Resummed distribution functions: making perturbation theory positive and normalized

A

bstract

Fixed-order perturbative calculations for differential cross sections can suffer from non-physical artifacts: they can be non-positive, non-normalizable, and non-finite, none of which occur in experimental measurements. We propose a framework, the Resummed Distribution Function (RDF), that, given a perturbative calculation for an observable to some finite order in α _s , will “resum” the expression in a way that is guaranteed to match the original expression order-by-order and be positive, normalized, and finite. Moreover, our ansatz parameterizes all possible finite, positive, and normalized completions consistent with the original fixed-order expression, which can include N ⁿ LL resummed expressions. The RDF also enables a more direct notion of perturbative uncertainties, as we can directly vary higher-order parameters and treat them as nuisance parameters. We demonstrate the power of the RDF ansatz by matching to thrust to