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Related papers: Two-loop master integrals for a planar and a non-p…

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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

I study the Feynman integrals needed to compute two-loop self-energy functions for general masses and external momenta. A convenient basis for these functions consists of the four integrals obtained at the end of Tarasov's recurrence…

High Energy Physics - Phenomenology · Physics 2014-11-17 Stephen P. Martin

It is shown that for every problem within dimensional regularization, using the Integration-By-Parts method, one is able to construct a set of master integrals such that each corresponding coefficient function is finite in the limit of…

High Energy Physics - Phenomenology · Physics 2008-11-26 K. G. Chetyrkin , M. Faisst , C. Sturm , M. Tentyukov

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

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

For the two-loop next-to-leading-order electroweak (NLO EW) corrections to $gg \rightarrow ZH$, the light-fermion contributions can be classified into eight distinct topologies. Using the canonical differential-equations method, we perform…

High Energy Physics - Phenomenology · Physics 2026-05-01 Shu-Xiang Li , Ren-You Zhang , Xiao-Feng Wang , Pan-Feng Li , Xiang-Jie Wei , Yi Wang , Yi Jiang , Qing-hai Wang

We evaluate the master integrals for the two-loop, planar box-diagrams contributing to the elastic scattering of muons and electrons at next-to-next-to leading-order in QED. We adopt the method of differential equations and the Magnus…

High Energy Physics - Phenomenology · Physics 2022-10-13 Pierpaolo Mastrolia , Massimo Passera , Amedeo Primo , Ulrich Schubert

We present analytic results for all planar two-loop Feynman integrals contributing to five-particle scattering amplitudes with one external massive leg. We express the integrals in terms of a basis of algebraically-independent…

High Energy Physics - Phenomenology · Physics 2022-02-09 Dmitry Chicherin , Vasily Sotnikov , Simone Zoia

We evaluate the three-loop five-point pentagon-box-box massless integral family in the dimensional regularization scheme, via canonical differential equation. We use tools from computational algebraic geometry to enable the necessary…

High Energy Physics - Phenomenology · Physics 2025-01-15 Yuanche Liu , Antonela Matijašić , Julian Miczajka , Yingxuan Xu , Yongqun Xu , Yang Zhang

We develop a unitarity method to compute one-loop amplitudes with massless propagators in d=4-2*epsilon dimensions. We compute double cuts of the loop amplitudes via a decomposition into a four-dimensional and a -2*epsilon-dimensional…

High Energy Physics - Phenomenology · Physics 2008-11-26 Charalampos Anastasiou , Ruth Britto , Bo Feng , Zoltan Kunszt , Pierpaolo Mastrolia

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

We compute the master integrals for two-loop QCD corrections to quasi parton distribution functions (PDFs) in large momentum effective theory. Analytical results of the master integrals are derived using the method of differential…

High Energy Physics - Phenomenology · Physics 2020-10-28 Long-Bin Chen , Wei Wang , Ruilin Zhu

We calculate the three-loop master integrals contributing to the three-loop five-point amplitude on the special Coulomb branch of $\mathcal{N}=4$ SYM theory. For the genuine pentagon integrals, we follow the approach of Ref. [JHEP 12 (2025)…

High Energy Physics - Theory · Physics 2026-05-19 Andrei V. Belitsky , Leonid V. Bork , Roman N. Lee , Andrei I. Onishchenko , Vladimir A. Smirnov

All scalar master integrals (MIs) for massive 2-loop QED Bhabha scattering are identified. The 2- and 3-point MIs have been calculated in terms of harmonic polylogarithms with the differential equation method. The calculation of 4-point MIs…

High Energy Physics - Phenomenology · Physics 2007-05-23 M. Czakon , J. Gluza , T. Riemann

We calculate master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals,…

High Energy Physics - Phenomenology · Physics 2021-05-05 R. N. Lee , A. I. Onishchenko

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 consider the question about the number of master integrals for a multiloop Feynman diagram. We show that, for a given set of denominators, this number is totally determined by the critical points of the polynomials entering either of the…

High Energy Physics - Phenomenology · Physics 2015-06-17 Roman N. Lee , Andrei A. Pomeransky

An exact expression for the master integral I_2 arising in three-loop on-shell HQET propagator diagrams with mass is derived and its analytical expansion in the dimensional regularization parameter epsilon is given.

High Energy Physics - Phenomenology · Physics 2008-11-26 A. G. Grozin , T. Huber , D. Maitre

We study one and two-loop triangle integrals with massless propagators and all external legs off shell. We show that there is a kinematic region where the results can be expressed in terms of a basis of single-valued polylogarithms in one…

High Energy Physics - Phenomenology · Physics 2015-06-11 Federico Chavez , Claude Duhr

For a three-dimensional higher-derivative scalar superfield model, and a four-dimensional higher-derivative chiral superfield model, where which the higher-derivative operators are described by polynomials of arbitrary degrees, we…

High Energy Physics - Theory · Physics 2021-01-18 F. S. Gama , J. R. Nascimento , A. Yu. Petrov