Two Topics in Elementary Particle Physics: (1) Quark Graphs and Angular Distributions in the Decays of the Axial-Vector Mesons. (2) Universal Current-Current Theories and the Non-Leptonic Hyperon Decays

Citation

Colglazier, Elmer William, Jr. (1971) Two Topics in Elementary Particle Physics: (1) Quark Graphs and Angular Distributions in the Decays of the Axial-Vector Mesons. (2) Universal Current-Current Theories and the Non-Leptonic Hyperon Decays. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/HBFX-4095. https://resolver.caltech.edu/CaltechTHESIS:04192018-085253797

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 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 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)_LZ 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)_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 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.

Thesis Files