Related papers: Numerical integration of the double- and triple-bo…
I discuss an application of numerical techniques for massive two-loop Feynman diagram evaluation to a phenomenologically very important rare decay process, B -> X_s l+l-. This process, currently being measured at B factories, has been…
This paper considers computational methods that split a vector field into three components in the case when both the vector field and the split components might be unbounded. We first employ classical Taylor expansion which, after some…
We evaluate the three-loop five-point pentagon-box-box massless integral family in the dimensional regularization scheme, via canonical differential equation. We use tools from computational algebraic geometry to enable the necessary…
In order to prepare the ground for evaluating classes of three-loop sum-integrals that are presently needed for thermodynamic observables, we take a fresh and systematic look on the few known cases, and review their evaluation in a unified…
We introduce a method to obtain the analytic solution of the higher-order Baxter equation for twist-two and twist-three operators of planar N=4 SYM. Our result proofs the conjectured formula for the three-loop anomalous dimension of…
Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…
The class of the two-loop massless crossed boxes, with light-like external legs, is the final unresolved issue in the program of computing the scattering amplitudes of 2 --> 2 massless particles at next-to-next-to-leading order. In this…
In symbolic integration, the Risch--Norman algorithm aims to find closed forms of elementary integrals over differential fields by an ansatz for the integral, which usually is based on heuristic degree bounds. Norman presented an approach…
Inverse scattering involving microwave and ultrasound waves require numerical solution of nonlinear optimization problem. To alleviate the computational burden of a full three-dimensional (3-D) inverse problem, it is a common practice to…
We present the computation of the contributions to N3LO inclusive Higgs boson production due to two-loop amplitudes. Our result is a Laurent expansion in the dimensional regulator, with coefficients that are linear combinations of harmonic…
We present an integral equation-based method for the numerical solution of two-point boundary value systems. Special care is devoted to the mathematical formulation, namely the choice of the background Green's function that leads to a…
Combining sum factorization, weighted quadrature, and row-based assembly enables efficient higher-order computations for tensor product splines. We aim to transfer these concepts to immersed boundary methods, which perform simulations on a…
Building on the idea of numerically integrating differential equations satisfied by Feynman integrals, we propose a novel strategy for handling branch cuts within a numerical framework. We develop an integrator capable of evaluating a basis…
In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the…
We analyze and implement the Local Analytic Sector Subtraction (LASS) scheme for handling infrared singularities in next-to-next-to-leading order (NNLO) calculations in perturbative QCD. We examine the key aspects of the scheme including…
This paper investigates a class of algorithms for numerical integration of a function in d dimensions over a compact domain by Monte Carlo methods. We construct a histogram approximation to the function using a partition of the integration…
We show how to compute the two-loop sunset integrals at finite volume, for non-degenerate masses and non-zero momentum. We present results for all integrals that appear in the Chiral Perturbation Therory ($\chi$PT) calculation of the…
In this paper I give an evaluation of a functional integral by means of a series in functional derivatives, first of all we propose a differential equation of first order and solve it by iterative methods, to obtain a series for the…
A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of…
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…