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