Universal dual amplitudes and asymptotic expansions for gg→Hgg\to H and H→γγH\to \gamma\gamma in four dimensions

Though the one-loop amplitudes of the Higgs boson to massless gauge bosons are finite because there is no direct interaction at tree-level in the Standard Model, a well-defined regularization scheme is still required for their correct evaluation. We reanalyze these amplitudes in the framework of the four-dimensional unsubtraction and the loop-tree duality (FDU/LTD), and show how a local renormalization solves potential regularization ambiguities. The Higgs boson interactions are also used to illustrate new additional advantages of this formalism. We show that LTD naturally leads to very compact integrand expressions in four space-time dimensions of the one-loop amplitude with virtual electroweak gauge bosons. They exhibit the same functional form as the amplitudes with top quarks and charged scalars, thus opening further possibilities for simplifications in higher-order computations. Another outstanding application is the straightforward implementation of asymptotic expansions by using dual amplitudes. One of the main benefits of the LTD representation is that it is supported in a Euclidean space. This characteristic feature naturally leads to simpler asymptotic expansions.Comment: 11 pages, no figures. Minor modifications, discussion improved. Final version published in EPJ

Recent developments from the loop-tree duality

In this talk, we review the most recent developments of the four-dimensional unsubstraction (FDU) and loop-tree duality (LTD) methods. In particular, we make emphasis on the advantages of the LTD formalism regarding asymptotic expansions of loop integrands.Comment: 8 pages, 1 figure. Presented at 13th International Symposium on Radiative Corrections RADCOR2017, 24-29 September 2017, St. Gilgen, Austri

On the interplay between the loop-tree duality and helicity amplitudes

The spinor-helicity formalism has proven to be very efficient in the calculation of scattering amplitudes in quantum field theory, while the loop tree duality (LTD) representation of multi-loop integrals exhibits appealing and interesting advantages with respect to other approaches. In view of the most recent developments in LTD, we exploit the synergies with the spinor-helicity formalism to analyse illustrative one- and two-loop scattering processes. We focus our discussion on the local UV renormalisation of IR and UV finite amplitudes and present a fully automated numerical implementation that provides efficient expressions which are integrable directly in four space-time dimensions.Comment: 12 pages, 5 figures. In v2: discussion on the application of two-loop local renormalisation added; references update

To dd, or not to dd: Recent developments and comparisons of regularization schemes

We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the computation of simple quantities in the various schemes, we point out similarities and differences between them.Comment: 61 pages, 12 figures; version sent to EPJC, references update

Open loop amplitudes and causality to all orders and powers from the loop-tree duality

Multiloop scattering amplitudes describing the quantum fluctuations at high-energy scattering processes are the main bottleneck in perturbative quantum field theory. The loop-tree duality is a novel method aimed at overcoming this bottleneck by opening the loop amplitudes into trees and combining them at integrand level with the real-emission matrix elements. In this Letter, we generalize the loop-tree duality to all orders in the perturbative expansion by using the complex Lorentz-covariant prescription of the original one-loop formulation. We introduce a series of mutiloop topologies with arbitrary internal configurations and derive very compact and factorizable expressions of their open-to-trees representation in the loop-tree duality formalism. Furthermore, these expressions are entirely independent at integrand level of the initial assignments of momentum flows in the Feynman representation and remarkably free of noncausal singularities. These properties, that we conjecture to hold to other topologies at all orders, provide integrand representations of scattering amplitudes that exhibit manifest causal singular structures and better numerical stability than in other representations.Comment: Final version to appear in Physical Review Letter

A stroll through the loop-tree duality

The Loop-Tree Duality (LTD) theorem is an innovative technique to deal with multi-loop scattering amplitudes, leading to integrand-level representations over a Euclidean space. In this article, we review the last developments concerning this framework, focusing on the manifestly causal representation of multi-loop Feynman integrals and scattering amplitudes, and the definition of dual local counter-terms to cancel infrared singularities

