  We propose a new schematic model for mesons in which the building blocks are
quarks and flavor-antisymmetric diquarks. The outcome is a new classification
of the entire meson spectrum into quark-antiquark and diquark-antidiquark
states which does not give rise to a radial quantum number: all mesons which
have so far been believed to be radially excited are orbitally excited
diquark-antidiquark states; similarly, there are no radially excited baryons.
Further, mesons that were previously viewed as "exotic" are no longer exotic as
they are now naturally integrated into the classification as
diquark-antidiquark states. The classification also leads to the introduction
of isorons (iso-hadrons), which are analogs of atomic isotopes, and their magic
quantum numbers, which are analogs of the magic numbers of the nuclear shell
model. The magic quantum numbers of isorons match the quantum numbers expected
for low-lying glueballs in lattice QCD. We observe that interquark forces in
mesons behave substantially differently from those in baryons: qualitatively,
they are color-magnetic in mesons but color-electrostatic in baryons. We
comment on potential models and the hydrogen atom. The implications of our
results for confinement, asymptotic freedom, and a new set of relations between
two fundamental properties of hadrons - their size and their energy - are
discussed in our companion paper [arXiv:0910.2231].
