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 $\ensuremath{\alpha}=0$ fixed poles in current scattering amplitudes are polynomials in ${q}^{2}$ makes it possible to relate the $\ensuremath{\sigma}$ 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 $\mathrm{ep}$, $\mathrm{en}$, $\ensuremath{\nu}p$, and $\ensuremath{\nu}n$ scattering, deep-inelastic data, the $\ensuremath{\sigma}$ term, baryon mass differences, and the bare quark masses; approximate values for the bare quark masses and the parameter ${\ensuremath{\mu}}_{0}$ can be obtained.