Topological theory of hadrons. I. Mesons

Spin is incorporated into the hadronic topological expansion scheme. Spin analogs of Chan-Paton factors are introduced in a way that avoids the troubles encountered in earlier attempts. Those troubles, at the meson level, were, first, the occurrence of twice the wanted number of pseudoscalar and vector mesons; second, the occurrence of parity-doublet partners of the pseudoscalar and vector mesons; and third, the occurrence of these parity-doublet partners as particles of negative metric, called ghosts. These troubles are all avoided by introducing a new topological level, called zero entropy, that lies below the ordered level. At the zero-entropy level quarks of opposite chirality are treated as distinct particles. The theory has been extended to all hadrons, and the basic particles are exactly those of the constituent-quark model, which for baryons start with the (${56}^{+}$) and (${70}^{-}$). The theory is formulated in the $M$-function framework, where the "quarks" are represented by two-component spinors, and it entails $\mathrm{SU}{\mathrm{}\left(6\right)\mathrm{}}_W$ symmetry of the hadronic vertices at a low level of the topological expansion.