  The quantum effects encapsulated in loop corrections are crucial in quantum
field theory for a wide variety of formal and phenomenological applications. In
this article we propose and check a definition of the so-called single cut
contributions needed to complete on-shell recursion relations for the integrand
of scattering amplitudes in generic power-counting renormalisable theories at
conjecturally any loop order. Our proposal meshes well with standard
dimensional regularisation and applies in particular directly to much of the
standard model of particle physics. Apart from a diagrammatic construction, at
one loop order we provide a direct cross-check for box coefficients.
Interestingly, at one loop our proposal can be related to a specific subset of
all double unitarity cuts as well as tree-level poles by iterated recursion. We
focus in particular on demonstrating the method in rational-term one-loop
examples in pure Yang-Mills theory. For the finite amplitudes we present
all-order arguments. First steps toward gravity integrands are taken.
