Title: The algebraic structure of cut Feynman integrals and the diagrammatic coaction,
Abstract: We study the algebraic and analytic structure of Feynman integrals by
proposing an operation that maps an integral into pairs of integrals obtained
from a master integrand and a corresponding master contour. This operation is a
coaction. It reduces to the known coaction on multiple polylogarithms, but
applies more generally, e.g. to hypergeometric functions. The coaction also
applies to generic one-loop Feynman integrals with any configuration of
internal and external masses, and in dimensional regularization. In this case,
we demonstrate that it can be given a diagrammatic representation purely in
terms of operations on graphs, namely contractions and cuts of edges. The
coaction gives direct access to (iterated) discontinuities of Feynman integrals
and facilitates a straightforward derivation of the differential equations they
admit. In particular, the differential equations for any one-loop integral are
determined by the diagrammatic coaction using limited information about their
maximal, next-to-maximal, and next-to-next-to-maximal cuts.