Related papers: Evaluating double and triple (?) boxes
General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.
We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of…
This manuscript addresses the analysis and design of feedback laws for the stabilization of bilinear control systems in infinite-dimensional spaces. It first examines weak, strong, and polynomial stabilization within a Hilbert space…
Unbounded (and bounded) Toeplitz operators (TO) with rational symbols are analysed in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains,…
In this sequel calculation of the one-loop Feynman integral pertaining to a massive box diagram contributing to the photon-photon scattering amplitude in quantum electrodynamics, we present the six solutions as yet unknown in the…
We calculate the general planar dual-conformally invariant double-pentagon and pentabox integrals in four dimensions. Concretely, we derive one-fold integral representations for these elliptic integrals over polylogarithms of weight three.…
We calculate analytically the master integrals of a planar double-box family for top-quark pair production using the method of differential equations. With a proper choice of the bases, the differential equations can be transformed to the…
Some recent results on evaluating Feynman integrals are reviewed. The status of the method based on Mellin-Barnes representation as a powerful tool to evaluate individual Feynman integrals is characterized. A new method based on Groebner…
When calculating higher terms of the epsilon-expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with…
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…
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…
It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples…
A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums.…
In this article, we present the package {\tt Blade} as the first implementation of the block-triangular form improved Feynman integral reduction method. The block-triangular form has orders of magnitude fewer equations compared to the plain…
The construction of Mellin-Barnes (MB) representations for non-planar Feynman diagrams and the summation of multiple series derived from general MB representations are discussed. A basic version of a new package AMBREv.3.0 is supplemented.…
The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for untangled (i.e. non-concatenated and unknotted) rings,…
Recently, infinite families of massive Feynman integrals were found to feature an unexpected Yangian symmetry. In the massless case, similar integrability properties are understood via the interpretation of individual Feynman integrals as…
The method of differential equations in canonical form has proven a powerful tool for solving multiloop Feynman integrals. In this note we test this procedure away from four dimensions. Namely, we consider the simple example of a massless…
We summarize two geometrical approaches to analytically evaluate higher-fold Mellin-Barnes (MB) integrals in terms of hypergeometric functions. The first method is based on intersections of conic hulls, while the second one, which is more…
Manifestly N=2 supersymmetric Feynman rules are found for different off-shell realizations of the massless hypermultiplet in projective superspace. When we reduce the Feynman rules to an N=1 superspace we obtain the correct component…