We calculated the decay widths of the 1 3 F 2 and 1 3 F 4 ss mesons and compared them to the measured properties of the ξ(2220) (now known as the f 4 (2220)). Including previously neglected decay modes we found that the width of the 3 F 2 state ss meson is much larger than previously believed making this explanation unlikely. On the other hand the predicted width of the 3 F 4 state, although broader than the observed width, is consistent within the uncertainties of the model. This interpretation predicts large partial widths to KK * (892) and K * (892)K * (892) final states which should be looked for.A second possibility that would account for the different properties of the ξ(2220) seen in different experiments is that two hadronic states exist at this mass. The first would be a broader 3 F 4 ss state which is seen in hadron beam experiments while the second would be a narrow state with high glue content seen in the gluon rich J/ψ radiative decay. Further experimental results are *

We studied properties of the strange axial mesons in the relativized quark model. We calculated the K 1 decay constant in the quark model and showed how it can be used to extract theis the most sensitive measurement and also the most reliable since the largest of the theoretical uncertainties factor out. However the current bounds extracted from the TPC/Two-Gamma collaboration measurements are rather weak: we typically obtain −30 o < ∼ θ K < ∼ 50 o at 68% C.L. We also calculated the strong OZI-allowed decays in the pseudoscalar emission model and the flux-tube breaking model and extracted a 3 P 1 − 1 P 1 mixing angle of θ K ≃ 45 o . Our analysis also indicates that the heavy quark limit does not give a good description of the strange mesons.

This thesis examines three problems of the quark model, split between two general areas.The first area involves models of meson decay. The calculations of decay widths in two such models, the 3 P 0 model and the flux-tube breaking model, were automated so that they could be easily done for any decay. The models were then used to investigate two particular problems. The first is the nature of the f 4 (2220) -although tentatively identified as the 3 F 4 ss meson by the Particle Data Group, its identity has been uncertain since its discovery in 1983. An exhaustive calculation of the strong decay modes of the 3 F 2 and 3 F 4 ss mesons was performed in order to examine the possibility that the state is a meson. It was found that the f 4 (2220) cannot be the 3 F 2 ss meson, and is unlikely to be the 3 F 4 , although given the uncertainties of the models the latter possibility cannot be ruled out. Instead the following explanation is proposed: that the broad state seen in hadron beam experiments is the 3 F 4 ss meson, and the narrow state seen in J/ψ radiative decay is a glueball. Further experimental data is needed to finally identify the f 4 (2220).The second problem investigated using meson decay models is the determination of the mixing angle between the K 1 (1270) and K 1 (1400) mesons. This was done by comparing predictions of the meson decay models for five partial decay widths and two ratios of D to S amplitudes to experimental data. A mixing angle of approximately 44 • was extracted, and the implications to the quark model Hamiltonian are discussed.The third problem falls in the second general area: final state interactions (FSI's).The effect of the strong interactions between the outgoing pions was examined for the reaction γγ → ππ near threshold. For charged pions, the experimental data agrees with the results calculated both with and without the effects of FSI's -better iii data is need to distinguish between the two. However, agreement was not obtained for neutral pions. It is believed that the discrepancy may be due to the effects of resonance production. If this proves to be the case, then the techniques used in this work could be extended to try to understand a long-standing puzzle: the nature of the unexplained structures seen in the cross sections of γγ → two vector mesons. iv AcknowledgmentsThis work was made possible by the support of a large number of people. I would especially like to thank my supervisor Stephen Godfrey, for doing those things that supervisors do. Also our collaborator (on the γγ → ππ work) Eric Swanson. A large number of other people answered physics questions (or tried to) -in particular Peter Watson and Mike Doncheski (Mike also read this thesis for me). A number of people answered computer questions -in particular Mike Boyce, Matthew Jones, Alan Barney and Wade Xiong. The theory post-docs and my fellow grad students in physics kept life interesting -in particular

A quark model calculation of the processes γγ → π + π − and γγ → π 0 π 0 is performed. At tree level, only charged pions couple to the initial state photons and neutral pions are not expected in the final state. However, a small but significant γγ → π 0 π 0 cross section is observed. We demonstrate that this may be accounted for by a rotation in isospin space induced by final state interactions. The resulting π + π − cross section is in good agreement with experiment while the π 0 π 0 cross section is in qualitative agreement with the data.

We demonstrate how to parametrize the Cabibbo-Kobayashi-Maskawa (CKM) matrix in terms of its eigenvalues and eigenvectors, generalizing a recent idea of Kielanowski's. In this version we are able to reproduce a symmetric CKM matrix with only two angles while predicting a range in the amount of CP violation. The relation between this parametrization and the standard one is studied. Some variations of this parametrization are worked out. 43 2386 -, and J = Im( V 1 V2, VLV,*l is J = & cos(2/3, ) sin2(28, ) sin2( 2p2)( 3 +2x -x 2 ) 3 / 2 .I f we ignore experimental constraints, the maximum range o f J that we can get by varying 81, 82, and x is