相关论文: Evaluation of a Class of Two-Scale Three-Loop Vacu…

Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, only results for integrals with one and two independent mass scales are known, but in the electroweak…

We calculate analytically a class of three-loop vacuum diagrams with two different mass values, one of which is one-third as large as the other, using the method of Chetyrkin, Misiak, and M\"{u}nz in the dimensional regularization scheme.…

I describe a method to calculate a class of three-loop selfenergy diagrams for arbitrary internal masses and external momentum. This method combines analytical results and numerical integration, and is suitable for implementation in a…

Tensor reduction of vacuum diagrams uses contraction and decomposition matrices. We present general recurrence relations for the calculation of those matrices and an explicit formula for the 3-loop decomposition matrix and its determinant.

General algorithms for tensor reduction of two-loop massive vacuum diagrams are discussed. Some explicit useful formulae are presented.

We obtain finite parts (as well as $\epsilon$-pole parts) of massive three-loop vacuum diagrams with three-point and/or four-point interaction vertices by reducing them to tetrahedron diagrams with both massive and massless lines, whose…

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 study the problem of calculating two-loop three-point diagrams with irreducible numerators (i.e. numerators which cannot be expressed in terms of the denominators). For the case of massless internal particles and arbitrary (off-shell)…

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…

This paper provides details of the massless three-loop three-point integrals calculation at the symmetric point. Our work aimed to extend known two-loop results for such integrals to the three-loop level. Obtained results can find their…

Four 3-loop two-point functions are studied analytically and numerically using a simplified sector decomposition method. The coefficients of the ultraviolet divergent part are determined analytically, and those of the finite part are…

We evaluate the three-loop massive vacuum bubble diagrams in terms of polylogarithms up to weight six. We also construct the basis of irrational constants being harmonic polylgarithms of arguments $e^{k i \pi/3}$.

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…

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…

Explicit general formulae for the tensor reduction of two-loop massive vacuum diagrams are presented. The problem of calculating the corresponding coefficients is shown to be equivalent to the problem of constructing differential operators…

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…

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…

A number of exact results for two-loop three-point diagrams with massless internal particles and arbitrary (off-shell) external momenta are presented. Divergent contributions are calculated in the framework of dimensional regularization.

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…

In this paper we describe a new method of calculation of master integrals based on the solution of systems of difference equations in one variable. An explicit example is given, and the generalization to arbitrary diagrams is described. As…