We present an analytic calculation of electron and tau O(α) loop effects on the muon anomalous magnetic moment. Computation of such three-loop diagrams with three mass scales is possible using asymptotic and eikonal expansions. An evaluation of a new type of eikonal integrals is presented in some detail.

A full analytic calculation of the two-loop diagrams contributing to the static potential in QCD is presented in detail. Using a renormalization group improvement, the “three-loop” potential in momentum space is thus derived and the third coefficient of the β-function for the V -scheme is given. The Fourier transformation to position space is then performed, and the result is briefly discussed.

The “basketball diagram” is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field ...

A full analytic calculation of the two-loop diagrams contributing to the static potential in QCD is presented in detail. Using a renormalization group improvement, the “three-loop” potential in momentum space is thus derived and the third coefficient of the β-function for the V -scheme is given. The Fourier transformation to position space is then performed, and the result is briefly discussed.

We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topolo-gies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in c...

Prompted by recent progress in the study of N = 4 super Yang-Mills amplitudes, and evidence that similar approaches are relevant to N = 8 supergravity, we investigate possible iterative structures and applications of Wilson loop techniques in maximal supergravity. We first consider the two-loop, four-point MHV scattering amplitude in N = 8 supergravity, confirming that the infrared divergent pa...

A FORM based package (ON-SHELL2) for the calculation of two loop self-energy diagrams with one nonzero mass in internal lines and the external momentum on the same mass shell is elaborated. The algorithm, based on recurrence relations obtained from the integration-by-parts method, allows us to reduce diagrams with arbitrary indices (powers of scalar propagators) to a set of master integrals. Th...