Extended QCD
Two milestones on the path to the theory of QCD were the invention of the quark model [1, 2], and the discovery that pions arise as Goldstone bosons due to a chiral symmetry breaking condensate of fermions in the vacuum [3]. The latter phenomenon has been verified in lattice QCD (where the vacuum exhibits a quark condensate, rather than the nucleon condensate originally envisaged), but the quark model remains just a heuristic picture – albeit a successful one – with no direct connection to QCD beyond sharing fermion degrees of freedom and some of the same symmetries. In fact, the quark model, with its massive, weakly interacting quarks, has no realization of chiral symmetry, and no way to explain a massless pion in the chiral limit. An attempt to reconcile the quark model with spontaneously broken chiral symmetry was made in the chiral quark model of Georgi and Manohar [4] where quarks and gluons coexist with pions at low energy. The model assumes a weak gluon coupling below the chiral symmetry breaking scale in order to explain why constituent quarks appear to be weakly interacting, but results in an unrealistically low confinement scale and light glueballs. The model also does not quantitatively explain what happens to the quark-antiquark bound state with the quantum numbers of the pion, and similarly has not been derived from QCD. Recently the energy range over which this model should apply was extended by invoking the large-Nc expansion [5], but the basic question of how weakly interacting (yet confined) massive quarks can arise from QCD remains unresolved.