The recursive structure of Baikov representations II: the top-down reduction with intersection theory

Following our previous study of the recursive structure of Baikov representations, we discuss its application in the integration-by-parts reduction of Feynman integrals. We combine the top-down reduction approach with the recursive structure, which can greatly simplify the calculation for each sector in many cases. We introduce a new concept called the top-sector ISP reduction, which generalizes the maximal-cut reduction by retaining the sub-sector information. After subtracting the top-sector components, we provide a general method to transform the remaining integrand explicitly to sub-sectors, such that the reduction procedure can be carried out recursively. In this work, we use the intersection theory to demonstrate our method, although it can be applied to any implementation of the integration-by-parts reduction.