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Recent progress in unitarity techniques for one-loop scattering amplitudes makes a numerical implementation of this method possible. We present a 4-dimensional unitarity method for calculating the cut-constructible part of amplitudes and…

High Energy Physics - Phenomenology · Physics 2009-09-17 R. K. Ellis , W. T. Giele , Z. Kunszt

In this article we present a method to generate analytic expressions for the integral coefficients of loop amplitudes using numerical evaluations only. We use high-precision arithmetic to explore the singularity structure of the…

High Energy Physics - Phenomenology · Physics 2023-10-09 Giuseppe De Laurentis , Daniel Maître

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

The method for functional reduction of Feynman integrals, proposed by the author, is used to calculate one-loop integrals corresponding to diagrams with four external lines. The integrals that emerge from amplitudes for the scattering of…

High Energy Physics - Phenomenology · Physics 2023-07-12 O. V. Tarasov

We present a new method for computing multi-loop scattering amplitudes in Quantum Field Theory. It extends the Generalized Unitarity method by constraining not only the integrand of the amplitude but also its full integrated form. Our…

High Energy Physics - Theory · Physics 2025-12-18 Piotr Bargiela

Loop amplitudes are conveniently expressed in terms of master integrals whose coefficients carry the process dependent information. Similarly before integration, the loop integrands may be expressed as a linear combination of propagator…

High Energy Physics - Theory · Physics 2016-12-28 Harald Ita

We present novel techniques for the computation of three-loop four-parton scattering amplitudes in full color, non-planar gauge theories. We elaborate on how the analytic results for these amplitudes can be used to confirm the conjectured…

High Energy Physics - Phenomenology · Physics 2022-08-18 Amlan Chakraborty , Giulio Gambuti

This thesis is focused on the development of new mathematical methods for computing multi-loop scattering amplitudes in gauge theories. In this work we combine, for the first time, the unitarity-based construction for integrands, and the…

High Energy Physics - Phenomenology · Physics 2014-10-21 Ulrich Schubert

We show how Stokes' Theorem, in the fashion of the Generalised Cauchy Formula, can be applied for computing double-cut integrals of one-loop amplitudes analytically. It implies the evaluation of phase-space integrals of rational functions…

High Energy Physics - Phenomenology · Physics 2009-09-11 Pierpaolo Mastrolia

The various sources of Rational Terms contributing to the one-loop amplitudes are critically discussed. We show that the terms originating from the generic (n-4)-dimensional structure of the numerator of the one-loop amplitude can be…

High Energy Physics - Phenomenology · Physics 2008-11-26 Giovanni Ossola , Costas G. Papadopoulos , Roberto Pittau

We apply the recently proposed amplitude reduction at the integrand level method, to the computation of the scattering process 2 photons -> 4 photons, including the case of a massive fermion loop. We also present several improvements of the…

High Energy Physics - Phenomenology · Physics 2009-04-21 Giovanni Ossola , Costas G. Papadopoulos , Roberto Pittau

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 formulate new integration rules for one-loop scattering equations analogous to those at tree-level, and test them in a number of non-trivial cases for amplitudes in scalar $\phi^3$-theory. This formalism greatly facilitates the…

High Energy Physics - Theory · Physics 2016-01-20 Christian Baadsgaard , N. E. J. Bjerrum-Bohr , Jacob L. Bourjaily , Poul H. Damgaard , Bo Feng

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 present a new procedure using on-shell recursion to determine coefficients of integral functions appearing in one-loop scattering amplitudes of gauge theories, including QCD. With this procedure, coefficients of integrals, including…

High Energy Physics - Phenomenology · Physics 2009-11-11 Zvi Bern , N. E. J. Bjerrum-Bohr , David C. Dunbar , Harald Ita

Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their…

High Energy Physics - Phenomenology · Physics 2016-12-14 Tiziano Peraro

The unitarity method for calculating one-loop amplitudes provides algorithms of polynomial complexity. This is primarily beneficial for the computation of multi-leg one loop amplitudes and it is therefore of great interest to develop a…

High Energy Physics - Phenomenology · Physics 2009-04-14 R. Keith Ellis , Walter T. Giele , Zoltan Kunszt

Using the results recently obtained for computing integrals over (non-minimal) pure spinor superspace, we compute the coefficient of the massless two-loop four-point amplitude from first principles. Contrasting with the mathematical…

High Energy Physics - Theory · Physics 2015-05-18 Humberto Gomez , Carlos R. Mafra

We present compact analytic formulae for the one-loop amplitudes for Higgs + 4 parton scattering, $0 \to g g g g h$, $0 \to \bar{q} q gg h$ and $0\to \bar{q} q \bar{q}^\prime q^\prime h$, mediated by a loop of massive coloured quarks. We…

High Energy Physics - Phenomenology · Physics 2022-06-24 Lucy Budge , John M. Campbell , Giuseppe De Laurentis , R. Keith Ellis , Satyajit Seth

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