Related papers: New representation of the two-loop crossed vertex …
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 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…
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…
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…
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 propose a new approach that allows for the separate numerical calculation of the real and imaginary parts of finite loop integrals. We find that at one-loop the real part is given by the Loop-Tree Duality integral supplemented with…
We discuss the calculation of two-point three-loop functions with an arbitrary number of massive propagators and one large external momentum. The relevant subdiagrams are generated automatically. The resulting massless two-point integrals…
This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…
The scalar two-loop self-energy master diagram is studied in the case of arbitrary masses. Analytical results in terms of Lauricella- and Appell-functions are presented for the imaginary part. By using the dispersion relation a…
Motivated by the precision results in the electroweak theory studies of two-loopFeynman diagrams are performed. Specifically this paper gives a contribution to the knowledge of massive two-loop self-energy diagrams in arbitrary and…
We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…
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…
A framework to represent and compute two-loop $N$-point Feynman diagrams as double-integrals is discussed. The integrands are 'generalised one-loop type" multi-point functions multiplied by simple weighting factors. The final integrations…
This article displays a proof of concept of the mixed analytical/numerical method, presented in previous publications, to compute two-loop functions with up to five massive propagators in a scalar theory having three- and four-leg vertices…
Evaluation of three- and four-point diagrams with massless internal particles and arbitrary external momenta is considered. Exact results for some two-loop diagrams (planar and non-planar three-point contributions and the "double box"…
We extend existing dispersive approach in subloop insertion to the case of crossed two-loop box type topologies. Based on the ideas of the Feynman trick, mass shift approach and dispersive representation of two-point Passarino-Veltman…
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…
We present a dispersion relation formalism to calculate a massive scalar two-loop vertex function. Such calculation is of direct relevance in the evaluation of the hadronic light-by-light contribution to the muon's anomalous magnetic moment…
We give the results of complete analytical computations of two- and three-point loop integrals ocurring in heavy particle theories, with and without velocity change, for arbitrary values of external momenta and masses.
I study the Feynman integrals needed to compute two-loop self-energy functions for general masses and external momenta. A convenient basis for these functions consists of the four integrals obtained at the end of Tarasov's recurrence…