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We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with…

High Energy Physics - Phenomenology · Physics 2018-04-04 Roman N. Lee , Alexander V. Smirnov , Vladimir A. Smirnov

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

The two-loop QCD corrections to vector boson pair production at hadron colliders involve a new class of Feynman integrals: two-loop four-point functions with two off-shell external legs. We describe their reduction to a small set of master…

High Energy Physics - Phenomenology · Physics 2013-08-26 Thomas Gehrmann , Lorenzo Tancredi , Erich Weihs

We confirm by explicit computation the conjectured all-orders iteration of planar maximally supersymmetric N=4 Yang-Mills theory in the nontrivial case of five-point two-loop amplitudes. We compute the required unitarity cuts of the…

High Energy Physics - Theory · Physics 2008-11-26 Z. Bern , M. Czakon , D. A. Kosower , R. Roiban , V. A. Smirnov

We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and…

High Energy Physics - Phenomenology · Physics 2026-03-06 Pau Petit Rosàs

Motivated by the precision results in the electroweak theory studies of two-loopFeynman diagrams are performed. Specifically this paper gives a contribution to the knowledge of massive two-loop self-energy diagrams in arbitrary and…

High Energy Physics - Phenomenology · Physics 2011-09-30 S. Bauberger , F. A. Berends , M. Boehm , M. Buza

The calculation of rare loop decays in the Standard Model of Particle Physics and its extensions is an extremely tedious work. The Mathematica package MasterTwo facilitates this task. It automatically calculates all loop integrals reducible…

High Energy Physics - Phenomenology · Physics 2020-06-09 Sabine Schilling

Recent progress in the calculation of the two-loop on-shell mass counterterms within the electroweak Standard Model (SM) for the massive particles are discussed. We are in progress of developing a package for full two-loop SM calculations…

High Energy Physics - Phenomenology · Physics 2007-05-23 F. Jegerlehner , M. Yu. Kalmykov

We discuss the analytical solution of the two-loop sunrise graph with arbitrary non-zero masses in two space-time dimensions. The analytical result is obtained by solving a second-order differential equation. The solution involves elliptic…

High Energy Physics - Phenomenology · Physics 2015-06-15 Luise Adams , Christian Bogner , Stefan Weinzierl

We calculate the complete set of two-loop Master Integrals with two off mass-shell legs with massless internal propagators, that contribute to amplitudes of diboson $V_1V_2$ production at the LHC. This is done with the Simplified…

High Energy Physics - Phenomenology · Physics 2015-07-22 Costas G. Papadopoulos , Damiano Tommasini , Christopher Wever

In this thesis, major developments in the publicly available program SecDec are presented, extending the numerical evaluation of multi-loop multi-scale integrals from Euclidean to physical kinematics. The power of this new feature is shown…

High Energy Physics - Phenomenology · Physics 2014-10-30 Sophia Borowka

We show how to compute the two-loop sunset integrals at finite volume, for non-degenerate masses and non-zero momentum. We present results for all integrals that appear in the Chiral Perturbation Therory ($\chi$PT) calculation of the…

High Energy Physics - Lattice · Physics 2014-12-03 Johan Bijnens , Emil Boström , Timo A. Lähde

We present a fast Gauss transform in one dimension using nearly optimal sum-of-exponentials approximations of the Gaussian kernel. For up to about ten-digit accuracy, the approximations are obtained via best rational approximations of the…

Numerical Analysis · Mathematics 2019-09-24 Shidong Jiang

We compute the two-loop master integrals for leading-color QCD scattering amplitudes including a closed light-quark loop in $t\bar{t}H$ production at hadron colliders. Exploiting numerical evaluations in modular arithmetic, we construct a…

High Energy Physics - Phenomenology · Physics 2024-07-18 F. Febres Cordero , G. Figueiredo , M. Kraus , B. Page , L. Reina

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

We obtain for the first time the two-loop amplitudes for Higgs plus three gluons in Higgs effective field theory including dimension-seven operators. This provides the S-matrix elements for the top mass corrections for Higgs plus a jet…

High Energy Physics - Theory · Physics 2018-09-11 Qingjun Jin , Gang Yang

We present an efficient self-contained algorithm for computing the modified Bessel function of the first kind $I_{\nu}(z)$, implemented in a robust Fortran code supporting double and quadruple (quad) precision. The algorithm overcomes the…

Numerical Analysis · Mathematics 2025-05-16 Mofreh R. Zaghloul , Steven G. Johnson

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

In the paper, we obtain an expression for a two-loop master-diagram by using the Mellin$-$Barnes transformation. In the two-dimensional case we managed to factorize the answer and write it as a bilinear combination of hypergeometric…

High Energy Physics - Theory · Physics 2023-10-05 S. E. Derkachev , A. V. Ivanov , L. A. Shumilov

We study a recently-proposed approach to the numerical evaluation of multi-loop Feynman integrals using available sector decomposition programs. As our main example, we consider the two-loop integrals for the $\alpha \alpha_s$ corrections…

High Energy Physics - Phenomenology · Physics 2017-11-08 Andreas von Manteuffel , Robert M. Schabinger