Phase-space sectors for colour-ordered momentum mappings in local subtraction up to N$$^3$$LO

Abstract Momentum maps connecting phase spaces of different multiplicities are widely used in precision calculations in QCD and collider phenomenology in general. The antenna mapping is a colour-ordered map which allows to absorb the recoil of an arbitrary number of emissions onto two hard radiators. Due to the rapid convergence in soft and collinear configurations, the antenna mapping is extensively used for fixed-order calculations within the antenna subtraction method, as well as in parton showers such as the VINCIA shower. However, colour-ordered momentum mappings cannot be directly applied in the presence of multiple unordered emissions of quarks and gluons, which typically appear beyond the leading-colour approximation. To address this technical challenge, we present, in the context of the antenna subtraction method, a simple decomposition of the phase space into sectors to isolate classes of infrared configurations which can be unambiguously assigned to a specific momentum ordering. In each sector, the singularities of any matrix element can be subtracted relying on a colour-ordered map. We illustrate the required phase-space sectors for up to three unordered emissions. The mapping algorithm described here has been recently employed for the first differential N $$^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>3</mml:mn> </mml:mmultiscripts> </mml:math> LO calculation of jet production at electron–positron colliders.