Deep-Inelastic Scattering, the Subtraction of Divergent Sum Rules, and Chiral-Symmetry Breaking in the Gluon Model

Abstract

The formal light-cone properties of commutators involving current divergences are studied in the gluon model. Relations are derived which make it possible (in principle) to distinguish the vector- from the (pseudo) scalar-gluon model. In the vector-gluon model these relations provide an experimental determination of the bare quark masses. The additional assumption that the residues of any $\alpha =0\mathrm{}$ fixed poles in current scattering amplitudes are polynomials in $q^2$ makes it possible to relate the $\sigma$ term in pion-nucleon scattering to convergent integrals over neutrino-scattering structure functions; the polynomial assumption dictates a prescription for subtracting a (linearly) divergent sum rule derived previously. The same technique generates subtracted sum rules for the (neutrino- and spin-dependent) structure functions $W_3$ and $G_2$. With the parton-model assumption that the leading scaling behavior of current-divergence and divergence-divergence scattering is given by free-field theory, it is possible to relate fixed-pole residues in $\mathrm{ep}$, $\mathrm{en}$, $\nu p$, and $\nu n$ scattering, deep-inelastic data, the $\sigma$ term, baryon mass differences, and the bare quark masses; approximate values for the bare quark masses and the parameter ${\mu }_0$ can be obtained.