Related papers: Multi-loop calculations: numerical methods and app…
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 modern quantum field theory, one of the most important tasks is the calculation of loop integrals. Loop integrals appear when evaluating the Feynman diagrams with one or more loops by integrating over the internal momenta. Even though…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
We present algorithms to evaluate two types of multiple sums, which appear in higher-order loop computations. We consider expansions of a generalized hypergeometric-type sums, $\sum_{n_1,...,n_N} [Gamma(a1.n+c1) Gamma(a2.n}+c2) ...…
This paper is devoted to overview of the authors works for numerical solution of singular integral equations (SIE), polysingular integral equations and multi-dimensional singular integral equations of the second kind. The authors…
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…
In this thesis, major developments in the publicly available program SecDec are presented, extending the numerical evaluation of multi-loop multi-scale integrals from Euclidean to physical kinematics. The power of this new feature is shown…
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 numerical unitarity approach has been important for obtaining reliable QCD predictions for the LHC. Here I discuss the extension of the approach beyond the leading quantum corrections for computing multi-loop amplitudes. The numerical…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
We discuss recent progress towards extending the Helac framework to the calculation of two-loop amplitudes. A general algorithm for the automated computation of two-loop integrands is described. The algorithm covers all the steps of the…
A brief account is given of the problems involved in extended the pinch technique beyond the one-loop level, and of investigations into one possible approach to solving them.
Multiscale models allow for the treatment of complex phenomena involving different scales, such as remodeling and growth of tissues, muscular activation, and cardiac electrophysiology. Numerous numerical approaches have been developed to…
In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
We present the first numerical computation of two-loop amplitudes based on the unitarity method. As a proof of principle, we compute the four-gluon process. We discuss the new method, analyze its numerical properties and apply it to…
This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the…
This article reviews on-shell methods for analytic computation of loop amplitudes, emphasizing techniques based on unitarity cuts. Unitarity techniques are formulated generally but have been especially useful for calculating one-loop…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…