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Related papers: NUMERICAL APPROACH TO TWO-LOOP THREE POINT FUNCTIO…

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We consider the massless two-loop two-point function with arbitrary powers of the propagators and derive a representation, from which we can obtain the Laurent expansion to any desired order in the dimensional regularization parameter eps.…

High Energy Physics - Phenomenology · Physics 2009-11-10 Isabella Bierenbaum , Stefan Weinzierl

We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial…

High Energy Physics - Theory · Physics 2019-05-21 A. V. Kotikov , S. Teber

We systematically analyze the $d=5$ Weinberg operator at 2-loop order. Using a diagrammatic approach, we identify two different interesting categories of neutrino mass models: (i) Genuine 2-loop models for which both, tree-level and 1-loop…

High Energy Physics - Phenomenology · Physics 2015-03-26 D. Aristizabal Sierra , A. Degee , L. Dorame , M. Hirsch

We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at…

High Energy Physics - Phenomenology · Physics 2020-12-30 S. Abreu , H. Ita , F. Moriello , B. Page , W. Tschernow , M. Zeng

As the new-generation precision experiments such as MOLLER and P2 look for physics beyond Standard Model, it is becoming increasingly important to evaluate the higher-order electroweak radiative corrections to a sub-percent level of…

High Energy Physics - Theory · Physics 2019-12-11 A. Aleksejevs , S. Barkanova

In this paper, we generalize the unitarity method to two-loop diagrams and use it to discuss the integral bases of reduction. To test out method, we focus on the four-point double-box diagram as well as its related daughter diagrams, i.e.,…

High Energy Physics - Theory · Physics 2015-06-18 Bo Feng , Jun Zhen , Rijun Huang , Kang Zhou

A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of…

High Energy Physics - Phenomenology · Physics 2009-11-10 S. Actis , A. Ferroglia , G. Passarino , M. Passera , S. Uccirati

We present a review of the Bielefeld-Dubna activities on multiloop calculations.

High Energy Physics - Phenomenology · Physics 2007-05-23 J. Fleischer , M. Tentyukov

We present the two-loop sunrise integral with arbitrary non-zero masses in two space-time dimensions in terms of elliptic dilogarithms. We find that the structure of the result is as simple and elegant as in the equal mass case, only the…

High Energy Physics - Phenomenology · Physics 2015-06-19 Luise Adams , Christian Bogner , Stefan Weinzierl

A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different…

High Energy Physics - Phenomenology · Physics 2009-11-10 A. Ferroglia , G. Passarino , M. Passera , S. Uccirati

Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, only results for integrals with one and two independent mass scales are known, but in the electroweak…

High Energy Physics - Phenomenology · Physics 2021-04-08 Ayres Freitas

An algorithm to construct analytic approximations to two-loop diagrams describing their behaviour at small non-zero thresholds is discussed. For some special cases (involving two different-scale mass parameters), several terms of the…

High Energy Physics - Phenomenology · Physics 2015-06-25 F. A. Berends , A. I. Davydychev , V. A. Smirnov

Three-loop vertex diagrams in HQET needed for sum rules for B^0 - \bar{B}^0 mixing are considered. They depend on two residual energies. An algorithm of reduction of these diagrams to master integrals has been constructed. All master…

High Energy Physics - Phenomenology · Physics 2014-11-18 Andrey G. Grozin , Roman N. Lee

The method introduced in a previous paper to simplify the tensorial reduction in multi-leg loop calculations is extended to generic one-loop integrals, with arbitrary internal masses and external momenta.

High Energy Physics - Phenomenology · Physics 2009-10-30 Roberto Pittau

General algorithms for tensor reduction of two-loop massive vacuum diagrams are discussed. Some explicit useful formulae are presented.

High Energy Physics - Phenomenology · Physics 2007-05-23 A. I. Davydychev , J. B. Tausk

We present a dispersion relation formalism to calculate a massive scalar two-loop vertex function. Such calculation is of direct relevance in the evaluation of the hadronic light-by-light contribution to the muon's anomalous magnetic moment…

High Energy Physics - Phenomenology · Physics 2014-11-13 Vladyslav Pauk , Marc Vanderhaeghen

In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small $q^2$, in $d$ dimensions, using identities derived from integration by parts. Expansions are given, in terms of…

High Energy Physics - Phenomenology · Physics 2011-08-17 D. J. Broadhurst , J. Fleischer , O. V. Tarasov

We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist $\tau =2$ local operator insertions corresponding to spin $N$. They contribute to the massive operator matrix elements in QCD describing…

High Energy Physics - Phenomenology · Physics 2015-06-19 Jakob Ablinger , Johannes Blümlein , Clemens Raab , Carsten Schneider , Fabian Wißbrock

I present the two-loop self-energy functions for scalar bosons in a general renormalizable theory, within the approximation that vector bosons are treated as massless or equivalently that gauge symmetries are unbroken. This enables the…

High Energy Physics - Phenomenology · Physics 2008-11-26 Stephen P. Martin

An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the…

High Energy Physics - Phenomenology · Physics 2014-11-20 Ayres Freitas , Yi-Cheng Huang