  In most meson strong decay and unquenched (coupled-channel) quark models, the
pair-creation operator is a scalar product of vectors in the spin and spatial
degrees of freedom. While differing in the spatial part, most models have the
same spin part, which creates a qq* pair coupled to spin triplet, with the
spins of the initial quarks as spectators. This is a basic assumption of the
3P0 model, and is well-known to arise also in the flux tube model, starting
from the strong coupling expansion of lattice QCD. In this article the same
structure is shown to emerge in the Cornell model, in the dominant
contributions of a more general microscopic decay model, and in the
pseudoscalar-meson emission model. A solution is obtained for arbitrary matrix
elements in these ``non-flip, triplet'' models, expressed as a weighted sum
over spatial matrix elements. The coefficients in the expansion, which involve
the spin degrees of freedom and the associated angular momentum algebra, are
model-independent. Tables of the angular momentum coefficients are presented
which can be used in future calculations, avoiding tedious Clebsch-Gordan sums.
The symmetry and orthogonality properties of the coefficients are discussed, as
well as their application to transitions involving hybrid mesons and states of
mixed spin. New selection rules are derived, and existing ones generalised. The
coefficients lead to model-independent relations among decay amplitudes and
widths which can be tested in experiment and lattice QCD. They can also be used
to explain how mass shifts in the unquenched quark model do not spoil
successful predictions of the ordinary (quenched) quark model.
