Multi-loop Amplitudes and Resummation

Abstract

We explore the relation between resummation and explicit multi-loop calculations for QCD hard-scattering amplitudes. We describe how the factorization properties of amplitudes lead to the exponentiation of double and single poles at each order of perturbation theory. For these amplitudes, previously-observed relations between single and double poles in different 2 to 2 processes can now be interpreted in terms of universal functions associated with external partons and process-dependent anomalous dimensions that describe coherent soft radiation. Catani's proposal for multiple poles in dimensionally-continued amplitudes emerges naturally.

Comments: 14 pages, LateX2e using elsart.cls (included). Typographical errors corrected and expansion in renormalized coupling clarified. Thanks added to Z. Bern and L. Dixon for critical readings of the original version