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We present the integrand reduction via multivariate polynomial division as a natural technique to encode the unitarity conditions of Feynman amplitudes. We derive a recursive formula for the integrand reduction, valid for arbitrary…

High Energy Physics - Phenomenology · Physics 2015-06-16 P. Mastrolia , E. Mirabella , G. Ossola , T. Peraro

We compute the electron self-energy in Quantum Electrodynamics to three loops in terms of iterated integrals over kernels of elliptic type. We make use of the differential equations method, augmented by an $\epsilon$-factorized basis, which…

High Energy Physics - Theory · Physics 2024-11-08 Claude Duhr , Federico Gasparotto , Christoph Nega , Lorenzo Tancredi , Stefan Weinzierl

The $tW$ associated production has the second-largest cross section among three single top production channels. A complete study of NNLO QCD corrections to $tW$ production is still missing in literature. We present the calculation of part…

High Energy Physics - Phenomenology · Physics 2021-11-30 Ming-Ming Long , Ren-You Zhang , Wen-Gan Ma , Yi Jiang , Liang Han , Zhe Li , Shuai-Shuai Wang

We present recent developments on the topic of the integrand reduction of scattering amplitudes. Integrand-level methods allow to express an amplitude as a linear combination of Master Integrals, by performing operations on the…

High Energy Physics - Phenomenology · Physics 2013-12-06 Hans van Deurzen , Gionata Luisoni , Pierpaolo Mastrolia , Edoardo Mirabella , Giovanni Ossola , Tiziano Peraro , Ulrich Schubert

We present the analytic calculation of two-loop master integrals that are relevant for $tW$ production at hadron colliders. We focus on the integral families with only one massive propagator. After choosing a canonical basis, the…

High Energy Physics - Phenomenology · Physics 2021-12-08 Long-Bin Chen , Jian Wang

We describe the calculation of all planar master integrals that are needed for the computation of NNLO QCD corrections to the production of two off-shell vector bosons in hadron collisions. The most complicated representatives of integrals…

High Energy Physics - Phenomenology · Physics 2015-06-18 Johannes M. Henn , Kirill Melnikov , Vladimir A. Smirnov

We present a general procedure for obtaining the coefficients of the scalar bubble and triangle integral functions of one-loop amplitudes. Coefficients are extracted by considering two-particle and triple unitarity cuts of the corresponding…

High Energy Physics - Phenomenology · Physics 2008-11-26 Darren Forde

We provide high-energy approximations for all one-loop scalar 3- and 4-point functions and the corresponding tensor integrals that appear in scattering processes with four external on-shell particles. Our expressions are valid if all…

High Energy Physics - Phenomenology · Physics 2008-11-26 M. Roth , A. Denner

One- and two-dimensional harmonic polylogarithms, HPLs and GPLs, appear in calculations of multi-loop integrals. We discuss them in the context of analytical solutions for two-loop master integrals in the case of massive Bhabha scattering…

High Energy Physics - Phenomenology · Physics 2009-11-11 M. Czakon , J. Gluza , T. Riemann

We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master…

High Energy Physics - Theory · Physics 2016-11-23 Burkhard Eden , Vladimir A. Smirnov

We complete the analytic evaluation of the master integrals for the two-loop non-planar box diagrams contributing to the top-pair production in the quark-initiated channel, at next-to-next-to-leading order in QCD. The integrals are…

High Energy Physics - Phenomenology · Physics 2022-10-12 Stefano Di Vita , Thomas Gehrmann , Stefano Laporta , Pierpaolo Mastrolia , Amedeo Primo , Ulrich Schubert

Building on the idea of numerically integrating differential equations satisfied by Feynman integrals, we propose a novel strategy for handling branch cuts within a numerical framework. We develop an integrator capable of evaluating a basis…

High Energy Physics - Phenomenology · Physics 2025-07-18 Pau Petit Rosàs , William J. Torres Bobadilla

We report on recent progress for the QCD corrections to top quark pair plus jet production. In particular, we discuss a recent computation for the two-loop master integrals associated to a two-loop five-point pentagon-box integral…

High Energy Physics - Phenomenology · Physics 2023-10-17 Matteo Becchetti

We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example.

High Energy Physics - Theory · Physics 2016-02-02 Bernd A. Kniehl , Oleg V. Tarasov

Four 3-loop two-point functions are studied analytically and numerically using a simplified sector decomposition method. The coefficients of the ultraviolet divergent part are determined analytically, and those of the finite part are…

High Energy Physics - Phenomenology · Physics 2024-10-01 Elise de Doncker , Tadashi Ishikawa , Kiyoshi Kato , Fukuko Yuasa

We study several multiscale one-loop five-point families of Feynman integrals. More specifically, we employ the Simplified Differential Equations approach to obtain results in terms of Goncharov polylogarithms of up to transcendental weight…

High Energy Physics - Phenomenology · Physics 2021-09-14 Nikolaos Syrrakos

In this article we present a high-precision evaluation of the expansions in $\e=(4-d)/2$ of (up to) four-loop scalar vacuum master integrals, using the method of difference equations developed by S. Laporta. We cover the complete set of…

High Energy Physics - Phenomenology · Physics 2009-11-11 Y. Schroder , A. Vuorinen

In this paper we calculate at high-precision the expansions in e=(4-D)/2 of the master integrals of 4-loop vacuum bubble diagrams with equal masses, using a method based on the solution of systems of difference equations. We also show that…

High Energy Physics - Phenomenology · Physics 2009-11-07 Stefano Laporta

The screened QED corrections of the first orders in \alpha and 1/Z to the g factor and the hyperfine splitting of lithiumlike ions are evaluated within ab initio quantum electrodynamical approach. The complete gauge-invariant set of the…

Atomic Physics · Physics 2014-11-18 D. A. Glazov , A. V. Volotka , V. M. Shabaev , I. I. Tupitsyn , G. Plunien

We present analytical results for master integrals emerging in the computation of differential rates for inclusive weak decays of heavy flavors at next-to-leading order (NLO) in QCD. As an immediate physical application, these master…

High Energy Physics - Phenomenology · Physics 2022-01-05 Th. Mannel , D. Moreno , A. A. Pivovarov