New insights on an old problem: resummation of the D-parameter

Abstract

Abstract The D-parameter is one of the oldest and most experimentally well-studied hadronic observables for e + e − collisions. Nevertheless, unlike other classic observables like the C-parameter or thrust, the D-parameter has never been resummed throughout its entire singular phase space. Using insights and techniques motivated by modern multi-differential jet substructure calculations, we are able to predict the D-parameter distribution with no additional phase space cuts. Our approach is to measure both the C- and D-parameters on hadronic final states in e + e − collisions. We can tune the value of the C-parameter with respect to the D-parameter to specify simple, physical configurations of final state particles in which to perform calculations. There are three parametric regions that exist: D ≪C 2 ∼1, D ≪C 2 ≪1, and D ∼C 2 ≪1, and we calculate the D-parameter in each region separately. In the first two of these three regions, we present all-orders factorization theorems and explicitly demonstrate resummation to next-to-leading logarithmic accuracy. The region in which D ∼ C 2 ≪ 1 corresponds to the dijet limit and where the D-parameter loses the property of additivity. In this region we introduce a systematically-improvable procedure exploiting properties of conditional probabilities and resum to approximate next-to-leading logarithmic accuracy. The contributions from these regions can be consistently combined, and the value of the C-parameter integrated over to produce the cross section for the D-parameter. With these results, we match to leading fixed order as proof of principle and compare our resummed and matched prediction to data from LEP.