Abstract
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 A 1 → ρπ and B → ωπ, predicting 2(g 1 /g 0 )A 1 = (g 0 /g 1 ) 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 the 0 + , 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) L Z relations hold among all the D waves and among all the S waves, but not between the two groups. 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) L Z . 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 o, and merely assuming lower bounds on widths of both physical states establishes the limits 10° ≤ o ≤ 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 A 1 for the lower state 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 mixed SU(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 a suppressed 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 J pc = 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 quark model, predict the ΔI = 1/2 rule.
Published Version
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