Efficient matrix-element matching with sector showers

Abstract

A Markovian shower algorithm based on "sector antennae" is presented and its main properties illustrated. Tree-level full-color matrix elements can be automatically incorporated in the algorithm and are re-interpreted as process-dependent 2 → n antenna functions. In hard parts of phase-space, these functions generate tree-level matrix-element corrections to the shower. In soft parts, they should improve the logarithmic accuracy of it. The number of matrix-element evaluations required per order of matching is 1, with an unweighting efficiency that remains very high for arbitrary numbers of legs. Total rates can be augmented to NLO precision in a straightforward way. As a proof of concept, we present an implementation in the publicly available Vincia plug-in to the Pythia 8 event generator, for hadronic Z 0 decays including tree-level matrix elements through O(α 4 s ).

Antenna showers with one-loop matrix elements

“…We also include the so-called ariadne factor, P Ari , defined by 20) with s N the invariant mass squared of the colour neighbour on the other side of the splitting gluon and s P = m 2 IK the invariant mass squared of the parent (splitting) antenna. This does not modify the singular behavior (as will be elaborated upon below), and was shown to give significantly better agreement with the Z → qqqq matrix element in [30].…”

“…Firstly, the linearized variables imply less severe constraints on the subsequent evolution than the quadratic ones. This is easy to understand given that the linearized variables, Q lin , are related to the quadratic ones, Q qdr , by 30) and hence Q lin > Q qdr , implying a higher absolute restart scale for the linearized ordering variables. It is also apparent that, for a given choice of linearity, mass-ordering reduces the phasespace for further evolution more than p ⊥ -ordering does, which in turn is more constraining than energy-ordering.…”

“…A prescription for matching the showers to reproduce tree-level matrix elements exactly (over all of phase space) was developed in [24], with uncertainty variations provided in the form of vectors of alternative weights for each event. In [30] and [31] substantial speedups of the matching algorithm were obtained by dividing phase space into so-called sectors, and by deriving a formalism for using individual helicity am-…”

Timelike dipole-antenna showers with massive fermions

“…This is a feature which is not possible with other approaches to multileg matching, such as MENLOPS [15], CKKW [16,17] and related approaches [18][19][20], or MLM (see [21] for a description). The speed of the resulting matched calculations is also greatly improved as compared to the existing approaches, as discussed in [22].…”

Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations

“…The formalism can be extended to include massive fermions [71][72][73][74]. Antenna subtraction has also been used as the starting point for a parton shower algorithm [75][76][77][78], using the fact that antennae capture the unresolved limits of QCD amplitudes to achieve a leading-log resummation.…”