (K +,n) (K -,p) (K -,n) data ● But what about K 0 and anti-K 0 ? – no data – use isospin to get cross sections from charged kaon data =>   p =  K +n,  K0bar n      p ● For interaction of cascade-generated particles, also need ( ,p) ,n) ,p)  – a little data for these – use isospin, strangeness, charge conservation to fill in

6. Extending the Bertini Cascade: Cross Sections (2) ● All data taken from CERN particle reaction catalogs ● Data for all kaon and hyperon-induced reactions thin out at about 15 GeV => inherent limit of the model ● At the higher energies (>5 GeV) use total inelastic cross section data to partition cross section strength among various channels where it is not known

7. Extending the Bertini Cascade: Final State Generation (1) ● For each interaction type (K +,p), (  +,n),..., the model keeps a list of final state channels: – store multiplicity and particle type – angular distibution parameters – all functions of incident energy ● Un-modified model handles up to 6-body final states – valid up to 10 GeV ● Extended model handles up to 7-body final states – valid up to ~15 GeV – includes kaons and lowest mass hyperons – does not include resonances

8. Extending the Bertini Cascade: Final State Generation (2) ● Angular distributions – lots of data for two-body final states below 3 GeV => parameterize as function of incident energy – for > 2-body, use phase space calculation – above 3 GeV, everything is forward peaked, parameterize using exponential decay – luckily, more than one interaction occurs in cascade => distributions are smeared and precise data are not required ● Momentum distributions – some data for 3-body final states – otherwise use phase space calculation

9. Extending the Bertini Cascade: Intra-nuclear Propagation ● Model propagates particles from the final state of the elementary interaction to the site of the next interaction – requires a knowledge of the nuclear potential for each particle type – current model uses a detailed 3D model of the nucleus – p, n potentials well-known, pion potential less well-known – potentials for strange particles almost unknown ● Model includes other propagation features: – Pauli blocking for nucleons – nucleon-nucleon correlations (pion absorption) – kaon absorption not yet included

10. Validation ● Quasi-elastic K + scattering – Kormanyos et al., 1995 – Targets: D, C, Ca, Pb – 0.7 GeV/c incident K +, detect K + at 24 o and 43 0 – Sensitive to Fermi motion, depth of potential for kaons ● Strangeness exchange (K -,    – Bruckner et al., 1975, 1976 – Targets: Be, C, O, S, Ca – 0.9 GeV/c incident K -, detect 0 o pions – Sensitive to nuclear potential seen by kaons, hyperons

11. Qausi-elastic: 705 MeV/c K+ on Pb

12. Quasi-elastic: 705 MeV/c K+ on Ca

13. Qausi-elastic: 705 MeV/c K+ on C

14. Quasi-elastic: 705 MeV/c K+ on D

15. Note on previous 4 slides: ● Comparisons to LEP model are not shown because: – no final state K + produced at these energies – none seen until incident momentum exceeds 2 GeV/c – model converts K + to K 0 L, K 0 S and pions

16. Strangeness Exchange: 0.9 GeV/c (K -,  - ) on Ca

17. Strangeness Exchange: 0.9 GeV/c (K -,  - ) on S

18. Strangeness Exchange: 0.9 GeV/c (K -,  - ) on O

19. Strangeness Exchange: 0.9 GeV/c (K -,   ) on C

20. Strangeness Exchange: 0.9 GeV/c (K -,  - ) on Be

21. Conclusions: K + Quasi-elastic Scattering ● For all nuclei tested, Bertini cascade is clearly better than LEP at < 2 GeV/c – LEP removes kaons, Bertini conserves them – Bertini reproduces energy of quasi-elastic peak ● Some drawbacks: – Bertini under-estimates the width of the QE peak ● better kaon-nuclear potentials might fix this – overall normalization is about 30% low for all targets ● this could be due to uncertainties in the total inelastic cross section, which itself is parameterized

22. Conclusions: Strangeness Exchange ● For all nuclei tested at 0.9 GeV/c Bertini cascade is again better than LEP – LEP is not so bad for heavy nuclei, but Bertini is better – for light nuclei, only Bertini reproduces the quasi-elastic peak – for all targets, Bertini reproduces the normalization fairly well => total inelastic cross section at 0.9 GeV/c is OK ● Some drawbacks: – for light nuclei Bertini does not reproduce the energy of the QE peak ● better kaon-nuclear potentials might fix this

23. Plans for Future Development ● Near term – complete the parameterization of momentum and angular distributions for strange particle final states – tune kaon- and hyperon-nuclear potential depths to better reproduce data – test the extended model for incident K 0 L and  ● Longer term – add strange pair production to p-, n- and pion-induced reactions – extend validity of p-, n- and pion-induced reactions to 15 GeV – add anti-proton and anti-neutron induced reactions