Related papers: Dispersive calculation of the massless multi-loop …
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…
An explicit investigation about the equal-mass two-loop sunrise Feynman graph is performed. Such perturbative amplitude is related with many important physical process treated in the standard model context. The background of this…
This paper discusses the methods and the results used in an accompanying paper describing the matching of effective chiral Lagrangians in dimensional and lattice regularizations. We present methods to compute 2-loop massless sunset diagrams…
A short pedagogical introduction to a differential method used to calculate multi-loop scalar integrals is presented. As an example it is shown how to obtain, using the method, large mass expansion of the two loop sunrise master integrals.
We discuss the analytical solution of the two-loop sunrise graph with arbitrary non-zero masses in two space-time dimensions. The analytical result is obtained by solving a second-order differential equation. The solution involves elliptic…
We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial…
We present the two-loop sunrise integral with arbitrary non-zero masses in two space-time dimensions in terms of elliptic dilogarithms. We find that the structure of the result is as simple and elegant as in the equal mass case, only the…
The $\epsilon$-expansion of several two-loop self-energy diagrams with different thresholds and one mass are calculated. On-shell results are reduced to multiple binomial sums which values are presented in analytical form.
This class of diagrams has numerous applications. Many interesting results have been obtained for it.
We consider the scalar integral associated to the 3-loop sunrise graph with a massless line, two massive lines of equal mass $M$, a fourth line of mass equal to $Mx$, and the external invariant timelike and equal to the square of the fourth…
Problems occurring in physically important non-trivial examples of loop calculations are discussed. A procedure of deriving expansions of two-loop self-energy diagrams with different masses is constructed. The cases of small and large…
The 4-loop sunrise graph with two massless lines, two lines of equal mass M and a line of mass m, for external invariant timelike and equal to m^2 is considered. We write differential equations in x=m/M for the Master Integrals of the…
We consider two loop sunset diagrams with two mass scales m and M at the threshold and pseudotreshold that cannot be treated by earlier published formula. The complete reduction to master integrals is given. The master integrals are…
In this talk, we discuss our recent computation of the two-loop sunrise integral with arbitrary non-zero particle masses. In two space-time dimensions, we arrive at a result in terms of elliptic dilogarithms. Near four space-time…
The main steps of the process of obtaining the result [1] in terms of elliptic polylogarithms for a two-loop sunrise integral with two different internal masses with pseudothreshold kinematics for all orders of the dimensional regulator are…
Using dispersive techniques, it is possible to avoid ultraviolet divergences in the calculation of Feynman diagrams, making subsequent regularization of divergent diagrams unnecessary. We give a simple introduction to the most important…
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…
In this paper, we consider the two-loop sunset diagram with two different masses, m and M, at spacelike virtuality q^2 = -m^2. We find explicit representations for the master integrals and an analytic result through O(epsilon) in…
The differential equations for the 2-loop sunrise graph, at equal masses but arbitrary momentum transfer, are used for the analytic evaluation of the coefficients of its Laurent-expansion in the continuous dimension $d$.
We derive recurrence relations for the calculation of multiloop sunset-type diagrams with large powers of massive propagators. The technique is formulated in configuration space and exploits the explicit form of the massive propagator…