How much joint resummation do we need?

TL;DR

This paper explores the advantages and limitations of joint resummation techniques in QCD, specifically for angularities in $e^+e^-$ collisions, demonstrating improved predictions with multiple resummed observables.

Contribution

It provides a case study calculating joint resummation of multiple angularities at NLL accuracy and assesses its impact on event shape predictions.

Findings

Joint resummation significantly improves predictions for two angularities.

Diminishing returns observed for joint resummation with more than two angularities.

Reweighting phase-space generators with resummed predictions enhances accuracy.

Abstract

Large logarithms that arise in cross sections due to the collinear and soft singularities of QCD are traditionally treated using parton showers or analytic resummation. Parton showers provide a fully-differential description of an event but are challenging to extend beyond leading logarithmic accuracy. On the other hand, resummation calculations can achieve higher logarithmic accuracy but often for only a single observable. Recently, there have been many resummation calculations that jointly resum multiple logarithms. Here we investigate the benefits and limitations of joint resummation in a case study, focussing on the family of $e^+e^-$ event shapes called angularities. We calculate the cross section differential in n angularities at next-to-leading logarithmic accuracy. We investigate whether reweighing a flat phase-space generator to this resummed prediction, or the corresponding distributions from Herwig and Pythia, leads to improved predictions for other angularities. We find an order of magnitude improvement for n = 2 over n = 1, highlighting the benefit of joint resummation, but diminishing returns for larger values of n.