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In this review some recent multi-loop results obtained in the framework of perturbative Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED) are discussed. After reviewing the most advanced techniques used for the computation of…

High Energy Physics - Phenomenology · Physics 2009-11-07 M. Steinhauser

A connection between one-loop $N$-point Feynman diagrams and certain geometrical quantities in non-Euclidean geometry is discussed. A geometrical way to calculate the corresponding Feynman integrals is considered. (This paper contains a…

High Energy Physics - Theory · Physics 2011-03-17 A. I. Davydychev , R. Delbourgo

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $\rho$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be…

High Energy Physics - Theory · Physics 2018-08-01 J. Ablinger , J. Blümlein , A. De Freitas , M. van Hoeij , E. Imamoglu , C. G. Raab , C. -S. Radu , C. Schneider

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

We calculate analytically the two-loop triangle integrals entering the $\mathcal{O}(\alpha\alpha_s)$ corrections to the $HZV$ vertex with $V=Z^*,\gamma^*$ using the method of differential equations. Our result provides a prototype to study…

High Energy Physics - Phenomenology · Physics 2019-10-23 Yuxuan Wang , Xiaofeng Xu , Li Lin Yang

Measurements of electroweak precision observables at future electron-positron colliders, such as the CEPC, FCC-ee, and ILC, will be sensitive to physics at multi-TeV scales. To achieve this sensitivity, precise predictions for the Standard…

High Energy Physics - Phenomenology · Physics 2021-04-07 Lisong Chen , Ayres Freitas

In a recent paper we have presented an automated subtraction method for divergent multi-loop/leg integrals in dimensional regularisation which allows for their numerical evaluation, and applied it to diagrams with massless internal lines.…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. Binoth , G. Heinrich

We describe a constructive procedure to separate overlapping infrared divergences in multi-loop integrals. Working with a parametric representation in D=4-2*epsilon dimensions, adequate subtractions lead to a Laurent series in epsilon,…

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

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 review the techniques necessary for the calculation of virtual electroweak and soft photonic corrections at the one-loop level. In particular we describe renormalization, calculation of one-loop integrals and evaluation of one-loop…

High Energy Physics - Phenomenology · Physics 2008-11-26 Ansgar Denner

We compute a complete set of the two-loop Feynman integrals that are required for the next-to-next-to-leading order QCD corrections to on-shell top-pair production in association with a $W$ boson at hadron colliders in the leading colour…

High Energy Physics - Phenomenology · Physics 2025-08-26 Matteo Becchetti , Dhimiter Canko , Vsevolod Chestnov , Tiziano Peraro , Mattia Pozzoli , Simone Zoia

Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…

High Energy Physics - Theory · Physics 2013-06-26 Johannes M. Henn

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 standard procedure for computing scalar multi-loop Feynman integrals consists in reducing them to a basis of so-called master integrals, derive differential equations in the external invariants satisfied by the latter and, finally, try…

High Energy Physics - Phenomenology · Physics 2017-04-05 Amedeo Primo , Lorenzo Tancredi

A comprehensive study is performed of two-loop Feynman diagrams with three external legs which, due to the exchange of massless gauge-bosons, give raise to infrared and collinear divergencies. Their relevance in assembling realistic…

High Energy Physics - Phenomenology · Physics 2009-11-11 Giampiero Passarino , Sandro Uccirati

We consider Feynman integrals with algebraic leading singularities and total differentials in $\epsilon\,\mathrm{d}\ln$ form. We show for the first time that it is possible to evaluate integrals with singularities involving unrationalizable…

High Energy Physics - Theory · Physics 2020-08-18 Matthias Heller , Andreas von Manteuffel , Robert M. Schabinger

We introduce a new family of numerical algorithms for approximating solutions of general high-dimensional semilinear parabolic partial differential equations at single space-time points. The algorithm is obtained through a delicate…

Numerical Analysis · Mathematics 2021-11-09 Weinan E , Martin Hutzenthaler , Arnulf Jentzen , Thomas Kruse

We discuss two-loop leading and angular-dependent next-to-leading logarithmic electroweak virtual corrections to arbitrary processes at energies above the electroweak scale. The relevant Feynman diagrams involving soft-collinear gauge…

High Energy Physics - Phenomenology · Physics 2008-11-26 Ansgar Denner , Michael Melles , Stefano Pozzorini

We study a set of two-loop non-planar master integrals needed for the NNLO QCD corrections to diphoton and dijet production at hadron colliders. The top-sector topology contains an internal massive fermion loop and is known to contain…

High Energy Physics - Theory · Physics 2024-02-13 Taushif Ahmed , Ekta Chaubey , Mandeep Kaur , Sara Maggio

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