Two loop calculations in massive field theories.*

We will report our work on new computational methods  for high order perturbation theory. In the context of the PRadII experiment, it is very important to have working tools for efficient evaluation of cut diagrams. However, the usual methods of deriving differential equations for Feynman integrals fail for cut diagrams. We developed an extension of the conventional methods for this case and applied it to Passarino-Veltman integrals. At PRadII precision, it is necessary to evaluate two loop integrals. We studied the double Bethe-Heitler process and the intermediate integrals that emerge in this case. We show that they do not evaluate to polylogarithms, thus providing another example of higher transcendental functions that emerge at two loop level, on par with the elliptic polylogarithms. We studied the singularity structure of these functions in the limit case of PRad II kinematics. Many of our methods are applicable for more general two loop diagrams, with and without cuts. For instance , we give a complete description of singularity loci of two loop diagrams with arbitrary masses and arbitrary number of external momenta. We discuss applications of these findings for efficient calculation of these diagrams, and for construction of uniformized models of particle configuration spaces at two loop order. We observe that these spaces provide a natural generalization of Grassmannians.