Related papers: Calculating multiloop integrals using dimensional …
We review the method of the calculation of multiloop integrals suggested in Ref.\cite{Lee2010}.
We show that dimensional recurrence relation and analytical properties of the loop integrals as functions of complex variable $\mathcal{D}$ (space-time dimensionality) provide a regular way to derive analytical representations of loop…
The approach to the constructing explicit solutions of the recurrence relations for multi-loop integrals are suggested. The resulting formulas demonstrate a high efficiency, at least for 3-loop vacuum integrals case. They also produce a new…
The systematic approach to solving the recurrence relations for multi-loop integrals is described. In particular, the criteria of their reducibility is suggested.
I present a few new and recent ideas of the multiloop calculations.
We formulate a method to find the meromorphic solutions of higher-order recurrence relations in the form of the sum over poles with coefficients defined recursively. Several explicit examples of the application of this technique are given.…
Explicit formulas for the solutions of the recurrence relations for 3--loop vacuum integrals are suggested. This formulas can be used for direct calculations and demonstrate a high efficiency. They also produce a new type of recurrence…
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.
A method for calculating the $1/d$ expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive…
I will present a new method for thinking about and for computing loop integrals based on differential equations. All required information is obtained by algebraic means and is encoded in a small set of simple quantities that I will…
We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems…
Explicit formulas for solutions of recurrence relations for 3--loop vacuum integrals are generalized for the $n$-loop case.
A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals w.r.t. the space-time dimension $d$ is proposed. The relation between $d$ and $d-2$ dimensional integrals is given in terms of a…
We describe a constructive procedure to separate overlapping infrared divergences in multi-loop integrals. Working with a parametric representation in D=4-2*epsilon dimensions, adequate subtractions lead to a Laurent series in epsilon,…
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…
The implementation of an algorithm for three-loop massive vacuum integrals, based on the explicit solution of the recurrence relations, in REDUCE and FORM is described.
We report on a program for the numerical evaluation of divergent multi-loop integrals. The program is based on iterated sector decomposition. We improve the original algorithm of Binoth and Heinrich such that the program is guaranteed to…
A method to isolate the poles of dimensionally regulated multi-loop integrals and to calculate the pole coefficients numerically is extended to be applicable to phase space integrals as well.
Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…
In a previous paper a new approach has been introduced for computing, recursively and numerically, one-loop tensor integrals. Here we describe a few modifications of the original method that allow a more efficient numerical implementation…