General strategy to achieve ε-factorized canonical form for master-integral differential equations

Develop a general method or algorithm to find gauge transformations that put the Picard–Fuchs system governing master integrals into the ε-factorized canonical form, i.e., a basis in which the connection matrices are ε times dlog forms of the kinematic variables.

Background

The ε-factorized (canonical) form of differential equations for master integrals greatly simplifies their solution, but obtaining it requires nontrivial gauge transformations. While local existence can be ensured under certain conditions, finding such transformations systematically remains challenging.

The authors point out that, even assuming ε-factorization exists, a broadly applicable strategy to reach it is lacking, limiting the automation and generalization of the method.