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We present a general subtraction scheme for NNLO calculations in massless QCD: the \textit{colourful antenna subtraction method}. It is a reformulation of the antenna subtraction approach designed to address some of the limitations of the…

High Energy Physics - Phenomenology · Physics 2024-12-06 T. Gehrmann , E. W. N. Glover , M. Marcoli

Negative dimensional integration method (NDIM) is a technique to deal with D-dimensional Feynman loop integrals. Since most of the physical quantities in perturbative Quantum Field Theory (pQFT) require the ability of solving them, the…

High Energy Physics - Theory · Physics 2009-10-30 Alfredo T. Suzuki , Alexandre G. M. Schmidt

Reference [1] introduces a method for computing numerically four-dimensional multi-loop integrals without performing an explicit analytic contour deformation around threshold singularities. In this paper, we extend such a technique to…

High Energy Physics - Phenomenology · Physics 2024-07-26 Roberto Pittau

We report on the computation of a class of integrals that appear when integrating the so-called iterated singly-unresolved approximate cross section of the NNLO subtraction scheme of [1-4], over the factorised phase space of unresolved…

High Energy Physics - Phenomenology · Physics 2010-12-13 Gábor Somogyi , Paolo Bolzoni , Zoltán Trócsányi

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…

High Energy Physics - Phenomenology · Physics 2009-10-31 Francesco Caravaglios

In a recent paper we have presented an automated subtraction method for divergent multi-loop/leg integrals in dimensional regularisation which allows for their numerical evaluation, and applied it to diagrams with massless internal lines.…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. Binoth , G. Heinrich

We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…

Numerical Analysis · Mathematics 2013-05-23 J. E. Bunder , A. J. Roberts

We derive an analytic expression for the scalar one-loop pentagon and hexagon functions which is convenient for subsequent numerical integration. These functions are of relevance in the computation of next-to-leading order radiative…

High Energy Physics - Phenomenology · Physics 2013-12-02 T. Binoth , G. Heinrich , N. Kauer

We present methods to compute higher orders in the threshold expansion for the one-loop production of a Higgs boson in association with two partons at hadron colliders. This process contributes to the N$^3$LO Higgs production cross section…

High Energy Physics - Phenomenology · Physics 2015-09-30 Charalampos Anastasiou , Claude Duhr , Falko Dulat , Elisabetta Furlan , Franz Herzog , Bernhard Mistlberger

We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…

Numerical Analysis · Mathematics 2015-04-10 Sergio Blanes , Fernando Casas , J. M. Sanz-Serna

A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…

High Energy Physics - Phenomenology · Physics 2010-02-03 F. del Aguila , R. Pittau

So far, the use of different variants of dimensional regularization has been investigated extensively for two-loop virtual corrections. We extend these studies to real corrections that are also required for a complete computation of…

High Energy Physics - Phenomenology · Physics 2020-04-22 Christoph Gnendiger , Adrian Signer

We describe a first attempt to calculate scalar 2-loop box-functions with arbitrary internal masses, applying a novel method proposed in hep-ph/9407234. Four of the eight integrals are accessible to integration by means of the residue…

High Energy Physics - Phenomenology · Physics 2011-09-13 R. Kreckel , D. Kreimer , K. Schilcher

After a brief general introduction about the integrand-reduction method, we will review the main features of the GoSam 2.0 automated framework for one-loop calculations and illustrate its application to SM processes involving the production…

High Energy Physics - Phenomenology · Physics 2016-01-19 Giovanni Ossola

We present algorithms for computing weakly singular and near-singular integrals arising when solving the 3D Helmholtz equation with curved boundary elements. These are based on the computation of the preimage of the singularity in the…

Numerical Analysis · Mathematics 2022-06-28 Hadrien Montanelli , Matthieu Aussal , Houssem Haddar

Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for…

Numerical Analysis · Mathematics 2018-10-10 Akash Anand , Awanish Kumar Tiwari

In this paper we present the master integrals necessary for the analytic calculation of the box diagrams with one electron loop (N_{F}=1) entering in the 2-loop (\alpha^3) QED virtual corrections to the Bhabha scattering amplitude of the…

High Energy Physics - Phenomenology · Physics 2009-11-10 R. Bonciani , A. Ferroglia , P. Mastrolia , E. Remiddi , J. J. van der Bij

In this review, we present a new method for computing physical cross sections at NLO accuracy in QCD without using the standard Dimensional Regularisation. The algorithm is based on the Loop-Tree Duality theorem, which allow us to obtain…

High Energy Physics - Phenomenology · Physics 2016-11-23 R. J. Hernández-Pinto , F. Driencourt-Mangin , G. Rodrigo , G. F. R. Sborlini

In this paper, we aim to compute numerical approximation integral by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called…

Numerical Analysis · Mathematics 2015-07-22 Toni Sayah

We introduce a new numerical method for the computation of the inverse nonlinear Fourier transform and compare its computational complexity and accuracy to those of other methods available in the literature. For a given accuracy, the…

Numerical Analysis · Mathematics 2015-11-26 Stella Civelli , Luigi Barletti , Marco Secondini