Feynman Diagrams from Conformal Integrals

We show that momentum space Feynman diagrams involving internal massless fields can be cast as conformal integrals. This leads to a classification of all Feynman diagrams into conformal families, labelled by conformal integrals. Computing the conformal integral in each family suffices to compute all the Feynman diagrams in the family exactly. Using known exact results for some conformal integrals, we present the solutions to the other Feynman diagrams in the corresponding families. These are answers to either finite or dimensionally regularized Feynman diagrams to all orders in the regularization parameter.