  The leading-order chiral Lagrangian for the baryon octet and decuplet states
coupled to Goldstone bosons and external sources contains six low-energy
constants. Five of them are fairly well known from phenomenology, but the sixth
one is practically unknown. This coupling constant provides the strength of the
(p-wave) coupling of Goldstone bosons to decuplet states. Its size and even
sign are under debate. Quark model and QCD for a large number of colors provide
predictions, but some recent phenomenological analyses suggest even an opposite
sign for the Delta-pion coupling. The Goldberger-Treiman relation connects this
coupling constant to the axial charge of the Delta baryon. This suggests a
Wu-type experiment to determine the unknown low-energy constant. While this is
not feasible in the Delta sector because of the large hadronic width of the
Delta, there is a flavor symmetry related process that is accessible: the weak
semileptonic decay of the Omega baryon to a spin 3/2 cascade baryon. A broad
research program is suggested that can pin down at least the rough size and the
sign of the last unknown low-energy constant of the leading-order Lagrangian.
It encompasses experimental measurements, in particular the forward-backward
asymmetry of the semileptonic decay, together with a determination of the
quark-mass dependences using lattice QCD for the narrow decuplet states and
chiral perturbation theory to extrapolate to the Delta sector. Besides
discussing the strategy of the research program, the present work provides a
feasibility check based on a simple leading-order calculation.
