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Related papers: Five-loop massless propagator integrals

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We compute the full set of two-loop Feynman integrals appearing in massless two-loop four-point functions with two off-shell legs with the same invariant mass. These integrals allow to determine the two-loop corrections to the amplitudes…

High Energy Physics - Phenomenology · Physics 2014-06-13 Thomas Gehrmann , Andreas von Manteuffel , Lorenzo Tancredi , Erich Weihs

The old "glue--and--cut" symmetry of massless propagators, first established in [1], leads --- after reduction to master integrals is performed --- to a host of non-trivial relations between the latter. The relations constrain the master…

High Energy Physics - Phenomenology · Physics 2015-03-14 P. A. Baikov , K. G. Chetyrkin

We present analytical results for all master integrals for massless three-point functions, with one off-shell leg, at four loops. Our solutions were obtained using differential equations and direct integration techniques. We review the…

We present the bare one-, two-, and three-loop form factors in massless Quantum Chromodynamics as linear combinations of finite master integrals. Using symbolic integration, we compute their $\epsilon$ expansions and thereby reproduce all…

High Energy Physics - Phenomenology · Physics 2016-08-30 Andreas von Manteuffel , Erik Panzer , Robert M. Schabinger

The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron--positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three…

High Energy Physics - Phenomenology · Physics 2011-09-29 T. Gehrmann , E. Remiddi

I obtain identities satisfied by the 3-loop self-energy master integrals with four or five propagators with generic masses, including the derivatives with respect to each of the squared masses and the external momentum invariant. These…

High Energy Physics - Phenomenology · Physics 2023-03-29 Stephen P. Martin

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 evaluate the massless one-loop hexagon integral in six dimensions. The result is given in terms of standard polylogarithms of uniform transcendental weight three, its functional form resembling the one of the remainder function of the…

High Energy Physics - Theory · Physics 2015-05-27 Vittorio Del Duca , Claude Duhr , Vladimir A. Smirnov

We compute the master integrals containing 2 and 3 massive propagators entering the planar amplitudes of the 2-loop electroweak form factor. The masses of the $W$, $Z$ and Higgs bosons are assumed to be degenerate. This work is a…

High Energy Physics - Phenomenology · Physics 2009-11-10 U. Aglietti , R. Bonciani

We compute the two-loop master integrals for non-leptonic heavy-to-heavy decays analytically in a recently-proposed canonical basis. For this genuine two-loop, two-scale problem we first derive a basis for the master integrals that…

High Energy Physics - Phenomenology · Physics 2015-05-20 Tobias Huber , Susanne Krankl

We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes. We employ the method of canonical differential equations to construct a minimal…

High Energy Physics - Phenomenology · Physics 2021-11-12 Dmitry Chicherin , Vasily Sotnikov

We present the calculation of massless two-loop Master Integrals relevant to five-point amplitudes with one off-shell external leg and derive the complete set of planar Master Integrals with five on-mass-shell legs, that contribute to many…

High Energy Physics - Phenomenology · Physics 2016-05-04 Costas G. Papadopoulos , Damiano Tommasini , Christopher Wever

A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums.…

High Energy Physics - Phenomenology · Physics 2007-05-23 Stefan Bekavac

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

The calculation of the two-loop corrections to the three jet production rate and to event shapes in electron-positron annihilation requires the computation of a number of up to now unknown two-loop four-point master integrals with one…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. Gehrmann , E. Remiddi

We study multi-propagator angular integrals, a class of phase-space integrals relevant to processes with multiple observed final states and a test-bed for transferring loop-integral technology to phase space integrals without reversed…

High Energy Physics - Phenomenology · Physics 2025-10-17 Juliane Haug , Vladimir A. Smirnov , Fabian Wunder

We consider the case of a two-loop five-point pentagon-box integral configuration with one internal massive propagator that contributes to top-quark pair production in association with a jet at hadron colliders. We construct the system of…

High Energy Physics - Phenomenology · Physics 2023-03-31 Simon Badger , Matteo Becchetti , Ekta Chaubey , Robin Marzucca

We consider the complete set of planar two-loop five-point Feynman integrals with two off-shell external legs. These integrals are relevant, for instance, for the calculation of the second-order QCD corrections to the production of two…

High Energy Physics - Theory · Physics 2024-11-07 Samuel Abreu , Dmitry Chicherin , Vasily Sotnikov , Simone Zoia

An asymptotic expansion of the two-loop two-point ``master'' diagram with two masses $m$ and $M$, on the mass shell $Q^2=M^2$, is presented. The treatment of the non-analytical terms arising in the expansion around the branching point is…

High Energy Physics - Phenomenology · Physics 2009-10-28 Andrzej Czarnecki , Vladimir A. Smirnov

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