Analytic properties of Feynman integrals for scattering amplitudes
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Wasser, Pascal
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Abstract
We classify Feynman integrals by analyzing the singularity structure of their integrands. For different integral families, we identify all integrals that can be written as sums of dlog forms with constant coefficients. These coefficients are known as the leading singularities of the integrand and we show how to compute them in two complementary ways: a graphical method using one-loop building blocks to construct the solution loop by loop, and an algorithmic approach that we also implemented using Mathematica'. Using the algorithmic approach we compute complete dlog bases for the planar and non-planar massless double box integral families and the two planar three loop four point integral families. We show that these dlog bases can be used as integral bases that satisfy differential equations in the canonical form which are particularly easy to solve.