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We present the calculation of the mixed two-loop QCD/electroweak corrections to hadronic W boson decays within the Standard Model. The optical theorem is applied to the W boson two-point function. The multi-scale integrals are computed with…

High Energy Physics - Phenomenology · Physics 2015-12-01 Dominik Kara

We calculate all three-loop, five-point, massless planar Feynman integral families in the dimensional regularization scheme. This is a new milestone in Feynman integral computations. The analysis covers four distinct families of Feynman…

High Energy Physics - Phenomenology · Physics 2025-12-22 Dmitry Chicherin , Yu Wu , Zihao Wu , Yongqun Xu , Shun-Qing Zhang , Yang Zhang

We present a new methodology, suitable for implementation on computer, to perform the $\epsilon$-expansion of hypergeometric functions with linear $\epsilon$ dependent Pochhammer parameters in any number of variables. Our approach allows…

Mathematical Physics · Physics 2023-03-28 Souvik Bera

A new method is developed to calculate multiloop Feynman diagrams in non-relativistic field theories. A consistent scheme for regularizing and renormalizing loop integrals is established and shown to reproduce the results of dimensional…

Nuclear Theory · Physics 2007-05-23 Michael Binger

We study two-loop corrections to the scattering amplitude of four massive leptons in quantum electrodynamics. These amplitudes involve previously unknown elliptic Feynman integrals, which we compute analytically using the differential…

High Energy Physics - Phenomenology · Physics 2023-11-14 Maximilian Delto , Claude Duhr , Lorenzo Tancredi , Yu Jiao Zhu

We elaborate on the expansion of hypergeometric functions about rational parameters, where we focus mainly on the integer and half-integer case. The strategy and the basic steps of a recently developed algorithm for the expansion about…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. Huber

We introduce a novel, systematic method for the complete symbolic reduction of multi-loop Feynman integrals, leveraging the power of generating functions. The differential equations governing these generating functions naturally yield…

High Energy Physics - Phenomenology · Physics 2026-01-30 Bo Feng , Xiang Li , Yuanche Liu , Yan-Qing Ma , Yang Zhang

A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model.…

High Energy Physics - Phenomenology · Physics 2008-11-26 G. Passarino

The high-energy behaviour of scattering amplitudes involving massive particles has attracted interest in recent years. In these proceedings, we report on the analytic tool AsyInt for solving massive multi-loop Feynman integrals in the…

High Energy Physics - Phenomenology · Physics 2025-10-14 Hantian Zhang

It is known that one-loop Feynman integrals possess an algebraic structure encoding some of their analytic properties called the coaction, which can be written in terms of Feynman integrals and their cuts. This diagrammatic coaction, and…

High Energy Physics - Theory · Physics 2019-12-16 Samuel Abreu , Ruth Britto , Claude Duhr , Einan Gardi , James Matthew

In this paper we develop further and refine the method of differential equations for computing Feynman integrals. In particular, we show that an additional iterative structure emerges for finite loop integrals. As a concrete non-trivial…

High Energy Physics - Theory · Physics 2015-06-19 Simon Caron-Huot , Johannes M. Henn

Parametric Feynman integrals with the regions of integration defined by some polynomials are considered in this paper. It is shown that integrals with irregular integration regions can be converted to standard parametric integrals, for…

High Energy Physics - Phenomenology · Physics 2025-08-27 Wen Chen

The numerical evaluation of multi-loop scattering amplitudes in the Feynman representation usually requires to deal with both physical (causal) and unphysical (non-causal) singularities. The loop-tree duality (LTD) offers a powerful…

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

We present an algorithm to evaluate multiloop Feynman integrals with an arbitrary number of internal massive lines, with the masses being in general complex-valued, and its implementation in the \textsc{Mathematica} package…

High Energy Physics - Phenomenology · Physics 2022-10-24 Tommaso Armadillo , Roberto Bonciani , Simone Devoto , Narayan Rana , Alessandro Vicini

Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector…

High Energy Physics - Phenomenology · Physics 2016-01-12 Zhao Li , Jian Wang , Qi-Shu Yan , Xiaoran Zhao

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

Application of the geometrically-inspired representations to the epsilon-expansion of the two-point function with different masses is considered. Explicit result for an arbitrary term of the expansion is obtained in terms of log-sine…

High Energy Physics - Theory · Physics 2007-05-23 A. I. Davydychev

Polylogrithmic functions, such as the logarithm or dilogarithm, satisfy a number of algebraic identities. For the logarithm, all the identities follow from the product rule. For the dilogarithm and higher-weight classical polylogarithms,…

Machine Learning · Computer Science 2022-06-10 Aurélien Dersy , Matthew D. Schwartz , Xiaoyuan Zhang

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