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Extending the Bertini Cascade Model to Kaons

Dennis H. Wright (SLAC) Monte Carlo 2005 17-21 April 2005. Extending the Bertini Cascade Model to Kaons. Outline. The Bertini cascade vs. LEP model Extending the Bertini model to kaons cross sections final state generation

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Extending the Bertini Cascade Model to Kaons

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

  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 p have received most of the attention at these energies: • comprisemostofthehadronicshower • treatedby 3 Geant4 models • Kaons, hyperons and anti-particles are of interest too • onlyoneGeant4 model handles them • more accurate alternative required

  4. Bertini Cascade vs. Low Energy Parameterized Model • LowEnergyParameterizedModel (LEP) • handles p, n, p, 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 • BertiniCascadeModel • currentlyhandlesonly p, n, p, butstraightforwardtoextendtokaons,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 K0 and anti-K0 ? • nodata • useisospintogetcrosssectionsfromchargedkaondata=>sK0p=sK+n , sK0barn=sK-p • For interaction of cascade-generated particles, also need (L,p) (L,n) (S,p) ...... • alittle data forthese • useisospin,strangeness,chargeconservationtofillin

  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) • Foreachinteractiontype(K+,p),(S+,n),...,themodelkeepsalistoffinalstatechannels: • store multiplicity and particle type • angular distibution parameters • all functions of incident energy • Un-modifiedmodelhandlesupto6-bodyfinalstates • validupto10GeV • Extendedmodelhandlesupto7-bodyfinalstates • validupto ~15GeV • includeskaonsandlowestmasshyperons • doesnotincluderesonances

  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-elasticK+scattering • Kormanyos et al., 1995 • Targets: D, C, Ca, Pb • 0.7 GeV/c incident K+ , detect K+ at 24o and 430 • Sensitive to Fermi motion, depth of potential for kaons • Strangeness exchange (K- , p-) • Bruckner et al., 1975, 1976 • Targets: Be, C, O, S, Ca • 0.9 GeV/c incident K- , detect 0o 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: • ComparisonstoLEPmodelarenotshownbecause: • no final state K+ produced at these energies • none seen until incident momentum exceeds 2 GeV/c • model converts K+ to K0L , K0S and pions

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

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

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

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

  20. Strangeness Exchange: 0.9 GeV/c (K-, p-) 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 • Nearterm • complete theparameterizationofmomentumandangulardistributionsforstrangeparticlefinalstates • tunekaon-andhyperon-nuclearpotentialdepthstobetterreproducedata • testtheextendedmodelfor incident K0L and L • 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

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