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

No Radial Excitations in Low Energy QCD. I. Diquarks and Classification of Mesons