How much joint resummation do we need?

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.