arXiv subjects

E. de Doncker

Publications and source records attributed to E. de Doncker.

8 recordsLinked to original sources

arXiv2018

Regularization with Numerical Extrapolation for Finite and UV-Divergent Multi-loop Integrals

We give numerical integration results for Feynman loop diagrams such as those covered by Laporta [1] and by Baikov and Chetyrkin [2], and which may give rise to loop integrals with UV singularities. We explore automatic adaptive integration using multivariate techniques from the PARINT package for multivariate integration, as well as iterated in- tegration with programs from the QUADPACK package, and a trapezoidal method based on a double exponential trans- formation. PARINT is layered over MPI (Message Passing Interface), and incorporates advanced parallel/distributed techniques including load balancing among processes that may be distributed over a cluster or a network/grid of nodes. Results are included for 2-loop vertex and box diagrams and for sets of 2-, 3- and 4-loop self-energy diagrams with or without UV terms. Numerical regularization of integrals with singular terms is achieved by linear and non-linear extrapolation methods.

hep-ph↗

arXiv2012

Numerical Computation of Two-loop Box Diagrams with Masses

A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass configurations. As an example, the computation of two-loop planar and non-planar box diagrams is shown. The results are confirmed by comparisons with other techniques, including the reduction method, and by a consistency check using the dispersion relation.

hep-ph↗

arXiv2012

Numerical approach to multi-loop integrals

For the calculation of multi-loop Feynman integrals, a novel numerical method, the Direct Computation Method (DCM) is developed. It is a combination of a numerical integration and a series extrapolation. In principle, DCM can handle diagrams of arbitrary internal masses and external momenta, and can calculate integrals with general numerator function. As an example of the performance of DCM, a numerical computation of two-loop box diagrams is presented. Further discussion is given on the choice of control parameters in DCM. This method will be an indispensable tool for the higher order radiative correction when it is tested for a wider class of physical parameters and the separation of divergence is done automatically.

hep-ph↗

arXiv2011

Numerical Approach to Calculation of Feynman Loop Integrals

In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried out in a fully numerical way, our approach is applicable to one-, two- and multi-loop diagrams. Without any analytic treatment it can compute diagrams with not only real masses but also complex masses for the internal particles. As concrete examples we present numerical results of a scalar one-loop box integral with complex masses and two-loop planar and non-planar box integrals with masses. We discuss the quality of our numerical computation by comparisons with other methods and also propose a self consistency check.

hep-ph↗

arXiv2009

Numerical Evaluation of Feynman Integrals by a Direct Computation Method

A purely numerical method, Direct ComputationMethod is applied to evaluate Feynman integrals. This method is based on the combination of an efficient numerical integration and an efficient extrapolation. In addition, high-precision arithmetic and parallelization technique can be used in this method if required. We present the recent progress in development of this method and show results such as one-loop 5-point and two-loop 3-point integrals.

hep-ph↗

arXiv2007

Status reports from the GRACE Group

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 based on the $ε$-algorithm. In our approach, the super high precision control in the numerical manipulation is essential to handle the infrared singularity. We adopt a multi-precision library named {\tt HMLib} for the precision control in the calculations.

hep-ph↗

arXiv2007

Precise Numerical Evaluation of the Scalar One-Loop Integrals with the Infrared Divergence

We present a new approach for obtaining very precise integration results for infrared vertex and box diagrams, where the integration is carried out directly without performing any analytic integration of Feynman parameters. Using an appropriate numerical integration routine with an extrapolation method, together with a multi-precision library, we have obtained integration results which agree with the analytic results to 10 digits even for such a very small photon mass as $10^{-150}$ GeV in the infrared vertex diagram.

hep-ph↗

arXiv2004

Loop integration results using numerical extrapolation for a non-scalar integral

Loop integration results have been obtained using numerical integration and extrapolation. An extrapolation to the limit is performed with respect to a parameter in the integrand which tends to zero. Results are given for a non-scalar four-point diagram. Extensions to accommodate loop integration by existing integration packages are also discussed. These include: using previously generated partitions of the domain and roundoff error guards.

hep-ph↗