The antenna-subtraction formalism has demonstrated remarkable success in facilitating fully-differential predictions for a wide range of processes at next-to-next-to-leading order (NNLO) in the strong coupling. At the heart of the subtraction scheme, so-called antenna functions capture the infrared behaviour of the matrix elements that describe additional radiation and loop corrections with respect to the Born process. In the original formulation of the subtraction scheme, these antenna functions were built from physical matrix elements. This construction principle has two shortcomings; firstly, physical matrix elements do not always allow to identify hard radiators and secondly, they can in general introduce spurious singularities which have to be removed by additional counter terms.

In this seminar I will describe a general algorithm to construct real-radiation and mixed real-virtual antenna functions directly from a list of unresolved limits. It can be anticipated that the improved antenna functions reduce both the algebraic and computational complexity of NNLO subtraction terms. I will close by giving an outlook on how the techniques developed to calculate improved antenna functions can help to build second-order parton showers, a vital step towards a general framework to match shower algorithms to NNLO calculations.