Generalised Unitarity for Dimensionally Regulated Amplitudes

We present a novel set of Feynman rules and generalised unitarity cut-conditions for computing one-loop amplitudes via d-dimensional integrand reduction algorithm. Our algorithm is suited for analytic as well as numerical result, because all ingredients turn out to have a four-dimensional representation. We will apply this formalism to NLO QCD corrections.Comment: Presented at SILAFAE 2014, 24-28 Nov, Ruta N, Medellin, Colombi

On μe-scattering at NNLO in QED

We report on the current status of the analytic evaluation of the two-loop corrections to the μescattering in Quantum Electrodynamics, presenting state-of-the art techniques which have been developed to address this challenging task

Muon-electron scattering at NNLO

We present the first calculation of the complete set of NNLO QED corrections for muon-electron scattering. This includes leptonic, non-perturbative hadronic, and photonic contributions. All fermionic corrections as well as the photonic subset that only corrects the electron or the muon line are included with full mass dependence. The genuine four-point two-loop topologies are computed as an expansion in the small electron mass, taking into account both, logarithmically enhanced as well as constant mass effects using massification. A fast and stable implementation of the numerically delicate real-virtual contribution is achieved by combining OpenLoops with next-to-soft stabilisation. All matrix elements are implemented in the McMule framework, which allows for the fully-differential calculation of any infrared-safe observable. This calculation is to be viewed in the context of the MUonE experiment requiring a background prediction at the level of 10 ppm. Our results thus represent a major milestone towards this ambitious precision goal

Two-Loop Four-Fermion Scattering Amplitude in QED

We present the first fully analytic evaluation of the transition amplitude for the scattering of a massless into a massive pair of fermions at the two-loop level in quantum electrodynamics. Our result is an essential ingredient for the determination of the electromagnetic coupling within scattering reactions, beyond the currently known accuracy, which has a crucial impact on the evaluation of the anomalous magnetic moment of the muon. It will allow, in particular, for a precise determination of the leading hadronic contribution to the (g−2)μ in the MUonE experiment at CERN, and therefore can be used to shed light on the current discrepancy between the standard model prediction and the experimental measurement for this important physical observable

The two-loop four-fermion scattering amplitude in QED

We present the analytic evaluation of the two-loop corrections to the amplitude for the scattering of four fermions in Quantum Electrodynamics, $f^- + f^+ + F^- + F^+ \to 0$, with $f$ and $F$ representing a massless and a massive lepton, respectively. Dimensional regularization is employed to evaluate the loop integrals. Ultraviolet divergences are removed by renormalizing the coupling constant in the ${\overline{\text{MS}}}$-scheme, and the lepton mass as well as the external fields in the on-shell scheme. The analytic result for the renormalized amplitude is expressed as Laurent series around $d=4$ space-time dimensions, and contains Generalized Polylogarithms with up to weight four. The structure of the residual infrared divergences of the virtual amplitude is in agreement with the prediction of the Soft Collinear Effective Theory. Our analytic results are an essential ingredient for the computation of the scattering cross section for massive fermion-pair production in massless fermion-pair annihilation, i.e. $f^- f^+ \to F^- F^+$, and crossing related processes such as the elastic scattering $f F \to f F$, with up to Next-to-Next to Leading Order accuracy.Comment: 5 pages, 2 figures, 1 table + supplemental materia

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

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