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Related papers: Analytic results for one-loop integrals in dimensi…

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An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…

Computational Physics · Physics 2007-05-23 A. A. Zhmudsky

We propose a variant of elliptic multiple polylogarithms that have at most logarithmic singularities in all variables and satisfy a differential equation without homogeneous term. We investigate several non-trivial elliptic two-loop Feynman…

High Energy Physics - Theory · Physics 2019-01-30 Johannes Broedel , Claude Duhr , Falko Dulat , Brenda Penante , Lorenzo Tancredi

In a recent paper we have presented results for a set of massive scalar one-loop master integrals needed in the NNLO parton model description of the hadroproduction of heavy flavors. The one--loop integrals were evaluated in $n=4-2\ep$…

High Energy Physics - Phenomenology · Physics 2016-08-16 J. G. Körner , Z. Merebashvili , M. Rogal

We use dimensional regularization to evaluate quantum mechanical path integrals in arbitrary curved spaces on an infinite time interval. We perform 3-loop calculations in Riemann normal coordinates, and 2-loop calculations in general…

High Energy Physics - Theory · Physics 2009-10-31 F. Bastianelli , O. Corradini , P. van Nieuwenhuizen

We report our experiences with the generalized integration-by-parts algorithm [hep-ph/9609429] in the context of calculations of a realistic one-loop subset of diagrams.

High Energy Physics - Phenomenology · Physics 2007-05-23 D. Yu. Bardin , L. V. Kalinovskaya , F. V. Tkachov

We present fully analytic results for all master integrals for the three-loop banana graph with four equal and non-zero masses. The results are remarkably simple and all integrals are expressed as linear combinations of iterated integrals…

High Energy Physics - Theory · Physics 2019-10-23 Johannes Broedel , Claude Duhr , Falko Dulat , Robin Marzucca , Brenda Penante , Lorenzo Tancredi

We present a fully analytic approach for evaluating boundary integrals in two dimensions for Smoothed Particle Hydrodynamics (SPH). Conventional methods often rely on boundary particles or wall re-normalization approaches derived from…

Numerical Analysis · Mathematics 2025-07-30 Rene Winchenbach , Andreas Kolb

We determine the complete three-loop QCD soft anomalous dimension for multileg amplitudes involving a single massive coloured particle and any number of massless ones. This is achieved by applying a novel strategy based on a lightcone…

High Energy Physics - Phenomenology · Physics 2025-11-03 Einan Gardi , Zehao Zhu

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

The main difficulty in solving the Helmholtz equation within polygons is due to non-analytic vertices. By using a method nearly identical to that used by Fox, Henrici, and Moler in their 1967 paper; it is demonstrated that such eigenvalue…

Numerical Analysis · Mathematics 2016-03-01 Robert Jones

We present methods for evaluating the Feynman parameter integrals associated with the pentagon diagram in 4-2 epsilon dimensions, along with explicit results for the integrals with all masses vanishing or with one non-vanishing external…

High Energy Physics - Phenomenology · Physics 2010-11-15 Z. Bern , L. Dixon , D. A. Kosower

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

We present a set of algebraic functions for evaluating the coefficients of the scalar integral basis of a general one-loop amplitude. The functions are derived from unitarity cuts, but the complete cut-integral procedure has been carried…

High Energy Physics - Phenomenology · Physics 2008-11-26 Ruth Britto , Bo Feng

The dimensionally regularized massless on-shell planar triple box Feynman diagram with powers of propagators equal to one is analytically evaluated for general values of the Mandelstam variables s and t in a Laurent expansion in the…

High Energy Physics - Phenomenology · Physics 2009-11-10 V. A. Smirnov

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

This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided…

Numerical Analysis · Mathematics 2025-06-17 Zibo Zhao

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…

High Energy Physics - Phenomenology · Physics 2011-09-21 F. Yuasa , T. Ishikawa , Y. Kurihara , J. Fujimoto , Y. Shimizu , N. Hamaguchi , E. de Doncker , K. Kato

In this article we provide representations for the one-loop three point functions in 4 and 6 dimensions in the general case with complex masses. The latter are part of the GOLEM library used for the computation of one-loop multileg…

High Energy Physics - Phenomenology · Physics 2015-06-17 J. Ph. Guillet , E. Pilon , M. Rodgers , M. S. Zidi

We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the $\rho$ parameter. In particular, we present the calculation of the master integrals for which the corresponding…

High Energy Physics - Phenomenology · Physics 2018-07-17 J. Blümlein , A. De Freitas , M. van Hoeij , E. Imamoglu , P. Marquard , C. Schneider

We provide a complete set of results for the scalar 4-point function appearing in one-loop calculations in QCD, QED, the electroweak Standard Model and popular extensions thereof. Complex internal masses, which are needed for calculations…

High Energy Physics - Phenomenology · Physics 2010-12-14 A. Denner , S. Dittmaier