Iris Bree, Federico Gasparotto, Antonela Matijašić, Pouria Mazloumi, Dmytro Melnichenko, Sebastian Pögel, Toni Teschke, Xing Wang, Stefan Weinzierl, Konglong Wu, Xiaofeng Xu
We report on three improvements in the context of Feynman integral reduction and ϵ-factorized differential equations. First, we show that with a specific choice of prefactors, we trivialize the ϵ dependence of the integration-by-parts identities. Second, we observe that with a specific choice of order relation in the Laporta algorithm, we directly obtain a basis of master integrals, whose differential equation on the maximal cut is in Laurent polynomial form with respect to ϵ and compatible with a particular filtration. Third, we prove that such a differential equation can always be transformed to an ϵ-factorized form. This provides a systematic algorithm to obtain an ϵ-factorized differential equation for any Feynman integral. Furthermore, the choices for the prefactors and the order relation significantly improve the efficiency of the reduction algorithm.