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Related papers: Integral Coefficients for One-Loop Amplitudes

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Recently, the spinor helicity formalism and on-shell superspace were developed for six-dimensional gauge theories with (1,1) supersymmetry. We combine these two techniques with (generalised) unitarity, which is a powerful technique to…

High Energy Physics - Theory · Physics 2011-03-02 Andreas Brandhuber , Dimitrios Korres , Daniel Koschade , Gabriele Travaglini

We calculate field theory loop amplitudes by string methods, applied to half-maximal 4-point one-loop graviton amplitudes. Infrared divergences are regulated similarly to soft-collinear effective field theory (SCET): new mass scales are…

High Energy Physics - Theory · Physics 2026-03-31 Marcus Berg , Michael Haack , Yonatan Zimmerman

We present the first public version of Caravel, a C++17 framework for the computation of multi-loop scattering amplitudes in quantum field theory, based on the numerical unitarity method. Caravel is composed of modules for the…

High Energy Physics - Phenomenology · Physics 2021-07-28 S. Abreu , J. Dormans , F. Febres Cordero , H. Ita , M. Kraus , B. Page , E. Pascual , M. S. Ruf , V. Sotnikov

We describe the application of a novel approach for the reduction of scattering amplitudes, based on multivariate polynomial division, which we have recently presented. This technique yields the complete integrand decomposition for…

High Energy Physics - Phenomenology · Physics 2013-07-17 Pierpaolo Mastrolia , Edoardo Mirabella , Giovanni Ossola , Tiziano Peraro

We present methods for the numerical evaluation of the master integrals that appear in the calculation of scattering amplitudes at higher order in perturbative quantum field theory. We follow the general strategy of solving first-order…

High Energy Physics - Phenomenology · Physics 2025-01-06 Renato Maria Prisco , Jonathan Ronca , Francesco Tramontano

It is by now well established that, by means of the integration by part identities, all the integrals occurring in the evaluation of a Feynman graph of given topology can be expressed in terms of a few independent master integrals. It is…

High Energy Physics - Theory · Physics 2022-03-02 Ettore Remiddi

We compute the one-loop corrections to \tth up to order $\mathcal{O}(\epsilon^2)$ in the dimensional regularization parameter. We apply the projector method to compute polarized amplitudes, which generalize massless helicity amplitudes to…

High Energy Physics - Phenomenology · Physics 2023-12-18 Federico Buccioni , Philipp Alexander Kreer , Xiao Liu , Lorenzo Tancredi

We study the applicability of the Z-Sum approach to multi-loop calculations with massive particles in perturbative quantum field theory. We systematically analyze the case of one-loop scalar integrals, which represent the building blocks of…

High Energy Physics - Phenomenology · Physics 2015-05-28 Paulo A. Rottmann , Laura Reina

We review different notions of cuts appearing throughout the literature on scattering amplitudes. Despite similar names, such as unitarity cuts or generalized cuts, they often represent distinct computations and distinct physics. We…

High Energy Physics - Theory · Physics 2025-01-09 Ruth Britto , Claude Duhr , Holmfridur S. Hannesdottir , Sebastian Mizera

We present a method for the computation of hepta-cuts of two loop scattering amplitudes. Four dimensional unitarity cuts are used to factorise the integrand onto the product of six tree-level amplitudes evaluated at complex momentum values.…

High Energy Physics - Phenomenology · Physics 2012-04-18 Simon Badger , Hjalte Frellesvig , Yang Zhang

In four-dimensional theories with massless particles, the one-loop amplitudes can be expressed in terms of a basis of scalar integrals and rational terms. Since the scalar bubble integrals are the only UV divergent integrals, the sum of the…

High Energy Physics - Theory · Physics 2015-03-20 Yu-tin Huang , David A. McGady , Cheng Peng

In this Letter, we provide evidence for a new double-copy structure in one-loop amplitudes of the open superstring. Their integrands with respect to the moduli space of genus-one surfaces are cast into a form where gauge-invariant kinematic…

High Energy Physics - Theory · Physics 2018-07-11 Carlos R. Mafra , Oliver Schlotterer

We initiate a study of non-supersymmetric Born-Infeld electrodynamics in 4d at the quantum level. Explicit all-multiplicity expressions are calculated for the purely rational one-loop amplitudes in the self-dual ($++\ldots+$) and…

High Energy Physics - Theory · Physics 2020-03-18 Henriette Elvang , Marios Hadjiantonis , Callum R. T. Jones , Shruti Paranjape

We provide a complete set of results for the scalar 4-point function appearing in one-loop calculations in QCD, QED, the electroweak Standard Model and popular extensions thereof. Complex internal masses, which are needed for calculations…

High Energy Physics - Phenomenology · Physics 2010-12-14 A. Denner , S. Dittmaier

A method to separate pentagon contributions from the evaluation of the cut constructible part of primitive amplitudes within the framework of D-dimensional unitarity is proposed. The cut constructible part is thus reconstructed with…

High Energy Physics - Phenomenology · Physics 2009-11-30 Achilleas Lazopoulos

We present the first numerical computation of two-loop amplitudes based on the unitarity method. As a proof of principle, we compute the four-gluon process. We discuss the new method, analyze its numerical properties and apply it to…

High Energy Physics - Phenomenology · Physics 2017-10-11 S. Abreu , F. Febres Cordero , H. Ita , M. Jaquier , B. Page , M. Zeng

We present a semi-recursive method for calculating the rational parts of one-loop amplitudes when recursion produces double poles. We illustrate this with the graviton scattering amplitude M^{1-loop}(1-, 2+, 3+, 4+, 5+).

High Energy Physics - Theory · Physics 2010-12-13 David C. Dunbar , James H. Ettle , Warren B. Perkins

In unitarity cut method, compact input of on-shell tree level amplitudes is crucial to simplify calculations. Although BCFW on-shell recursion relation gives very compact tree level amplitudes, they usually contain spurious poles. In this…

High Energy Physics - Phenomenology · Physics 2009-02-02 Bo Feng , Gang Yang

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 construct a basis set of infra-red and/or collinearly divergent scalar one-loop integrals and give analytic formulas, for tadpole, bubble, triangle and box integrals, regulating the divergences (ultra-violet, infra-red or collinear) by…

High Energy Physics - Phenomenology · Physics 2011-06-30 R. Keith Ellis , Giulia Zanderighi