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Related papers: A numerical method for NNLO calculations

200 papers

The status of numerical evaluations of Mellin-Barnes integrals is discussed, in particular, the application of the quasi-Monte Carlo integration package QMC to the efficient calculation of multi-dimensional integrals.

High Energy Physics - Phenomenology · Physics 2019-12-25 Ievgen Dubovyk , Janusz Gluza , Tord Riemann

An approach to (normalized) infinite dimensional integrals, including normalized oscillatory integrals, through a sequence of evaluations in the spirit of the Monte Carlo method for probability measures is proposed. in this approach the…

Mathematical Physics · Physics 2015-06-05 Jean-Pierre Magnot

A connection between one-loop $N$-point Feynman diagrams and certain geometrical quantities in non-Euclidean geometry is discussed. A geometrical way to calculate the corresponding Feynman integrals is considered. (This paper contains a…

High Energy Physics - Theory · Physics 2011-03-17 A. I. Davydychev , R. Delbourgo

It is described how the method of sector decomposition can serve to disentangle overlapping infrared singularities, in particular those occurring in the calculation of the real emission part of e+e- to 2 jets and e+e- to 3 jets at NNLO.

High Energy Physics - Phenomenology · Physics 2009-11-10 G. Heinrich

In this talk, we discuss the speed-up of numerical calculations of jet observables by replacing the usual sum over all helicity amplitudes with an integral over a parametrisation for the parton polarisations called random polarisations.…

High Energy Physics - Phenomenology · Physics 2013-11-25 Daniel Goetz , Christopher Schwan , Stefan Weinzierl

We describe methods for evaluating one-loop integrals in $4-2\e$ dimensions. We give a recursion relation that expresses the scalar $n$-point integral as a cyclicly symmetric combination of $(n-1)$-point integrals. The computation of such…

High Energy Physics - Phenomenology · Physics 2008-11-26 Z. Bern , L. Dixon , D. A. Kosower

We present an improved version of our program package oneloop which -- written as a package for MAPLE -- solves one-loop Feynman integrals. The package is calculating one-, two- and three-point functions both algebraically and numerically…

High Energy Physics - Phenomenology · Physics 2009-10-30 L. Brücher , J. Franzkowski , D. Kreimer

Using the parallel/orthogonal space method, we calculate the planar two-loop three-point diagram and two rotated reduced planar two-loop three-point diagrams. Together with the crossed topology, these diagrams are the most complicated ones…

High Energy Physics - Phenomenology · Physics 2009-01-07 Stefan Groote , Markus M. Knodel

We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which…

High Energy Physics - Phenomenology · Physics 2013-12-16 T. Binoth , J. Ph. Guillet , G. Heinrich , E. Pilon , C. Schubert

We present a semi-numerical method to compute one-loop corrections to processes involving many particles. We treat in detail cases with up to five external legs and massless internal propagators, although the method is more general.

High Energy Physics - Phenomenology · Physics 2008-11-26 G. Zanderighi

The program package XLOOPS calculates massive one- and two-loop Feynman diagrams. It consists of five parts: i) a graphical user interface ii) routines for generating diagrams from particle input iii) procedures for calculating one-loop…

High Energy Physics - Phenomenology · Physics 2011-02-11 L. Brücher , J. Franzkowski , A. Frink , D. Kreimer

Some of the tools and techniques that have recently been used to compute Higgs boson pair production at NLO in QCD are discussed. The calculation relies on the use of integral reduction, to reduce the number of integrals which must be…

High Energy Physics - Phenomenology · Physics 2016-08-15 S. P. Jones

We propose a new method for numerical calculation of link plynomials for knots given in 3 dimensions. We calculate derivatives of the Jones polynomial in a computational time proportional to $N^{\alpha}$ with respect to the system size $N$…

High Energy Physics - Theory · Physics 2009-10-22 Tetsuo Deguchi , Kyoichi Tsurusaki

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…

High Energy Physics - Phenomenology · Physics 2009-11-10 E. de Doncker , Y. Shimizu , J. Fujimoto , F. Yuasa , K. Kaugars , L. Cucos , J. Van Voorst

We compute angular phase-space integrals with three and four denominators analytically, working within dimensional regularisation via the Mellin-Barnes (MB) representation. The approach converts multifold MB integrals into real parametric…

High Energy Physics - Phenomenology · Physics 2026-04-03 Taushif Ahmed , Syed Mehedi Hasan , Andreas Rapakoulias

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

We evaluate all phase space master integrals which are required for the total cross section of generic 2 -> 1 processes at NNLO as a series expansion in the dimensional regulator epsilon. Away from the limit of threshold production, our…

High Energy Physics - Phenomenology · Physics 2015-06-11 Charalampos Anastasiou , Stephan Buehler , Claude Duhr , Franz Herzog

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

Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…

Classical Analysis and ODEs · Mathematics 2015-06-26 Bille C. Carlson

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…

High Energy Physics - Phenomenology · Physics 2020-03-18 Costas G. Papadopoulos , Christopher Wever