Abstract
We formulate some first fundamental elements of an approach for assessing the logarithmic accuracy of parton-shower algorithms based on two broad criteria: their ability to reproduce the singularity structure of multi-parton matrix elements, and their ability to reproduce logarithmic resummation results. We illustrate our approach by considering properties of two transverse-momentum ordered final-state showers, examining features up to second order in the strong coupling. In particular we identify regions where they fail to reproduce the known singular limits of matrix elements. The characteristics of the shower that are responsible for this also affect the logarithmic resummation accuracies of the shower, both in terms of leading (double) logarithms at subleading NC and next-to-leading (single) logarithms at leading NC.
Highlights
Of NLO corrections across processes of varying jet multiplicity simultaneously [11,12,13], and the incorporation of NNLO corrections in colour-singlet production simulations [14,15,16]
For example: (1) the ability to match NNLO and higher-order calculations with parton showers is to some extent limited by the fact that parton showers do not reproduce the known structure of singularities that is present in a NNLO calculation
The Pythia and Dire showers both effectively cut off the divergence for 1 − z ∼ κ, but Pythia implements this through the kinematic map, while Dire does so through the splitting functions
Summary
There are many parton showers being used and under further development today. They generate emissions in a sequence according to a kinematic ordering variable. We rather choose to concentrate on two of them: (1) the Pythia shower on the grounds that it is today’s most extensively used shower; and (2) the Dire shower [31], on the grounds that it is the only shower explicitly available in two Monte Carlo simulation programs (Pythia [59] and Sherpa [60]) and that it is being used as a basis for the inclusion of higher-order splitting kernels [41,42,43] Both are transverse-momentum ordered and use recoil that is kept local within colour dipoles.. The difference between one shower and another lies not just in the choice of kinematic ordering variable v, and in the mapping function M and the splitting weight function P. Note that for the purpose of this article we will only consider final-state showers, with massless partons
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