Electroproduction scaling in an asymptotically free theory of strong interactions

We analyze electroproduction in a non-Abelian gauge model of the strong interactions using the techniques of Christ, Hasslacher, and Mueller. The theory is asymptotically free and consistent with scaling up to logarithms. All logarithmic factors appear as inverse powers of $\ln (-q^2)$ and hence vanish as $-q^2\to \infty$. When $-q^2$ gets very large, the structure functions become strongly peaked near $x=0\mathrm{}$, and as $-q^2\to \infty$ approach the singular scaling functions $2x{F}_1\mathrm{}\left(x\right)=F_2\mathrm{}\left(x\right)=a\delta \mathrm{}\left(x\right)\mathrm{}$, where the constant $a$ is determined. In a strong-interaction model based on the gauge group SU(3) with three triplets of fractionally charged quarks, $a=0.16\mathrm{}$.