Constructing multi-loop scattering amplitudes with manifest singularity structure

Abstract

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.

arXiv comment8 pages; in v2: references added relative to v1; in v3: introduction expanded and examples added along the lines suggested by the referees, further references and note added

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• The Four-Loop Cusp Anomalous Dimension from the $\mathcal{N}=4$ Sudakov Form Factor
• Leading singularities in Baikov representation and Feynman integrals with uniform transcendental weight
• A study of Feynman integrals with uniform transcendental weights and the symbology from dual conformal symmetry
• The Four-Loop $\mathcal{N}=4$ SYM Sudakov Form Factor
• Fermionic corrections to quark and gluon form factors in four-loop QCD
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