Related papers: A simple method for multi-leg loop calculations 2:…
The unitarity method for calculating one-loop amplitudes provides algorithms of polynomial complexity. This is primarily beneficial for the computation of multi-leg one loop amplitudes and it is therefore of great interest to develop a…
A simplified differential equations approach for Master Integrals is presented. It allows to express them, straightforwardly, in terms of Goncharov Polylogarithms. As a proof-of-concept of the proposed method, results at one and two loops…
We discuss briefly the first numerical implementation of the Loop-Tree Duality (LTD) method. We apply the LTD method in order to calculate ultraviolet and infrared finite multi-leg one-loop Feynman integrals. We attack scalar and tensor…
We give the results of complete analytical computations of two- and three-point loop integrals ocurring in heavy particle theories, with and without velocity change, for arbitrary values of external momenta and masses.
Using the parallel/orthogonal space method, we calculate the planar two-loop three-point diagram and two rotated reduced planar two-loop three-point diagrams. Together with the crossed topology, these diagrams are the most complicated ones…
We present analytical results for one-loop five-point master integrals with up to three off-shell legs. The method of canonical differential equations along with the Simplified Differential Equations approach is employed. All necessary…
We present a method to construct a suitable contour deformation in loop momentum space for multi-loop integrals. This contour deformation can be used to perform the integration for multi-loop integrals numerically. The integration can be…
In this talk we describe our approach for the computation of multi-leg one-loop amplitudes and present some first results relevant for LHC phenomenology.
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is…
A general method for reducing tensor form factors, that appear in one-loop calculations in dimensional regularization, to scalar integrals is presented. The method is an extension of the reduction scheme introduced by Passarino and Veltman…
In this article a group-theoretical aspect of the method of dimensional reduction is presented. Then, on the base of symmetry analysis for an anisotropic space geometrical description of dimensional reduction of equation for scalar field is…
A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…
Calculation of amplitudes in perturbative quantum field theory involve large loop integrals. The complexity of those integrals, in combination with the large number of Feynman diagrams, make the calculations very difficult. Reduction…
We calculate the complete set of two-loop Master Integrals with two off mass-shell legs with massless internal propagators, that contribute to amplitudes of diboson $V_1V_2$ production at the LHC. This is done with the Simplified…
This article describes a bipedal walking algorithm with inverse kinematics resolution based solely on geometric methods, so that all mathematical concepts are explained from the base, in order to clarify the reason for this solution. To do…
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 present a semi-numerical algorithm to calculate one-loop virtual corrections to scattering amplitudes. The divergences of the loop amplitudes are regulated using dimensional regularization. We treat in detail the case of amplitudes with…
We explicitly construct a class of multivariate generalized hypergeometric series which is conjectured in our previous paper [Alkalaev & Mandrygin 2025] to calculate multipoint one-loop parametric conformal integrals in $D$ dimensions. Our…
One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In this paper, we reconsider the problem by applying differential operators…
We study the problem of calculating two-loop three-point diagrams with irreducible numerators (i.e. numerators which cannot be expressed in terms of the denominators). For the case of massless internal particles and arbitrary (off-shell)…