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Related papers: Calculating multiloop integrals using dimensional …

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We develop the Tree-Loop Duality Relation for two- and three-loop integrals with multiple identical propagators (multiple poles). This is the extension of the Duality Relation for single poles and multiloop integrals derived in previous…

High Energy Physics - Phenomenology · Physics 2012-11-22 Isabella Bierenbaum , Sebastian Buchta , Petros Draggiotis , Ioannis Malamos , German Rodrigo

We describe a new method of calculation of generic multi-loop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using…

High Energy Physics - Phenomenology · Physics 2009-07-09 S. Laporta

New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts…

High Energy Physics - Theory · Physics 2010-04-05 A. P. Isaev

To entirely determine the resulting functions of one-loop integrals it is necessary to find the correct analytic continuation to all relevant kinematical regions. We argue that this continuation procedure may be performed in a general and…

High Energy Physics - Theory · Physics 2015-06-26 L. Bruecher , J. Franzkowski , D. Kreimer

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…

High Energy Physics - Phenomenology · Physics 2015-06-03 F. Yuasa , E. de Doncker , N. Hamaguchi , T. Ishikawa , K. Kato , Y. Kurihara , J. Fujimoto , Y. Shimizu

We consider the application of the DRA method to the case of several master integrals in a given sector. We establish a connection between the homogeneous part of dimensional recurrence and maximal unitarity cuts of the corresponding…

High Energy Physics - Phenomenology · Physics 2015-06-11 Roman N. Lee , Vladimir A. Smirnov

Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

Mathematical Physics · Physics 2020-09-03 Juuso Österman

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 compute all master integrals for massless three-loop four-particle scattering amplitudes required for processes like di-jet or di-photon production at the LHC. We present our result in terms of a Laurent expansion of the integrals in the…

High Energy Physics - Phenomenology · Physics 2020-05-20 Johannes Henn , Bernhard Mistlberger , Vladimir A. Smirnov , Pascal Wasser

The integration by parts recurrence relations allow to reduce some Feynman integrals to more simple ones (with some lines missing). Nevertheless the possibility of such reduction for the given particular integral was unclear. The recently…

High Energy Physics - Phenomenology · Physics 2009-10-31 P. A. Baikov

We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.

High Energy Physics - Phenomenology · Physics 2007-05-23 A. V. Kotikov

We present an efficient algorithm for calculating multiloop Feynman integrals perturbatively.

Quantum Physics · Physics 2009-10-31 Boris Kastening , Hagen Kleinert

We present a method to construct a suitable contour deformation in loop momentum space for multi-loop integrals. This contour deformation can be used to perform the integration for multi-loop integrals numerically. The integration can be…

High Energy Physics - Phenomenology · Physics 2015-06-12 Sebastian Becker , Stefan Weinzierl

We invent an automated method for computing the divergent part of Feynman integrals in dimensional regularization. Our method exploits simplifications from four-dimensional integration-by-parts identities. Leveraging algorithms from the…

High Energy Physics - Theory · Physics 2023-09-19 Johannes Henn , Rourou Ma , Kai Yan , Yang Zhang

Ab initio predictions of two-loop electroweak contributions to observables are increasingly essential for precision collider experiments, yet their evaluation remains very challenging. We connect recurrence techniques and dispersive method…

High Energy Physics - Phenomenology · Physics 2026-04-16 A. Aleksejevs , S. Barkanova , A. I. Davydychev

This article is the third and last of a series presenting an alternative method to compute the one-loop scalar integrals. It extends the results of first two articles to the infrared divergent case. This novel method enjoys a couple of…

High Energy Physics - Phenomenology · Physics 2020-02-26 J. Ph. Guillet , E. Pilon , Y. Shimizu , M. S. Zidi

We discuss new ideas for consideration of loop diagrams and angular integrals in $D$-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of…

High Energy Physics - Phenomenology · Physics 2021-06-11 Valery E. Lyubovitskij , Fabian Wunder , Alexey S. Zhevlakov

Recent results and methods of three-loop calculations in HQET are reviewed.

High Energy Physics - Phenomenology · Physics 2008-11-26 A. G. Grozin

This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…

High Energy Physics - Theory · Physics 2020-02-26 J. Ph. Guillet , E. Pilon , Y. Shimizu , M. S. Zidi

A method is introduced to calculate the UV-divergent parts at one-loop level in dimensional regularization. The method is based on the recursion, and the basic integrals are just the scaleless integrals after the recursive reduction, which…

High Energy Physics - Phenomenology · Physics 2012-02-21 Feng Feng