Scaling laws for large-momentum-transfer processes

Abstract

Dimensional scaling laws are developed as an approach to understanding the energy dependence of high-energy scattering processes at fixed center-of-mass angle. Given a reasonable assumption on the short-distance behavior of bound states, and the absence of an internal mass scale, we show that at large s and t, dσ/dt(A B→C D)∼s-n+2f(t/s); n is the total number of fields in A, B, C, and D which carry a finite fraction of the momentum. A similar scaling law is obtained for large-p⊥ inclusive scattering. When the quark model is used to specify n, we find good agreement with experiments. For instance, this accounts naturally for the (q2)-2 asymptotic behavior of the proton form factor. We examine in detail the field-theoretic foundations of the scaling laws and the assumption which needs to be made about the short-distance and infrared behavior of a bound state.