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Related papers: Integrand Reduction for Two-Loop Scattering Amplit…

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Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g -> gg splitting amplitudes in QCD, N=1, and N=4 super-Yang-Mills theories, which…

High Energy Physics - Phenomenology · Physics 2010-03-25 Zvi Bern , Lance J. Dixon , David A. Kosower

We give an explicit recursive formula for the all L-loop integrand for scattering amplitudes in N=4 SYM in the planar limit, manifesting the full Yangian symmetry of the theory. This generalizes the BCFW recursion relation for tree…

High Energy Physics - Theory · Physics 2011-01-17 Nima Arkani-Hamed , Jacob L. Bourjaily , Freddy Cachazo , Simon Caron-Huot , Jaroslav Trnka

We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general…

High Energy Physics - Phenomenology · Physics 2015-06-17 Simon Badger , Hjalte Frellesvig , Yang Zhang

We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for $n$ scattering particles into a $\sigma$-moduli multivariate polynomial of what we call the $\textit{standard form}$. We show that a…

High Energy Physics - Theory · Physics 2016-09-05 Michael Zlotnikov

We reduce all the most complicated Feynman integrals in two-loop five-light-parton scattering amplitudes to basic master integrals, while other integrals can be reduced even easier. Our results are expressed as systems of linear relations…

High Energy Physics - Phenomenology · Physics 2020-09-11 Xin Guan , Xiao Liu , Yan-Qing Ma

We recently presented a new method for the evaluation of one-loop amplitude of arbitrary scattering processes, in which the reduction to scalar integrals is performed at the integrand level. In this talk, we review the main features of the…

High Energy Physics - Phenomenology · Physics 2007-09-17 Giovanni Ossola

The infrared exponentiation properties of dimensionally-regularized multi-loop scattering amplitudes are typically hidden at the level of the integrand, materializing only after integral evaluation. We address this long-standing problem by…

High Energy Physics - Theory · Physics 2019-07-22 Robert M. Schabinger

We review recent progress in D-dimensional integrand reduction algorithms for two loop amplitudes and give examples of their application to non-planar maximal cuts of the five-point all-plus helicity amplitude in QCD.

High Energy Physics - Phenomenology · Physics 2014-07-14 Simon Badger , Hjalte Frellesvig , Yang Zhang

In this thesis, we study the integrands of a special four-point correlation function formed of protected half-BPS operators and scattering amplitudes in planar supersymmetric $\mathcal{N}=4$ Yang-Mills. We use the `soft-collinear bootstrap'…

High Energy Physics - Theory · Physics 2018-06-07 Vuong-Viet Tran

We present a new approach to the reduction of one-loop amplitudes obtained by reconstructing the tensorial expression of the scattering amplitudes. The reconstruction is performed at the integrand level by means of a sampling in the…

High Energy Physics - Phenomenology · Physics 2010-11-08 G. Heinrich , G. Ossola , T. Reiter , F. Tramontano

We extend the applications of prescriptive unitarity beyond the planar limit to provide local, polylogarithmic, integrand-level representations of six-particle MHV scattering amplitudes in both maximally supersymmetric Yang-Mills theory and…

High Energy Physics - Theory · Physics 2021-06-01 Jacob L. Bourjaily , Enrico Herrmann , Cameron Langer , Andrew J. McLeod , Jaroslav Trnka

We present analytic results for the finite diagrams contributing to the two-loop eight-point MHV scattering amplitude of planar N=4 SYM. We use a recently proposed representation for the integrand of the amplitude in terms of (momentum)…

High Energy Physics - Theory · Physics 2011-07-21 Luis F. Alday

The calculation of scattering amplitudes at higher orders in perturbation theory has reached a high degree of maturity. However, their usage to produce physical predictions within Monte Carlo programs is often precluded by the slow…

High Energy Physics - Phenomenology · Physics 2025-09-24 Víctor Bresó , Gudrun Heinrich , Vitaly Magerya , Anton Olsson

In this presentation, we review the general features of integrand-reduction techniques, with a particular focus on their generalization beyond one loop. We start with a brief discussion of the one-loop scenario, a case in which…

High Energy Physics - Phenomenology · Physics 2016-08-01 Giovanni Ossola

We present a method for the integrand-level reduction of two-loop helicity amplitudes in both $d=4-2\epsilon$ and $d=4$ dimensions. The amplitude is expressed in terms of a set of Feynman integrals and their coefficients that depend on the…

High Energy Physics - Phenomenology · Physics 2025-11-14 Giuseppe Bevilacqua , Dhimiter Canko , Costas Papadopoulos , Aris Spourdalakis

We develop an iterative method for constructing four-dimensional generalized unitarity cuts in $\mathcal{N} = 2$ supersymmetric Yang-Mills (SYM) theory coupled to fundamental matter hypermultiplets ($\mathcal{N} = 2$ SQCD). For iterated…

High Energy Physics - Theory · Physics 2019-10-08 Gregor Kälin , Gustav Mogull , Alexander Ochirov

We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several…

High Energy Physics - Theory · Physics 2011-04-22 James M. Drummond , Johannes M. Henn , Jaroslav Trnka

We employ a scalar model to exemplify the use of contour deformations when solving Lorentz-invariant integral equations for scattering amplitudes. In particular, we calculate the onshell 2 -> 2 scattering amplitude for the scalar system.…

High Energy Physics - Phenomenology · Physics 2019-11-06 Gernot Eichmann , Pedro Duarte , M. T. Peña , Alfred Stadler

The existence of a finite basis of algebraically independent one-loop integrals has underpinned important developments in the computation of one-loop amplitudes in field theories and gauge theories in particular. We give an explicit…

High Energy Physics - Theory · Physics 2011-10-19 Janusz Gluza , Krzysztof Kajda , David A. Kosower

We outline the concrete steps involved in building prescriptive master integrand bases for scattering amplitudes beyond the planar limit. We highlight the role of contour choices in such bases, and illustrate the full process by…

High Energy Physics - Theory · Physics 2022-09-07 Jacob L. Bourjaily , Cameron Langer , Yaqi Zhang