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Related papers: Integration Rules for Loop Scattering Equations

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We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop--tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the…

High Energy Physics - Phenomenology · Physics 2015-06-19 Sebastian Buchta , Grigorios Chachamis , Petros Draggiotis , Ioannis Malamos , German Rodrigo

We investigate how loop-level propagators arise from tree level via a forward-limit procedure in two modern approaches to scattering amplitudes, namely the BCFW recursion relations and the scattering equations formalism. In the first part…

High Energy Physics - Theory · Physics 2020-10-28 Joseph A. Farrow , Yvonne Geyer , Arthur E. Lipstein , Ricardo Monteiro , Ricardo Stark-Muchão

The use of complex analysis for computing one-loop scattering amplitudes is naturally induced by generalised unitarity-cut conditions, fulfilled by complex values of the loop variable. We report on two techniques: the cut-integration with…

High Energy Physics - Phenomenology · Physics 2008-11-26 Pierpaolo Mastrolia

We present a new algorithm for integration-by-parts (IBP) reduction of Feynman integrals with high powers of numerators or propagators, a demanding computational step in evaluating multi-loop scattering amplitudes. The algorithm allows us…

High Energy Physics - Theory · Physics 2026-02-24 Sid Smith

We show a direct matching between individual Feynman diagrams and integration measures in the scattering equation formalism of Cachazo, He and Yuan. The connection is most easily explained in terms of triangular graphs associated with…

High Energy Physics - Theory · Physics 2015-10-28 Christian Baadsgaard , N. E. J. Bjerrum-Bohr , Jacob L. Bourjaily , Poul H. Damgaard

We confront the recently proposed exact S-matrices for AdS(3)/CFT(2) with direct worldsheet calculations. Utilizing the BMN and Near Flat Space (NFS) expansions for strings on AdS(3) x S(3) x S(3) x S(1) and AdS(3) x S(3) x T(4) we compute…

High Energy Physics - Theory · Physics 2015-06-15 Per Sundin , Linus Wulff

Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…

High Energy Physics - Theory · Physics 2013-06-26 Johannes M. Henn

In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand…

High Energy Physics - Phenomenology · Physics 2021-09-30 German F. R. Sborlini

We show that a wide class of tree-level scattering amplitudes involving scalars, gauge bosons, and gravitons, up to three of which may be massive, can be expressed in terms of a Cachazo-He-Yuan representation as a sum over solutions of the…

High Energy Physics - Theory · Physics 2015-06-11 Stephen G. Naculich

We introduce a new, probability-level approach to calculations in scalar field particle scattering. The approach involves the implicit summation over final states, which makes causality manifest since retarded propagators emerge naturally.…

High Energy Physics - Phenomenology · Physics 2025-09-17 Robert Dickinson , Jeff Forshaw , Ross Jenkinson , Peter Millington

We present the building blocks that can be combined to produce tree-level S-matrix elements of a variety of theories with various spins mixed in arbitrary dimensions. The new formulas for the scattering of $n$ massless particles are given…

High Energy Physics - Theory · Physics 2015-06-23 Freddy Cachazo , Song He , Ellis Ye Yuan

One-loop scattering amplitudes in N=4 super Yang-Mills (SYM) theories are analyzed in the paradigm of maximal helicity violating Feynman diagrams. There are very limited number of loop integrals to be evaluated. For a process with n…

High Energy Physics - Theory · Physics 2010-04-05 Mingxing Luo , Congkao Wen

We review techniques for more efficient computation of perturbative scattering amplitudes in gauge theory, in particular tree and one-loop multi-parton amplitudes in QCD. We emphasize the advantages of (1) using color and helicity…

High Energy Physics - Phenomenology · Physics 2008-02-03 L. Dixon

Recent investigations into the geometric structure of scattering amplitudes have revealed the surprising existence of "hidden zeros": secret kinematic loci where tree-level amplitudes in Tr$(\phi^3)$ theory, the Non-Linear Sigma Model…

High Energy Physics - Theory · Physics 2025-09-23 Jeffrey V. Backus , Laurentiu Rodina

We review some recent developments in the understanding of field theories in the perturbative regime. In particular, we discuss the notions of analyticity, unitarity and locality, and therefore the singularity structure of scattering…

High Energy Physics - Theory · Physics 2015-06-18 Paolo Benincasa

The quantum effects encapsulated in loop corrections are crucial in quantum field theory for a wide variety of formal and phenomenological applications. In this article we propose and check a definition of the so-called single cut…

High Energy Physics - Theory · Physics 2016-10-18 Rutger H. Boels , Hui Luo

Lattice QCD studies of hadron-hadron interactions are performed by computing the energy levels of the system in a finite box. The shifts in energy levels proportional to inverse powers of the volume are related to scattering parameters in a…

High Energy Physics - Lattice · Physics 2014-11-17 Paulo F. Bedaque , Ikuro Sato , Andre Walker-Loud

A way to efficiently compute helicity amplitudes for arbitrary tree-level scattering processes in QCD is presented. The scattering amplitude is evaluated recursively through a set of Dyson-Schwinger equations. The computational cost of this…

High Energy Physics - Phenomenology · Physics 2009-11-11 Costas G. Papadopoulos , Malgorzata Worek

We combine recent applications of the two-dimensional quantum inverse scattering method to the scattering amplitude problem in four-dimensional N=4 Super Yang-Mills theory. Integrability allows us to obtain a general, explicit method for…

High Energy Physics - Theory · Physics 2014-04-09 Nils Kanning , Tomasz Lukowski , Matthias Staudacher

We present a method to compute the integrands of one-loop Einstein-Yang-Mills amplitudes for any number of external gauge and gravity multiplets. Our construction relies on the double-copy structure of Einstein-Yang-Mills as…

High Energy Physics - Theory · Physics 2023-03-01 Franziska Porkert , Oliver Schlotterer