Determining the Factorizability of Hard Scattering Cross-Sections

The rules of soft-collinear effective theory can be used naı̈vely to write hard scattering cross-sections as convolutions of separate hard, jet, and soft functions. We describe an intuitive method to determine, at a given order in perturbation theory, whether these functions are truly infrared safe or not and, thus, whether or not the cross-sections factorize. Using angularity distributions as an illustrative example, we look for regions of integration in the sum of Feynman diagrams contributing to the jet and soft functions where the integrals become infrared divergent. Our analysis is independent of an explicit infrared regulator, and simultaneously clarifies how to distinguish infrared and ultraviolet singularities when pure dimensional regularization is used to regulate both.