Spin-dependence and glueball mixing with θ(1640) in ordinary meson spectroscopy

It is shown from a fairly general point of view that meson spectroscopy implies that the spin-spin and tensor forces are due to very short-ranged interactions. The (Q₁, Q₂) ? (Q_A, Q_B) mixing of axial vector $\text{I =}\text{1}\text{2}$ mesons implies the presence of a substantial repulsive Thomas term as well as an attractive short-ranged spin-orbit force of comparable magnitude. This analysis makes no reference to detailed potentials or wave functions. Inverted multiplets are predicted as a consequence of the large repulsive Thomas term. The spin-dependent potentials can be interpreted as effective exchanges dominated by short-ranged vector exchange and a confining potential transforming as a Lorentz scalar, although small amounts of other exchanges are also possible. A model-dependent analysis of the gluon annihilation contribution to the mass matrix and two-body decays of the I = 0 2⁺⁺ mesons indicates significant gluon mixing in these states. The presence of a $\text{non-q}\text{q}$ state (glueball?) which mixes with f'(1514) and another I = 0 2⁺⁺ state is required by the mixing model. The possibility that this additional state is θ(1640) is considered. The mass of such a state satisfies f'(1514)<M(G₀)<θ(1640). The model predicts $\text{0.01 < Λ(θ → ηη)/Λ(θ →}\text{K}\text{K}\text{)<0.18}$, with the actual widths sensitive to the details of singlet-octet mixing in the η wave function.