Related papers: Methods to calculate scalar two-loop vertex diagra…
We present a review of the Bielefeld-Dubna activities on the multiloop calculations. In the first part a C-program DIANA (DIagram ANAlyser) for the automation of Feynman diagram evaluations is presented, in the second part various…
Methods developed by the Bielefeld-DESY-Dubna collaboration in recent years are: DIANA (DIagram ANAlyser), a program to produce ``FORM input'' for Feynman diagrams, starting from the Feynman rules; methods to calculate scalar diagrams:…
A brief overview of some recent publications related to the evaluation of two-loop Feynman diagrams is given. (Talk given at the International Symposium on Radiative Corrections CRAD96, Cracow, Poland, 1--5 August 1996)
A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…
We briefly review numerical methods for calculations beyond one loop and then describe new developments within the method of sector decomposition in more detail. We also discuss applications to two-loop integrals involving several mass…
I present a few new and recent ideas of the multiloop calculations.
Extending the method successful for one-loop integrals, the computation of two-loop diagrams with general internal masses is discussed. For the two-loop vertex of non-planar type, as an example, we show a calculation related to…
We present a method to calculate to very high precision the coefficients of the divergences occuring in two-loop diagrams for a massive scalar field on the lattice. The approach is based on coordinate space techniques and extensive use of…
We review the method of the calculation of multiloop integrals recently suggested in Ref.[Lee2010]. A simple method of derivation of the dimensional recurrence relation suitable for automatization is given. Some new analytic results are…
We review the method of the calculation of multiloop integrals suggested in Ref.\cite{Lee2010}.
A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass…
We present a new method of calculating scalar propagator and vertex functions in the two-loop approximation, for arbitrary masses of particles. It is based on a double integral representation, suitable for numerical evaluation. Real and…
I briefly summarize the talks on calculation of multiloop Feynman diagrams presented at ACAT'2002 (Moscow University).
We discuss a progress in calculation of Feynman integrals which has been done with help of the Differential Equation Method and demonstrate the results for a class of two-point two-loop diagrams.
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.
An efficient method to calculate tadpole diagrams is proposed. Its capability is demonstrated by analytically evaluating two four-loop tadpole diagrams of current interest in the literature, including their $O(\epsilon)$ terms in…
Detailed description of the calculation of the 2-loop self-energy for a scalar particle is presented. By employing a simple sector decomposition method, the ultraviolet divergent part is efficiently separated from the finite part. The…
Some methods for the numerical computation of two-loop non-infrared vertices are reviewed. A new method is also proposed and compared to the old ones. Finally, some preliminary results are presented, concerning the evaluation of the…
Using the parallel/orthogonal space method, we calculate the planar two-loop three-point diagram and two rotated reduced planar two-loop three-point diagrams. Together with the crossed topology, these diagrams are the most complicated ones…
We calculate the two-loop vertex function for the crossed topology, and for arbitrary masses and external momenta. We derive a double integral representation, suitable for a numerical evaluation by a Gaussian quadrature. Real and imaginary…