Sudakov evolution without unitarity

Abstract We present a method for sampling singular functions defined on (nested) multiparticle 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 (loosely derived from Sudakov Nesting of Hard Integrals), for hadronic Z decays, and use it to test the tree-level accuracy of the Vincia sector shower through $$\mathcal{O}(\alpha _s^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . Graphic Abstract