相关论文: Three-loop vacuum integrals in FORM and REDUCE
We use the method of differential equations to analytically evaluate all planar three-loop Feynman integrals relevant for form factor calculations involving massive particles. Our results for ninety master integrals at general $q^2$ are…
We derive analytic results for scalar massless bosonic vacuum sum-integrals at two loops. Building upon a recent factorization proof of massive two-loop vacuum integrals, we are able to solve the corresponding Matsubara sums and map the…
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…
Recursion relations for Hylleraas three-electron integral are obtained in a closed form by using integration by parts identities. Numerically fast and well stable algorithm for the calculation of the integral with high powers of…
In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…
In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive…
We study the problem how to deal with tensor-type two-loop integrals in the Loop Regularization (LORE) scheme. We use the two-loop photon vacuum polarization in the massless Quantum Electrodynamics (QED) as the example to present the…
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…
We present a new numerical dissipation algorithm, which can be efficiently used in combination with centered finite-difference methods. We start from a formulation of centered finite-volume methods for Numerical Relativity, in which…
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…
In this article, we present a new analytic result for a certain single-mass-scale four-loop vacuum (bubble) integral. We also discuss its systematic $\e$-expansion in $d=4-2\e$ as well as $d=3-2\e$ dimensions, the coefficients of which are…
We provide an update on a long-term project that aims at evaluating massive vacuum integrals at the five-loop frontier, with high precision and in various space-time dimensions. A number of applications are sketched, mainly concerning the…
Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms.…
We evaluate in closed form several classes of finite trigonometric sums. Two general methods are used. The first is new and involves sums of roots of unity. The second uses contour integration and extends a previous method used by two of…
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…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
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…
We introduce in typical examples new methods for the calculation of massive loop integrals appearing in the radiative correction calculations of the Standard Model.
We give technical details about the computational strategy employed in a recently completed investigation of the four-loop QCD free energy. In particular, the reduction step from generic vacuum bubbles to master integrals is described from…
The effective potential is known to be given by the vacuum diagrams. In this paper we show that the massive loop integrations corresponding to the vacuum diagrams can be expressed through the massless loop integrations with the…