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We present a method to numerically evaluate infrared-finite one- and two-loop integrals within the Four-Dimensional Regularization/Renormalization approach, in which a small mass serves as regulator. Typical integrals exhibit a logarithmic…
We discuss a new approach for the numerical evaluation of loop integrals. The fully numerical calculations of an infrared one-loop vertex and a box diagram are demonstrated. To perform these calculations, we apply an extrapolation method…
Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, only results for integrals with one and two independent mass scales are known, but in the electroweak…
I present a few new and recent ideas of the multiloop calculations.
We describe a general analytic-numerical reduction scheme for evaluating any 2-loop diagrams with general kinematics and general renormalizable interactions, whereby ten special functions form a complete set after tensor reduction. We…
Modern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders…
We present a new method for the numerical evaluation of arbitrary loop integrals in dimensional regularization. We first derive Mellin-Barnes integral representations and apply an algorithmic technique, based on the Cauchy theorem, to…
Ab initio predictions of two-loop electroweak contributions to observables are increasingly essential for precision collider experiments, yet their evaluation remains very challenging. We connect recurrence techniques and dispersive method…
We present TVID 2, a program to numerically evaluate an important class of planar three-loop self-energy master integrals with arbitrary masses. As with the predecessor version (TVID 1) the integrals are separated into a known piece,…
In this paper we consider multi-loop integrals appearing in MHV scattering amplitudes of planar N=4 SYM. Through particular differential operators which reduce the loop order by one, we present explicit equations for the two-loop…
We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example.
We study a recently-proposed approach to the numerical evaluation of multi-loop Feynman integrals using available sector decomposition programs. As our main example, we consider the two-loop integrals for the $\alpha \alpha_s$ corrections…
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.
The paper describes a new algorithm of construction of the nonlinear arithmetic triangle on the basis of numerical simulation and the binary system. It demonstrates that the numbers that fill the nonlinear arithmetic triangle may be…
This article is the first of a series of three presenting an alternative method to compute the one-loop scalar integrals. This novel method enjoys a couple of interesting features as compared with the method closely following 't Hooft and…
In a series of papers we have developed the method of iterated sector decomposition for the calculation of infrared divergent multi-loop integrals. Here we apply it to phase space integrals to calculate a contribution to the double real…
We propose a new approach that allows for the separate numerical calculation of the real and imaginary parts of finite loop integrals. We find that at one-loop the real part is given by the Loop-Tree Duality integral supplemented with…
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.
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)…
We study the applicability of the Z-Sum approach to multi-loop calculations with massive particles in perturbative quantum field theory. We systematically analyze the case of one-loop scalar integrals, which represent the building blocks of…