Abstract
We provide a leading singularity analysis protocol in Baikov representation, for the searching of Feynman integrals with uniform transcendental (UT) weight. This approach is powered by the recent developments in rationalizing square roots and syzygy computations, and is particularly suitable for finding UT integrals with multiple mass scales. We demonstrate the power of our approach by determining the UT basis for a two-loop diagram with three external mass scales.
Highlights
One crucial step in applying the canonical differential equation approach is to find an integral basis with uniform transcendental weight
We further develop the uniform transcendental (UT) integral determination method based on the leading singularity analysis of Feynman integrals in Baikov representation
This method is highly flexible and easy to use since 1) for each sector we can use either the original Baikov or loop-by-loop Baikov representation 2) we may trade “complicated” UT integrals in some sectors with reducible UT integrals in the corresponding super sectors, in the sector-bysector leading singularity analysis, to make the UT searching easier
Summary
2.1 Leading Singularities and dlog integrals Given an L-loop Feynman integral, Ia1,...,an = eLγE. The package allows to compute the LS of a user-defined integrand and is able to give conditions on an integrand-ansatz for the absence of double poles. We combine this algorithm with the Baikov representation and use an example in section 3 to explain in detail how to construct dlog integrals using this approach. This method has already been used in [18] to determine the canonical differential equation of a family of five-point integrals
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