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.
Highlights
Rows correspond to different orders of fixed-order perturbation theory, denoted by leading order (LO), next-to-leading order (NLO), etc
By default we show results from Herwig 7.1.4 for leading order e+e− → dijets at center-of-mass energy Q = 1 TeV
We have investigated the benefits and limitations of joint resummation of large logarithms, using as an example the resummation of n angularities in e+e− collisions
Summary
We start this section by presenting our setup, discussing the observables in more detail. We describe the reweighing procedure of flat k-body phase space with resummed predictions for n angularities, as well as the determination of the optimal set of angularities to be used as input, including the treatment of statistical uncertainties. The angle θi of each particle contributing to an angularity is measured with respect to the WTA axis of the corresponding jet, and the angularities eα that we consider are the sum of the angularities eJαet J of the individual jets, i.e. eα = eJαet 1 + eJαet 2. The various distributions of αi are constructed in 16 bins on the interval αi ∈ [−4, 0].
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