Comparing and Counting Logs in Direct and Effective Methods of Resummation

Understand

We compare methods to resum logarithms in event shape distributions as they have been used in perturbative QCD directly and in effective field theory.

• We demonstrate that they are equivalent.
• In showing this equivalence, we are able to put standard soft-collinear effective theory (SCET) formulae for cross sections in momentum space into a novel form more directly comparable with standard QCD formulae, and endow the QCD formulae with dependence on separated hard, jet, and soft scales, providing potential ways to improve estimates of theoretical uncertainty.
• We show how to compute cross sections in momentum space to keep them as accurate as the corresponding expressions in Laplace space.