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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

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 introduce a novel structure for Feynman integrals, reformulating them as integrals over a small set of parameters with a fully controllable integrand. The integrand closely resembles one-loop Feynman integrals, and they are very easy to…

High Energy Physics - Phenomenology · Physics 2024-12-31 Li-Hong Huang , Rui-Jun Huang , Yan-Qing Ma

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

Using the Feynman parameter method, we have calculated in an elegant manner a set of one$-$loop box scalar integrals with massless internal lines, but containing 0, 1, 2, or 3 external massive lines. To treat IR divergences (both soft and…

High Energy Physics - Phenomenology · Physics 2009-01-07 G. Duplancic , B. Nizic

We present a simple method which simplifies the evaluation of the on-shell multiple box diagrams reducing them to triangle type ones. For the $L$-loop diagram one gets the expression in terms of Feynman parameters with $2L$-fold…

High Energy Physics - Theory · Physics 2015-06-18 D. I. Kazakov

At variance with fully inclusive quantities, which have been computed already at the two- or three-loop level, most exclusive observables are still known only at one loop, as further progress was hampered up to very recently by the greater…

High Energy Physics - Phenomenology · Physics 2007-05-23 T. Gehrmann , E. Remiddi

Within the framework of the renormalization group approach to the models of critical dynamics, we propose a method for a considerable reduction of the number of integrals needed to calculate the critical exponents. With this method we…

Statistical Mechanics · Physics 2018-04-18 L. Ts. Adzhemyan , E. V. Ivanova , M. V. Kompaniets , S. Ye. Vorobyeva

We determine the master integrals for vertex and propagator diagrams that appear in effective field theories containing heavy fields. The integrals involve at least one heavy line, and the standard lines include an arbitrary mass scale. The…

High Energy Physics - Phenomenology · Physics 2022-01-19 B. Assi , B. A. Kniehl , A. I. Onishchenko

We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at…

High Energy Physics - Phenomenology · Physics 2020-12-30 S. Abreu , H. Ita , F. Moriello , B. Page , W. Tschernow , M. Zeng

A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different…

High Energy Physics - Phenomenology · Physics 2009-11-10 A. Ferroglia , G. Passarino , M. Passera , S. Uccirati

The well-known $D$-dimensional Feynman integrals were shown, by Halliday and Ricotta, to be capable of undergoing analytic continuation into the domain of negative values for the dimension of space-time. Furthermore, this could be…

High Energy Physics - Theory · Physics 2009-10-31 A. T. Suzuki , A. G. M. Schmidt

We develop an operator approach to the evaluation of multiple integrals for multiloop Feynman massless diagrams. A commutative family of graph building operators $H_\alpha$ for ladder diagrams is constructed and investigated. The complete…

High Energy Physics - Theory · Physics 2023-06-28 S. E. Derkachov , A. P. Isaev , L. A. Shumilov

We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external…

High Energy Physics - Phenomenology · Physics 2021-04-21 Guy R. Jehu

Two-loop corrections to scattering amplitudes are crucial theoretical input for collider physics. Recent years have seen tremendous advances in computing Feynman integrals, scattering amplitudes, and cross sections for five-particle…

High Energy Physics - Theory · Physics 2022-03-30 Johannes Henn , Tiziano Peraro , Yingxuan Xu , Yang Zhang

I describe a method to calculate a class of three-loop selfenergy diagrams for arbitrary internal masses and external momentum. This method combines analytical results and numerical integration, and is suitable for implementation in a…

High Energy Physics - Phenomenology · Physics 2009-10-28 Adrian Ghinculov

We present a method for rewriting dimensionally regulated Feynman parameter integrals in the Minkowski regime as a sum of real, positive integrands multiplied by complex prefactors. This representation eliminates the need for contour…

High Energy Physics - Phenomenology · Physics 2025-07-01 Stephen Jones , Anton Olsson , Thomas Stone

Recent developments in the computation of two-loop master integrals for massive Bhabha scattering are briefly reviewed. We apply a method based on expansions of exact Mellin-Barnes representations and evaluate all planar four-point master…

High Energy Physics - Phenomenology · Physics 2009-11-11 Stefano Actis , Michal Czakon , Janusz Gluza , Tord Riemann

In this work we calculate two two-loop massless Feynman integrals pertaining to self-energy diagrams using NDIM (Negative Dimensional Integration Method). We show that the answer we get is 36-fold degenerate. We then consider special cases…

High Energy Physics - Theory · Physics 2011-09-13 Alfredo T. Suzuki , Alexandre G. M. Schmidt

We present a systematic method for reducing an arbitrary one-loop N-point massless Feynman integral with generic 4-dimensional momenta to a set comprised of eight fundamental scalar integrals: six box integrals in D=6, a triangle integral…

High Energy Physics - Phenomenology · Physics 2009-11-10 G. Duplancic , B. Nizic