Related papers: General Formula for N-point One-loop Feynman Integ…
A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of…
We compute the six-dimensional hexagon integral with three non-adjacent external masses analytically. After a simple rescaling, it is given by a function of six dual conformally invariant cross-ratios. The result can be expressed as a sum…
As a key method to deal with loop integrals, Integration-By-Parts (IBP) method can be used to do reduction as well as establish the differential equations for master integrals. However, when talking about tensor reduction, the…
Off-shell string-inspired methods (OSSIM) calculate off-shell QCD Green's functions using Schwinger-Feynman proper-time techniques, always in the background field method (BFM) Feynman gauge for technical convenience, and so far only at one…
We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial…
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 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…
By worldsheet approach, $n$-point one-loop integrand can be expressed as a combination of $(n+2)$-point tree-level bi-adjoint scalar (BS) amplitudes under forward limit. The integrands constructed by this approach have two closely related…
Parametric Feynman integrals with the regions of integration defined by some polynomials are considered in this paper. It is shown that integrals with irregular integration regions can be converted to standard parametric integrals, for…
We present a new FORM program for analytically evaluating four-loop massless propagator-type Feynman integrals in an efficient way. Our program Forcer implements parametric reductions of the aforementioned class of Feynman integrals into a…
We present the powerful module-intersection integration-by-parts (IBP) method, suitable for multi-loop and multi-scale Feynman integral reduction. Utilizing modern computational algebraic geometry techniques, this new method successfully…
The concepts of Feynman integrals in white noise analysis are used to realize the Feynman integrand for a charged particle in a constant magnetic field as a Hida distribution. For this purpose we identify the velocity dependent potential as…
We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and…
We deal with the problem of description of nonsingular pairs of compatible flat metrics for the general $N$-component case. We describe the scheme of the integrating the nonlinear equations describing nonsingular pairs of compatible flat…
We apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. After a set of master integrals has been found using the integration-by-parts method, the crucial point of…
In the first-quantised worldline approach to quantum field theory, a long-standing problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In…
We present a new Fortran code to calculate the scalar one-loop four-point integral with complex internal masses, based on the method of 't Hooft and Veltman. The code is applicable when the external momenta fulfill a certain physical…
The scalar two-loop master diagram is revisited in the massive cases needed for the computation of boson and fermion propagators in QED and QCD. By means of the causal method it is possible in a straightforward manner to express the…
We present a new algorithm for the reduction of one-loop tensor Feynman integrals within the framework of the XLOOPS project, covering both mathematical and programming aspects. The new algorithm supplies a clean way to reduce the one-loop…
We show that all Feynman integrals in two Euclidean dimensions with massless propagators and arbitrary non-integer propagator powers can be expressed in terms of single-valued analogues of Aomoto-Gelfand hypergeometric functions. The latter…