The Thesis is divided into the following two parts:
(1) We examine three aspects of the axial-vector mesons: (i) angular distributions of the I = 1 states, (ii) mixing of the I = 1/2 states, and (iii) absence of the I = 0 states.
Using a model of mesons decaying via production of a quark-antiquark pair with the quantum numbers of the vacuum, we relate the angular distributions in the decays A1→ ρπ and B → ωπ, predicting 2(g1/g0)A1 = (g0/g1)B + 1. This relation is consistent with the present, somewhat ambiguous experimental data. Also, we describe satisfactorily, in terms of two parameters, the partial widths of the0+, 1+, and 2+ mesons decaying into 1-0- and 0-0- pairs. The prediction of the model is that SU(6)W x 0(2)LZ relations hold among all the D waves and among all the S waves, but not between the twogroups. In fact, our two-parameter fit to the data entails a ratio of S wave to D wave amplitudes of approximately the same magnitude but opposite sign to that implied by SU(6)W x 0(2)LZ. Unlike the widths, the angular distributions are sensitive to the relative sign and are thus crucial in determining that the fit of our model differs considerably from the SU(6)W solution.
Parameters of the fit are applied to the l+ kaons, which may mix with one another. The results are sensitive to the mixing angle ø, and merely assuming lower bounds on widths of both physical states establishes the limits 10° ≤ ø ≤ 35° As a result of this mixing, one predicts: (a) the suppression of the K*π mode of the lower peak, (b) the suppression of the ρK mode of the upper peak, and (c) decay distributions in the K*π mode similar to that of the A1 for the lowerstate and to that of the B for the higher.
The properties of the missing isoscalar mesons are described with particular emphasis on the ninth 1++ state. Expected properties of this meson, the D', include: (a) assignment to a weakly mixedSU(3) singlet, predicted by duality and confirmed by the Gell-Mann-Okubo mass formula; (b) a mass of ~950 MeV, predicted by super-convergence with assumptions about the relative couplings of D and D’; (c) decay modes ηππ and π+π-γ; and (d) the possibility of asuppressed ρ signal in the π+π- spectrum of the π+π-γ final state,despite the expectation that the pions are in a state with I = J = 1. These features suggest that a recently reported meson near this mass with decay modes ηππ and π+π-γ may be a candidate for this state, although Jpc = 1+- is also a definite possibility for the new meson.
(2) Because of the limited evidence for the V-A Cabibbo theory in the non-leptonic weak decays, we examine the compatibility with experiment of more general current-current theories. These theories, constrained by universality, are constructed from the neutral and charged currents obtainable in the quark model, i.e., scalar, pseudoscalar, vector, axial-vector, and tensore Using current algebra and PCAC, a certain class of these theories, including Cabibbo's, is found to be consistent with the S wave amplitudes for the non-leptonic hyperon decays. The P wave amplitudes remain unexplained. Nevertheless, another class of theories, also including V-A, plus the assumption of a symmetric quarkmodel, predict the ΔI = 1/2 rule.
