Cat's cradle diagrams for substructure studies

Abstract

We propose Cat's Cradle diagrams as a framework to analyse the perturbative accuracy of gauge quantum field theories across different kinematic regions, interpolating between the power countings of fixed-order perturbation theory and soft-collinear resummation. We propose a simple intermediate counting aimed at quantifying parametric accuracy for resolved jet substructure, nested so that $N^{n}LO\subset N^{n}LJ\subset N^{n+1}LL$. We show that the resolved jet-substructure power counting, $N^{n}LJ$, emphasises contributions that are important for resolved substructure but which are lumped together with less dominant terms in both of the two other countings. It may therefore furnish a complementary quantification of relative parametric accuracy in a kinematic region "midway" between the hard (fixed-order) and soft-collinear (resummation) regimes. We discuss practical applications to parton showers, in the context of a hard process with a characteristic hard scale of order 200 GeV.