Testing Theories of Chiral Symmetry

Abstract

We investigate various physical consequences of theories of chiral symmetry. Predictions of the symmetry are given for the meson electroproduction process at an on-shell kinematical point where unknown contributions are minimized. Sum rules are derived for the corrections. Then we present a sum rule for the ∑ term in meson-baryon scattering from the assumptions of Bjorken limit, precocious asymptopia, and finite-mass dispersion relations. We use the commutation relations of the gluon model as input for a numerical evaluation. Next the explicit canonical structure of the light-cone restriction of the commutator of the weak current with its divergence is considered in the interacting quark-gluon model quantized in the infinite–momentum frame. The implications on neutrino scattering are analyzed. W4 and W5 are predicted to scale nontrivially as v−2F4(ω) and v−2F5(ω), which provides a simple test of light-cone current algebra feasible in the near future. The ∑ term for weak currents is deduced from a causal representation near the light-cone, and a correction is also made in the W5 – sum rule obtained by naive infinite momentum techniques. As a by-product we obtain improved derivations of the Adler neutrino sum rules.