  It has been shown previously that in a relativistic constituent-quark model,
predictions for the electromagnetic form factor of the pi meson match not only
experimental data but also, in the limit of large momentum transfers, the
asymptotics derived from Quantum Chromodynamics (QCD). This is remarkable since
no parameters are introduced to provide for this infrared-ultraviolet link.
Here, we follow this approach, going beyond QCD. We obtain numerical relations
between the gauge coupling constant, the decay constant and the charge radius
of the pion-like meson in general strongly-coupled theories. These relations
are compared to published lattice results for SU(2) gauge theory with two
fermion flavours, and a good agreement is demonstrated. Further applications of
the approach, to be explored elsewhere, include composite Higgs and dark-matter
models.
