相关论文: Laurent series expansion of sunrise-type diagrams …

We present a method to compute the Laurent expansion of the two-loop sunrise integral with equal non-zero masses to arbitrary order in the dimensional regularisation $\varepsilon$. This is done by introducing a class of functions…

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 $d$.

In this lecture series I will give a fundamental insight into configuration space techniques which are of help to calculate a broad class of Feynman diagrams, the sunrise-type diagrams. Applications are shown along with basic concepts and…

We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of…

We use configuration space methods to write down one-dimensional integral representations for one- and two-loop sunrise diagrams (also called Bessel moments) which we use to numerically check on the correctness of the second order…

We integrate three-loop sunrise-type vacuum diagrams in $D_0=4$ dimensions with four different masses using configuration space techniques. The finite parts of our results are in numerical agreement with corresponding three-loop…

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…

By use of the threshold expansion we develop an algorithm for analytical evaluation, within dimensional regularization, of arbitrary terms in the expansion of the (two-loop) sunset diagram with general masses m_1, m_2 and m_3 near its…

The two loop equal mass sunrise graph is considered in the continuous d-dimensional regularisation for arbitrary values of the momentum transfer. After recalling the equivalence of the expansions at d=2 and d=4, the second order…

We consider the two-loop self-mass sunrise amplitude with two equal masses $M$ and the external invariant equal to the square of the third mass $m$ in the usual $d$-continuous dimensional regularization. We write a second order differential…

We summarize recent computations with a class of elliptic generalizations of polylogarithms, arising from the massive sunrise integral. For the case of arbitrary masses we obtain results in two and four space-time dimensions. The iterated…

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…

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…

We show that the Laurent series of the two-loop kite integral in $D=4-2\varepsilon$ space-time dimensions can be expressed in each order of the series expansion in terms of elliptic generalisations of (multiple) polylogarithms. Using…

We propose a novel method for reconstructing Laurent expansion of rational functions using $p$-adic numbers. By evaluating the rational functions in $p$-adic fields rather than finite fields, it is possible to probe the expansion…

We compute the (three) master integrals for the crossed ladder diagram with two exchanged quanta of equal mass. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the…

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…

We use dimensional regularization to calculate the ${\cal O}(\ep^2)$ expansion of all scalar one-loop one-, two-, three- and four-point integrals that are needed in the calculation of hadronic heavy quark production. The Laurent series up…

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…

For a large class of two-loop selfenergy- and vertex-type diagrams with only one non-zero mass ($M$) and the vertices also with only one non-zero external momentum squared ($q^2$) the first few expansion coefficients are calculated by the…