Constructing multi-loop scattering amplitudes with manifest singularity structure

The infrared exponentiation properties of dimensionally-regularized multi-loop scattering amplitudes are typically hidden at the level of the integrand, materializing only after integral evaluation. We address this long-standing problem by introducing an appropriate integral basis which is simultaneously finite and uniform weight. As an example, we cast the integrand for the QCD corrections to the two-loop massless quark electromagnetic form factor into a form where it is manifest that the $\epsilon^{-4}$ and $\epsilon^{-3}$ pole terms arise from the $\epsilon$ expansion of the square of our one-loop master integral.