Sudakov evolution without unitarity

TL;DR

The paper introduces Sunshine, a C++ algorithm for sampling singular functions in multi-particle phase spaces, improving phase-space generation by combining Sudakov sampling, nested phase spaces, and amplitude factorisations, tested on Z decays.

Contribution

It presents a novel method for phase-space sampling that generalizes parton-shower techniques, with a practical implementation and validation for hadronic Z decays.

Findings

Successful implementation of Sunshine algorithm in C++

Accurate tree-level results up to order α_s^2 for Z decays

Enhanced phase-space sampling efficiency for singular functions

Abstract

We present a method for sampling singular functions defined on (nested) multi-particle phase spaces, based on a generalisation of parton-shower phase-space generation techniques. At the heart of the method are three key ingredients: 1) the Sudakov sampling by which shower-style calculations sweep across phase space in an ordered manner, from hard to soft; 2) the sequential nesting of multiparticle phase spaces; and 3) the factorisations obeyed by singular multiparton amplitudes on the edges of these phase spaces. We demonstrate a C++ implementation of the proposed algorithm, dubbed Sunshine, for hadronic Z decays, and use it to test the tree-level accuracy of the Vincia sector shower through $\mathcal{O}(\alpha_s^2)$.