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

Constructing multi-loop scattering amplitudes with manifest singularity structure