Chiral magnetism (or magnetohadrochironics)

Abstract

In the infinite-momentum frame a hadron may be viewed as a one-dimensional stringlike structure composed of many constituents. We consider the dynamics of such a system and show how a spontaneous breakdown of chiral symmetry may occur. The effect is very similar to ferromagnetism. We formulate the theory of the distribution of quantum numbers in hadrons and establish the relation between this theory, chiral magnetism, soft-pion theorems, Regge behavior, and duality. In particular we show how the Harari-Gilman-Weinberg theory of chiral representation mixing follows from an approximation analogous to the treatment of a magnetic impurity in a ferromagnetic system. The first stage of approximation, when applied to a quark-parton system leads to a $\overline{q}q$ meson model. We demonstrate the need for spin-orbit coupling in the infinite-momentum quark system. Higher approximations are expected to lead to exotic states. A necessary consequence of our theory of spontaneous chiral-symmetry breakdown is the existence of a Pomeron-like vacuum trajectory with unit intercept. The natural order of magnitude of high-energy meson-meson total cross sections turns out to be ${{f}_{\ensuremath{\pi}}}^{\ensuremath{-}2}=10$ mb, as conjectured by Pagels. A specific model included in an appendix yields ${\ensuremath{\sigma}}_{\mathrm{tot}}(\ensuremath{\pi}\ensuremath{\pi})=2{{f}_{\ensuremath{\pi}}}^{\ensuremath{-}2}$. We do not explicitly deal with strangeness, or S${\mathrm{U}}_{3}$.