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We present a new method for the numerical evaluation of arbitrary loop integrals in dimensional regularization. We first derive Mellin-Barnes integral representations and apply an algorithmic technique, based on the Cauchy theorem, to…

High Energy Physics - Phenomenology · Physics 2009-11-11 Charalampos Anastasiou , Alejandro Daleo

The calculation of exclusive observables beyond the one-loop level requires elaborate techniques for the computation of multi-leg two-loop integrals. We discuss how the large number of different integrals appearing in actual two-loop…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. Gehrmann , E. Remiddi

We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems…

High Energy Physics - Phenomenology · Physics 2018-02-28 Xiao Liu , Yan-Qing Ma , Chen-Yu Wang

In this paper, we study systematically scalar one-loop two-, three-, and four-point Feynman integrals with complex internal masses. Our analytic results presented in this report are valid for both real and complex internal masses. The…

High Energy Physics - Phenomenology · Physics 2018-09-19 K. H. Phan , T. N. H. Pham

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

A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…

High Energy Physics - Phenomenology · Physics 2016-04-14 Johannes Bluemlein , Khiem Hong Phan , Tord Riemann

CARTAN is an easy-to-use symbolic, tensor component package based on the popular Mathematica program. CARTAN makes use of the powerful formalism of rigid frames, and can return results both in this frame and in the coordinate basis. CARTAN…

General Relativity and Quantum Cosmology · Physics 2008-02-03 Harald H. Soleng

We provide analytic results for two-loop four-point master integrals with one massive propagator and one massive leg relevant to single top production. Canonical bases of master integrals are constructed and the Simplified Differential…

High Energy Physics - Phenomenology · Physics 2023-05-31 Nikolaos Syrrakos

We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate…

High Energy Physics - Phenomenology · Physics 2015-06-03 Alexey Pak

We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The…

High Energy Physics - Phenomenology · Physics 2015-06-03 J. Fleischer , T. Riemann , V. Yundin

We present a set of Feynman integrals appearing in calculations of different QED processes to the one-loop accuracy. We consider scalar, vector, and tensor integrals with two, three, four and five denominators. The cases of equal and…

High Energy Physics - Phenomenology · Physics 2007-05-23 A. B. Arbuzov , A. V. Belitsky , E. A. Kuraev , B. G. Shaikhatdenov

The imaging performance and sensitivity of an X-ray telescope when observing astrophysical sources are primarily governed by the optical design, geometrical uncertainties (figure errors, surface roughness, and mirror alignment…

Instrumentation and Methods for Astrophysics · Physics 2024-05-13 Neeraj K. Tiwari , Santosh V. Vadawale , N. P. S. Mithun , C. S. Vaishnava , Bharath Saiguhan

In order to calculate cross sections with a large number of particles/jets in the final state at next-to-leading order, one has to reduce the occurring scalar and tensor one-loop integrals to a small set of known integrals. In massless…

High Energy Physics - Phenomenology · Physics 2009-10-31 G. Heinrich , T. Binoth

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

The three-loop master integrals for ladder-box diagrams with one massive leg are computed from an eighty-five by eighty-five system of differential equations, solved by means of Magnus exponential. The results of the considered box-type…

High Energy Physics - Phenomenology · Physics 2015-06-22 Stefano Di Vita , Pierpaolo Mastrolia , Ulrich Schubert , Valery Yundin

We perform analytical reductions of one-loop tensor integrals with 5 and 6 legs to scalar master integrals. They are based on the use of recurrence relations connecting integrals in different space-time dimensions. The reductions are…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. Diakonidis , J. Fleischer , J. Gluza , K. Kajda , T. Riemann , J. B. Tausk

We present a method to obtain analytic results in terms of multiple polylogarithms for one-loop triangle, box and pentagon integrals depending on an arbitrary number of scales and to any desired order in the Laurent expansion in the…

High Energy Physics - Phenomenology · Physics 2025-12-17 Claude Duhr , Paul Mork

We give a new method for the reduction of tensor integrals to finite integral representations and UV divergent analytic expressions. This includes a new method for the handling of the gamma-algebra. TYPO IN EQUATION (5) CORRECTED, MACROS…

High Energy Physics - Phenomenology · Physics 2009-10-22 Dirk Kreimer

In this talk, the program package GOSAM is presented, which can be used for the automated calculation of one-loop amplitudes for multi-particle processes. The integrands are generated in terms of Feynman diagrams and can be reduced by…

High Energy Physics - Phenomenology · Physics 2012-01-19 G. Cullen , N. Greiner , G. Heinrich , G. Luisoni , P. Mastrolia , G. Ossola , T. Reiter , F. Tramontano

We present the calculation of the three distinct non-planar hexa-box topologies for five-point one-mass processes. These three topologies are required to obtain the two-loop virtual QCD corrections for two-jet-associated W, Z or Higgs-boson…

High Energy Physics - Phenomenology · Physics 2022-04-13 Samuel Abreu , Harald Ita , Ben Page , Wladimir Tschernow