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The Weak Production of Hypernuclei

The Weak Production of Hypernuclei. D.D. van Niekerk (M.Sc. project) B.I.S. van der Ventel G.C. Hillhouse Department of Physics Stellenbosch University South Africa. Stellenbosch, South Africa. Outline. Motivation Our Model Formalism The Hadronic Vertex Kinematics

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The Weak Production of Hypernuclei

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  1. The Weak Production of Hypernuclei D.D. van Niekerk (M.Sc. project) B.I.S. van der Ventel G.C. Hillhouse Department of Physics Stellenbosch University South Africa

  2. Stellenbosch, South Africa

  3. Outline • Motivation • Our Model • Formalism • The Hadronic Vertex • Kinematics • The Transition Matrix • Leptonic Tensor • Hadronic Tensor • Constructing Wµ(Example) • Conclusion

  4. Motivation • Recent large scale interest in astrophysics and the role of neutrinos in stellar processes (i.e. supernovae) • Neutrino osscillations (changing of flavour) • BooNE / MiniBooNE (Fermilab) • J-PARC • Super-Kamiokande (50 GeV) • Nucleon decay postulated by supersymmetry • Hyperon and hypernuclei production form important part of neutrino-induced reaction cross sections

  5. Our Model • Based on relativistic Dirac equation • never been studied (nuclear process) • first attempt in a fully relativistic framework • Quasifree process (interaction takes place between neutrino and single bound nucleon) • Bound state wave functions are calculated using relativistic mean field formalism • Aim: • Obtain quantitive results that will give indication of nuclear model uncertainties • Provide theoretical basis for interpretation of experimental results

  6. Types of Reactions: • Charged Current (CC) (S = strangeness) • ΔS = 0 • ΔS = 1 • Neutral Current • ΔS = 0 • ΔS = 1 not observed

  7. Formalism

  8. bound hyperon Vertex Approximation bound nucleon Modelling the Hadronic Vertex • Quasifree Region • Use form factors

  9. K is kinematic factor determined from normalisation of flux etc. • First order diagram: • Lμνcontains projectile information • Wμν contains nuclear information

  10. Kinematics CC • In CC reactions we can detect the outgoing muon.

  11. Kinematics NC • In NC reactions we cannot detect the outgoing neutrino.

  12. Transition Matrix Element • Leptonic Current • Parity not conserved • Left-handed neutrinos • Propagator • Vector Boson (W+ or Z0) • Coupling strengths follow from GSW Theory (ηl and ηh)

  13. Leptonic Tensor • Lepton spinor • normalised as • helicity representation • Neutrino: m = 0 and h = -1 • Feynman trace techniques and identities of the gamma matrices can be used to simplify the expression for Lμν

  14. Hadronic Tensor • The hadronic tensor is expanded in a basis consisting of the independent four-momenta, the metric tensor and the Levi-Civita tensor

  15. This expansion is model independent • The Wi expansion coefficients are the structure functions • Extract Wi: done once

  16. The contraction of hadronic and leptonic tensors is done considering symmetric and anti-symmetric contractions separately • General equation • Model is needed for guidance

  17. Construction of hµ • Born Term Model (s,t and u channels) • Propagators: • spin ½ • spin 0 • Vertices: • Strong coupling (baryon-baryon-meson) in s,t,u channels • Coupling constant • Weak coupling (meson-meson) in t channel • Phenomenological meson form factors Mecklenberg W., Acta Physica Austriaca48, 293 (1976) • Weak coupling (baryon-baryon) in s,u channel • Form factors • Weak Current Operator

  18. + s Elementary process: t u

  19. Form Factors s-channel • neutron-proton vertex

  20. CVC relates weak vector form factors to isovector form factors of EM current • EM isovector current • Axial form factor determined phenomenologically

  21. Total (for s-channel)

  22. u-channel • Vertex: • Weak current i.t.o. SU(3) octet currents

  23. where • and • λi = 3X3 generators of SU(3) • γμ= 4X4 Dirac matrices

  24. EM current • For Oj any octet current operator • For EM current • Comparison yields

  25. For weak current • Belongs to same octet as EM current • Axial form factor • From s-channel

  26. u-channel • weak baryon-baryon vertex: • propagator: • strong baryon-baryon-meson vertex:

  27. Total (for u-channel)

  28. Summary

  29. Conclusion • We are constructing a relativistic model for the description of weak hypernuclei production of relevance to experiments at Fermilab (BooNE) and J-PARC • Hadronic tensor parametrised in model independent way to facilitate different hadronic models through structure functions • Code written in Fortran 95 and Mathematica. In process of obtaining results: • We are investigating the relation between the structure functions Wi and the kaon scattering angle as well as dependence of Wi on the momentum transfer • Calculate the cross section email: ddvniekerk@sun.ac.za

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