Title:Massless two-loop "master" and three-loop two point function in NDIM

Abstract:NDIM (Negative Dimensional Integration Method) is a technique for evaluating Feynman integrals based on the concept of analytic continuation. The method has been successfully applied to many diagrams in covariant and noncovariant gauge field interactions and has shown its utility as a powerful technique to handle Feynman loop integrations in quantum field theories. In principle NDIM can handle any loop calculation; however, in practical terms, the resulting multiseries with several variables in general cannot be summed up conveniently and its analytic properties are generally unknown.
The alternative then is to use order by order (loop by loop) integration in which the first integral is of the triangle diagram type. However, the naïve momentum integration of this leads to wrong results. Here we use the shortened version for the triangle in NDIM that is suitable for a loop by loop calculation and show that it leads (after appropriate analytic continuation to positive dimension) to agreement with the known result for the two-loop master diagram. From it, a three-loop is then calculated and shown again its consistency with the already published result for such a diagram.