Dimensional renormalization and factorization

Abstract The problem of formulating a high-energy factorization explicitly in terms of dimensionally renormalized operators and coefficient functions is analyzed in the context of deep-inelastic scattering in renormalizable scalar theories. The coefficient functions that emerge are found to be the finite parts of dimensionally continued on-shell amplitudes, and are readily amenable to explicit computation. As a byproduct, an explicit forest formula emerges for the mass-singularity poles of on-shell amplitudes in renormalizable theories. The extension to gauge theories is briefly discussed at the leading twist level. The method is compared to the alternative approach to factorization whereby a finite hard part is defined by factorizing off mass-singularities.