To d , or not to d : recent developments and comparisons of regularization schemes

We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the computation of simple quantities in the various schemes, we point out similarities and differences between them

May the four be with you: novel IR-subtraction methods to tackle NNLO calculations

In this manuscript, we summarise all discussions originated as a result of the WorkStop/ThinkStart 3.0: paving the way to alternative NNLO strategies that took place on 4.-6. November 2019 at the Galileo Galilei Institute for Theoretical Physics (GGI). We gratefully acknowledge the support of GGI and the COST Action CA16201 PARTICLEFACE. We wish to thank toW.M. Marroquin and M. Morandini for their help in organising the workshop. P. Banerjee acknowledges support by the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 701647. A.L. Cherchiglia, B. Hiller and M.Sampaio acknowledge support from Fundacao para a Ciencia e Tecnologia (FCT) through the projects UID/FIS/04564/2020 and CERN/FIS-COM/0035/2019. The work of L. Cieri has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 754496. The work of F. Driencourt-Mangin, G. Rodrigo, G. Sborlini and W.J. Torres Bobadilla is supported by the Spanish Government (Agencia Estatal de Investigacion), ERDF funds from European Commission (Grant No. FPA2017-84445-P), Generalitat Valenciana (Grant No. PROMETEO/2017/053) and from the SpanishGovernment (FJCI-2017-32128). T. Engel acknowledges support by the Swiss National Science Foundation (SNF) under contract 200021_178967. C. Gnendiger, R. Pittau, A. Signer and D. Stockinger wish to thank B. Page for his help in establishing (2.60). The work of R. J. Hernandez-Pinto is supported by CONACyT through the Project No. A1-S-33202 (Ciencia Basica) and Sistema Nacional de Investigadores. G. Pelliccioli was supported by the Bundesministerium fur Bildung und Forschung (BMBF, German Federal Ministry for Education and Research) under contract no. 05H18WWCA1. J. Pires was supported by Fundacao para a Ciencia e Tecnologia (FCT, Portugal) through the contract UIDP/50007/2020 and project CERN/FIS-PAR/0024/2019. The work of R. Pittau has been supported by the SpanishGovernment grant PID2019-106087GB-C21 and by the Junta de Andalucia project P18-FR-4314 (fondos FEDER). M. Sampaio acknowledges a research grant from CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico 303482/2017-6). C. Signorile-Signorile was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Grant no. 396021762 - TRR 257.In this manuscript, we report the outcome of the topical workshop: paving the way to alternative NNLO strategies (https://indico.ific.uv.es/e/WorkStop-ThinkStart_3.0), by presenting a discussion about different frameworks to perform precise higher-order computations for high-energy physics. These approaches implement novel strategies to deal with infrared and ultraviolet singularities in quantum field theories. A special emphasis is devoted to the local cancellation of these singularities, which can enhance the efficiency of computations and lead to discover novel mathematical properties in quantum field theories.European Commission 701647Portuguese Foundation for Science and Technology European Commission UID/FIS/04564/2020 CERN/FIS-COM/0035/2019European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant 754496Spanish Government (Agencia Estatal de Investigacion)ERDF funds from European Commission FPA2017-84445-PGeneralitat Valenciana European Commission PROMETEO/2017/053Spanish Government European Commission FJCI-2017-32128 PID2019-106087GB-C21Swiss National Science Foundation (SNSF) 200021_178967Consejo Nacional de Ciencia y Tecnologia (CONACyT) A1-S-33202Sistema Nacional de InvestigadoresFederal Ministry of Education & Research (BMBF) 05H18WWCA1Portuguese Foundation for Science and Technology UIDP/50007/2020 CERN/FIS-PAR/0024/2019Junta de Andalucia P18-FR-4314Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ) 303482/2017-6German Research Foundation (DFG) 396021762 - TRR 257GGIEuropean Cooperation in Science and Technology (COST) CA16201 PARTICLEFAC