Advances in Local Analytic Sector Subtraction: massive NLO and elements of NNLO automation

In this article we present a number of developments within the scheme of Local Analytic Sector Subtraction for infrared divergences in QCD. First, we extend the scheme to deal with next-to-leading-order (NLO) singularities related to massive QCD particles in the final state. Then, we document a new implementation of the NLO subtraction scheme in the MADNKLO automated numerical framework, which is constructed to host higher-order subtraction algorithms. In particular, we discuss improvements in its performances with respect to the original implementation. Finally we describe the MADNKLO implementation of the first elements relevant to Local Analytic Sector Subtraction at next-to-next-to-leading order (NNLO), in the case of massless QCD partons in the final state.