Chiral Perturbation Theory and the Weak Interaction

Citation

Bijnens, Johan Lambert (1985) Chiral Perturbation Theory and the Weak Interaction. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/64qa-xw17. https://resolver.caltech.edu/CaltechTHESIS:08042017-160047213

Abstract

We study the interface between the standard six-quark model and the observed low-energy weak phenomena. The main processes discussed are weak decays of kaons and hyperons. We study first the low-energy effective weak Hamiltonian at the quark level. This is derived using the renormalization group in leading logarithmic approximation.

Then some properties of this effective weak Hamiltonian that can be derived using chiral perturbation theory are studied. A review of chiral perturbation theory is included.

This formalism is used to study the relation between K̅⁰K⁰ mixing and a ΔI = 3/2 decay. We find that the logarithmic corrections to this relation are large, making it unreliable. The same formalism is used to discuss a relation between Kππ, Kπ and K-vacuum matrix elements used in most attempts to compute the Kππ matrix element relevant for the ΔI = 1/2 rule. The domain of validity of this relation is determined.

A review of inclusion of baryons in chiral perturbation theory is given and one-loop corrections to the Gell-Mann-Okubo relation; semileptonic hyperon decays and nonleptonic S and P wave decays are calculated. All corrections are small except the nonleptonic P wave decays and one S wave decay. The corrections to the Lee-Sugawara relation are large as a consequence of the latter.

Some predictions beyond chiral perturbation theory can be made within the soliton model of baryons. F/D ratios are predicted for hyperon magnetic moments, semileptonic decays and nonleptonic S wave decays in this model.

Thesis Files