Is there any good recent experimental data that tests whether the $\rho$ coupling constant depends only on the isospin multiplet of the produced particle?
EDIT: I got a downvote, so I should explain the motivation. In the 1960s, Sakurai's idea is that the $\rho$ is the gauge boson for the isospin flavor symmetry. This idea led people to study photon-omega mixing and photon-rho mixing (the idea was omega being the massive second photon for hypercharge), and these led to the idea of describing shadow-scattering of photons off large nuclei, through the photon-vector-hadron mixing. These phenomena are discussed at length by Kurt Gottfried in 1970, as cited and explained further in Feynman's 1972 book "Photon Hadron interactions".
These ideas died away with QCD, when the $\rho$ could no longer be considered an elementary particle or an elementary string state. But they were revived somewhat in the 1980s, as people began to consider hidden local symmetry, where there is an infinite tower of gauge symmetries. Hidden gauge symmetry seems sort of silly and umotivated at first, but the proper motivation is within string theory, and AdS/QCD explains how this picture can emerge, the tower of gauge symmetries are a Kaluza-Klein tower in an extra dimension, and the local-hidden-symmetry picture can appear naturally from strings. This makes all this stuff interesting again, both theoretically and experimentally.
So this means we should ask the question of what is the experimental data regarding the $\rho$ meson and its couplings again, does it look like a gauge boson for isospin? I don't know how experimentalists extract coupling constants, and this is generally difficult for hadrons, but somebody might have figured out how to do this by now, and given some data somewhere.
I seem to recall that there are arguments in the literature that the coupling of the $\rho$ to the pions, nucleons, etc must be the same as a gauge boson for Isospin, from general principles. I think these arguments are completely bogus. I think the only general principle which accounts for something of this sort is the necessary gauging of flavor symmetries in string theories.