Parton models and asymptotic freedom

Abstract

We generalize the scale-invariant parton model to describe fixed-point and asymptotically free guage and nongauge theories. $Q^2$-dependent scaling laws for the moments of $\nu W_2$ are derived. In fixed-point theories the moments scale as powers of $Q^2$, while in asymptotically free theories they scale as powers of ${\ln Q}^2$. The behaviors of the elastic form factors, the ratio $\frac{{\sigma }_S}{{\sigma }_T}$, and the mean-squared transverse momentum of hadron secondaries are discussed in the various theories. The experimental study of these quantities should distinguish clearly between the conventional parton-model and asymptotically free theories of strong interactions.