Extending the Bertini Cascade Model to Kaons Dennis H. Wright (SLAC) Monte Carlo 2005 17-21 April...
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Transcript of Extending the Bertini Cascade Model to Kaons Dennis H. Wright (SLAC) Monte Carlo 2005 17-21 April...
Extending the Bertini Cascade Model to Kaons
Dennis H. Wright (SLAC)Monte Carlo 200517-21 April 2005
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
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
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
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 ?
– 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
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
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
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
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
Validation
● Quasi-elastic K+ 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- ,
– 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
Qausi-elastic: 705 MeV/c K+ on Pb
Quasi-elastic: 705 MeV/c K+ on Ca
Qausi-elastic: 705 MeV/c K+ on C
Quasi-elastic: 705 MeV/c K+ on D
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 K0
L , K0
S and pions
Strangeness Exchange: 0.9 GeV/c (K-, -) on Ca
Strangeness Exchange: 0.9 GeV/c (K- , -) on S
Strangeness Exchange: 0.9 GeV/c (K- , -) on O
Strangeness Exchange: 0.9 GeV/c (K- , ) on C
Strangeness Exchange: 0.9 GeV/c (K-, -) on Be
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
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
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 K0
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