Transcript Extending the Bertini Cascade Model to Kaons

Extending the Bertini Cascade
Model to Kaons
Dennis H. Wright (SLAC)
Monte Carlo 2005
17-21 April 2005
Outline
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The Bertini cascade vs. LEP model
Extending the Bertini model to kaons
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cross sections
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final state generation
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intra-nuclear propagation
Validation
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quasi-elastic scattering
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strangeness exchange
Conclusions and Plans
Motivation
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Propagation of low and medium energy particles
– 5 GeV) is important for:
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validating medium energy experiments now in progress
calorimetry in planned high energy experiments
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comprise most of the hadronic shower
treated by 3 Geant4 models
Traditionally, p, n and p have received most of the
attention at these energies:
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(0
Kaons, hyperons and anti-particles are of interest too
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only one Geant4 model handles them
more accurate alternative required
Bertini Cascade vs. Low Energy
Parameterized Model
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Low Energy Parameterized Model (LEP)
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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
Bertini Cascade Model
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currently handles only p, n, p, 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)
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Model uses free-space cross sections for projectiles and
cascade particles interacting within nucleus =>
parameterize existing data
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Large amount of (K+,p) (K+,n) (K-,p) (K-,n) data
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But what about K0 and anti-K0 ?
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no data
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use isospin to get cross sections from charged kaon data =>
sK0p = sK+n , sK0bar n = sK-p
For interaction of cascade-generated particles, also need
(L,p) (L,n) (S,p) ......
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a little data for these
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use isospin, strangeness, charge conservation to fill in
Extending the Bertini Cascade:
Cross Sections (2)
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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)
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For each interaction type (K+,p), (S+,n), ... , the model keeps
a list of final state channels:
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store multiplicity and particle type
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angular distibution parameters
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all functions of incident energy
Un-modified model handles up to 6-body final states
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valid up to 10 GeV
Extended model handles up to 7-body final states
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valid up to ~15 GeV
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includes kaons and lowest mass hyperons
Extending the Bertini Cascade:
Final State Generation (2)
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Angular distributions
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lots of data for two-body final states below 3 GeV =>
parameterize as function of incident energy
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for > 2-body, use phase space calculation
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above 3 GeV, everything is forward peaked, parameterize
using exponential decay
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luckily, more than one interaction occurs in cascade =>
distributions are smeared and precise data are not required
Momentum distributions
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some data for 3-body final states
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otherwise use phase space calculation
Extending the Bertini Cascade:
Intra-nuclear Propagation
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Model propagates particles from the final state of the
elementary interaction to the site of the next interaction
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requires a knowledge of the nuclear potential for each
particle type
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current model uses a detailed 3D model of the nucleus
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p, n potentials well-known, pion potential less well-known
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potentials for strange particles almost unknown
Model includes other propagation features:
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Pauli blocking for nucleons
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nucleon-nucleon correlations (pion absorption)
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kaon absorption not yet included
Validation
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Quasi-elastic K+ scattering
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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
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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
Strangeness exchange (K- , p-)
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:
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Comparisons to LEP model are not shown because:
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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
Strangeness Exchange:
0.9 GeV/c (K-, p-) on Ca
Strangeness Exchange:
0.9 GeV/c (K- , p-) on S
Strangeness Exchange:
0.9 GeV/c (K- , p-) on O
Strangeness Exchange:
0.9 GeV/c (K- , p-) on C
Strangeness Exchange:
0.9 GeV/c (K-, p-) on Be
Conclusions:
K+ Quasi-elastic Scattering
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For all nuclei tested, Bertini cascade is clearly better than
LEP at < 2 GeV/c
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LEP removes kaons, Bertini conserves them
Bertini reproduces energy of quasi-elastic peak
Some drawbacks:
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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
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For all nuclei tested at 0.9 GeV/c Bertini cascade is
again better than LEP
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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:
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for light nuclei Bertini does not reproduce the energy of
the QE peak
● better kaon-nuclear potentials might fix this
Plans for Future Development
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Near term
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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 K0L and L
Longer term
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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