Related papers: Numerical multi-loop calculations: tools and appli…
We highlight the latest developments in computing higher-order scattering amplitudes with massive internal propagators. The contributing Feynman integrals often lead to special classes of functions, for example, functions associated with…
The method for functional reduction of Feynman integrals, proposed by the author, is used to calculate one-loop integrals corresponding to diagrams with four external lines. The integrals that emerge from amplitudes for the scattering of…
A program to calculate the three-particle hyperspherical brackets is presented. Test results are listed and it is seen that the program is well applicable up to very high values of the hypermomentum and orbital momenta. The listed runs show…
Starting from the parametric representation of a Feynman diagram, we obtain it's well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a…
Loop invariants are properties of a program loop that hold before and after each iteration of the loop. They are often employed to verify programs and ensure that algorithms consistently produce correct results during execution.…
This paper summarizes my doctoral research on evaluation algorithms for HEX-programs, which extend Answer Set Programming with means for interfacing external computations. The focus is on integrating different subprocesses of…
We present a semi-recursive method for calculating the rational parts of one-loop gravity amplitudes which utilises axial gauge diagrams to determine the non-factorising pieces of the amplitude. This method is used to compute the one-loop…
We briefly introduce new multiloop capabilities of the Mathematica package FeynCalc 10 and a collection of interfaces connecting FeynCalc to such popular tools as QGRAF, Fiesta, pySecDec, LoopTools, KIRA, FIRE or Fermat. In addition to…
We present a new procedure using on-shell recursion to determine coefficients of integral functions appearing in one-loop scattering amplitudes of gauge theories, including QCD. With this procedure, coefficients of integrals, including…
Provably correct software is one of the key challenges in our softwaredriven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction.…
Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a…
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…
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…
We present the version 2.0 of the program package GoSam, which is a public program package to compute one-loop QCD and/or electroweak corrections to multi-particle processes within and beyond the Standard Model. The extended version of the…
As the new-generation precision experiments such as MOLLER and P2 look for physics beyond Standard Model, it is becoming increasingly important to evaluate the higher-order electroweak radiative corrections to a sub-percent level of…
A method devised by the author is used to calculate analytical expressions for one loop integrals at finite temperature. A non-perturbative regularization of the integrals is performed, yielding expressions of non-polynomial nature. A…
To entirely determine the resulting functions of one-loop integrals it is necessary to find the correct analytic continuation to all relevant kinematical regions. We argue that this continuation procedure may be performed in a general and…
FormCalc is a Mathematica package for the automatic computation of tree-level and one-loop Feynman amplitudes. It accepts diagrams generated by FeynArts, simplifies them, and generates a complete Fortran code for their numerical evaluation.…
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.
Evaluation of a wide variety of Feynman diagrams with multi-loop integrals and physical parameters and its comparison with high energy experiments are expected to investigate new physics beyond the Standard Model. We have been developing a…