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 The Transition Matrix Leptonic Tensor Hadronic Tensor Constructing W µ (Example) Conclusion

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)MiniBooNE J-PARC Super-Kamiokande (50 GeV) Super-Kamiokande Nucleon decay postulated by supersymmetry Hyperon and hypernuclei production form important part of neutrino- induced reaction cross sections

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

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

Formalism Neutral Current (NC)Charged Current (CC)

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

K is kinematic factor determined from normalisation of flux etc. First order diagram: L μν contains projectile information W μν contains nuclear information

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

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

Transition Matrix Element Leptonic Current Parity not conserved Left-handed neutrinos Propagator Vector Boson (W + or Z 0 ) Coupling strengths follow from GSW Theory (η l and η h )

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 L μν

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

This expansion is model independent The W i expansion coefficients are the structure functions Extract W i : done once

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

Construction of h µ 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 Austriaca 48, 293 (1976) Weak coupling (baryon-baryon) in s,u channel Form factors Weak Current Operator

 s t u Elementary process:

s-channel neutron-proton vertex Form Factors

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

Total (for s-channel)

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

where and λ i = 3X3 generators of SU(3) γ μ = 4X4 Dirac matrices

EM current For O j any octet current operator For EM current Comparison yields

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

u-channel weak baryon-baryon vertex: propagator: strong baryon-baryon-meson vertex:

Total (for u-channel)

Summary

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 W i and the kaon scattering angle as well as dependence of Wi on the momentum transfer Calculate the cross section