γ5\gamma_{5} in FDH

We investigate the regularization-scheme dependent treatment of $\gamma_{5}$ in the framework of dimensional regularization, mainly focusing on the four-dimensional helicity scheme (FDH). Evaluating distinctive examples, we find that for one-loop calculations, the recently proposed four-dimensional formulation (FDF) of the FDH scheme constitutes a viable and efficient alternative compared to more traditional approaches. In addition, we extend the considerations to the two-loop level and compute the pseudo-scalar form factors of quarks and gluons in FDH. We provide the necessary operator renormalization and discuss at a practical level how the complexity of intermediate calculational steps can be reduced in an efficient way.Comment: 28 pages, 7 figure

Small-mass effects in heavy-to-light form factors

We present the heavy-to-light form factors with two different non-vanishing masses at next-to-next-to-leading order and study its expansion in the small mass. The leading term of this small-mass expansion leads to a factorized expression for the form factor. The presence of a second mass results in a new feature, in that the soft contribution develops a factorization anomaly. This cancels with the corresponding anomaly in the collinear contribution. With the generalized factorization presented here, it is possible to obtain the leading small-mass terms for processes with large masses, such as muon-electron scattering, from the corresponding massless amplitude and the soft contribution.Comment: 20 pages, 4 figures, 1 ancillary file, published versio

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

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

Regularization-scheme dependence of QCD amplitudes in the massive case

We investigate QCD amplitudes with massive quarks computed in the four-dimensional helicity scheme (FDH) and dimensional reduction at NNLO and describe how they are related to the corresponding amplitudes computed in conventional dimensional regularization. To this end, the scheme dependence of the heavy quark and the velocity-dependent cusp anomalous dimensions is determined using soft-collinear effective theory. The results are checked against explicit computations of massive form factors in FDH at NNLO. Our results complete the description of the scheme dependence of QCD amplitudes at NNLO