It is well-known that perturbative expansions of QFT observable suffer from infrared (IR) divergences both in the phase-space of real-emission contributions and in the loop amplitudes of virtual contributions.
Traditionally, the two are handled separately through a combination of local subtraction counterterm and dimensional regularisation. Local Unitarity is an alternative formulation, using the Loop-Tree Duality (LTD) theorem, and leveraging the Kinoshita–Lee–Nauenberg (KLN) cancellation pattern to achieve a direct cancellation of real-emission and loop IR divergences at the local level.
Together with an automated local renormalization procedure based on the R-operation (~local BPHZ), the resulting expression is locally finite and thus amenable to a fully numerical integration at arbitrary perturbative orders and for processes with final-state singularities only.
I will present an overview of the various ingredients involved in that construction and the challenges awaiting my new group at the University of Bern.
A special emphasis will be put on the following more recent developments:
a) Efficient momentum-space parameterization using tropical sampling.
b) Fast and stable LTD integrated evaluations using the cross-free family representation.
c) Threshold regularization using a subtraction method instead of contour deformations.