Symmetry violation in quark models of mesons

Abstract

Constituent and current quark models are employed to discuss many of the SU(3) and SU(2) violating strong and electromagnetic properties of pseudo scalar and vector mesons. The conventional ground state isoscalar meson mixing models are reviewed and extended to include radial excitations in the mass matrix. A phenomenological analysis of symmetry breaking in the models allows a successful simultaneous description of both the vector and pseudoscalar mass spectra, although attempts made to include the high statistics Crystal Ball result for the ratio o = ɼ (Ψ → η 'γ) /ɼ (Ψ → ηγ) = 5.88 ± 1.46 fail. A detailed description of meson radiative decay processes and the ratio of strong production amplitudes a o (π(^-)p→ η 'n) / o(π(^-)p→ηn) in a linear radial mixing model indicates that a consistent description of isoscalar meson properties can be made when p = 3.1, a value considerably less than the Crystal Ball result but in agreement with that obtained by the Dasp collaboration. The model parameters obtained in this analysis allow a satisfactory description of strong two body vector to pseudoscalar meson decays, and subsequent prediction of relationships between amplitudes forsimilar decays of the radial states. The model does not, however, provide an adequate account of the I ≠ O D, D(^*), F, F(^*) and to a lesser extent K and K(^*) meson states, a failing shared by all similar constituent models which are examined. Deficiencies in this description of meson structure which may explain the discrepancies are discussed. "The linear mass model used to predict p = 3.1 provides an ideal frame work for an examination of isospin violating meson properties. The phenomenological addition of strong and electromagnetic isospin violating parameters to the mass matrix allows the prediction of pseudoscalar and vector isoscalar- isovector mixing angles and isomultiplet mass differences. A satisfactory description of these mass differences and the branching ratio B(w → 2π) results, however, a prediction made for the ratio R = ɼ(Ψ'→ π(^o)Ψ) /ɼ(Ψ'→ η Ψ) is much smaller than measured values. The importance of contributions to these results from the isospin violating strong interactions is stressed. A current algebra approach to the ratios p and R is also undertaken. Axial Ward identities which include contributions from the triangle anomaly yield relations between the pseudoscalar meson masses and decay constants. These are included with equations describing P → 2γ decays and the ratio p which together are solved for the decay constants and topological charge components of the π(^o),η and η'. These allow a prediction for the ratio R which agrees with that obtained using the constituent quark model approach but is only half the magnitude of present experimental measurements.