Abstract
The abundance of infrared singularities in gauge theories due to unresolved emission of massless particles (soft and collinear) represents the main difficulty in perturbative calculations. They are typically regularized in dimensional regularization, and their subtraction is usually achieved independently for virtual and real corrections. In this paper, we introduce a new method based on the loop-tree duality (LTD) theorem to accomplish the summation over degenerate infrared states directly at the integrand level such that the cancellation of the infrared divergences is achieved simultaneously, and apply it to reference examples as a proof of concept. Ultraviolet divergences, which are the consequence of the point-like nature of the theory, are also reinterpreted physically in this framework. The proposed method opens the intriguing possibility of carrying out purely four-dimensional implementations of higher-order perturbative calculations at next-to-leading order (NLO) and beyond free of soft and final-state collinear subtractions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C.-N. Yang and R.L. Mills, Conservation of Isotopic Spin and Isotopic Gauge Invariance, Phys. Rev. 96 (1954) 191 [INSPIRE].
C.G. Bollini and J.J. Giambiagi, Dimensional Renormalization: The Number of Dimensions as a Regularizing Parameter, Nuovo Cim. B 12 (1972) 20 [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Regularization and Renormalization of Gauge Fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
G.M. Cicuta and E. Montaldi, Analytic renormalization via continuous space dimension, Lett. Nuovo Cim. 4 (1972) 329 [INSPIRE].
J.F. Ashmore, A Method of Gauge Invariant Regularization, Lett. Nuovo Cim. 4 (1972) 289 [INSPIRE].
S. Catani and M.H. Seymour, A General algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys. B 485 (1997) 291 [Erratum ibid. B 510 (1998) 503] [hep-ph/9605323] [INSPIRE].
S. Catani and M.H. Seymour, The dipole formalism for the calculation of QCD jet cross-sections at next-to-leading order, Phys. Lett. B 378 (1996) 287 [hep-ph/9602277] [INSPIRE].
S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order, Nucl. Phys. B 467 (1996) 399 [hep-ph/9512328] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Antenna subtraction at NNLO, JHEP 09 (2005) 056 [hep-ph/0505111] [INSPIRE].
S. Catani and M. Grazzini, An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC, Phys. Rev. Lett. 98 (2007) 222002 [hep-ph/0703012] [INSPIRE].
V. Del Duca, C. Duhr, G. Somogyi, F. Tramontano and Z. Trócsányi, Higgs boson decay into b-quarks at NNLO accuracy, JHEP 04 (2015) 036 [arXiv:1501.07226] [INSPIRE].
M. Czakon, A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett. B 693 (2010) 259 [arXiv:1005.0274] [INSPIRE].
R. Boughezal, C. Focke, X. Liu and F. Petriello, W -boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, Phys. Rev. Lett. 115 (2015) 062002 [arXiv:1504.02131] [INSPIRE].
J. Gaunt, M. Stahlhofen, F.J. Tackmann and J.R. Walsh, N-jettiness Subtractions for NNLO QCD Calculations, JHEP 09 (2015) 058 [arXiv:1505.04794] [INSPIRE].
S. Catani, T. Gleisberg, F. Krauss, G. Rodrigo and J.-C. Winter, From loops to trees by-passing Feynman’s theorem, JHEP 09 (2008) 065 [arXiv:0804.3170] [INSPIRE].
I. Bierenbaum, S. Catani, P. Draggiotis and G. Rodrigo, A Tree-Loop Duality Relation at Two Loops and Beyond, JHEP 10 (2010) 073 [arXiv:1007.0194] [INSPIRE].
I. Bierenbaum, S. Buchta, P. Draggiotis, I. Malamos and G. Rodrigo, Tree-Loop Duality Relation beyond simple poles, JHEP 03 (2013) 025 [arXiv:1211.5048] [INSPIRE].
S. Buchta, G. Chachamis, P. Draggiotis, I. Malamos and G. Rodrigo, On the singular behaviour of scattering amplitudes in quantum field theory, JHEP 11 (2014) 014 [arXiv:1405.7850] [INSPIRE].
S. Buchta, Theoretical foundations and applications of the Loop-Tree Duality in Quantum Field Theories, Ph.D. Thesis, Universitat de València, (2015), arXiv:1509.07167 [INSPIRE].
S. Buchta, G. Chachamis, P. Draggiotis, I. Malamos and G. Rodrigo, Towards a Numerical Implementation of the Loop-Tree Duality Method, Nucl. Part. Phys. Proc. 258-259 (2015) 33 [arXiv:1509.07386] [INSPIRE].
S. Buchta, G. Chachamis, P. Draggiotis and G. Rodrigo, Numerical implementation of the Loop-Tree Duality method, arXiv:1510.00187 [INSPIRE].
G.F.R. Sborlini, R. Hernandez-Pinto and G. Rodrigo, From dimensional regularization to NLO computations in four dimensions, PoS(EPS-HEP2015)479 [arXiv:1510.01079] [INSPIRE].
D.E. Soper, QCD calculations by numerical integration, Phys. Rev. Lett. 81 (1998) 2638 [hep-ph/9804454] [INSPIRE].
R. Pittau, A four-dimensional approach to quantum field theories, JHEP 11 (2012) 151 [arXiv:1208.5457] [INSPIRE].
A.M. Donati and R. Pittau, Gauge invariance at work in FDR: H → γγ, JHEP 04 (2013) 167 [arXiv:1302.5668] [INSPIRE].
R.A. Fazio, P. Mastrolia, E. Mirabella and W.J. Torres Bobadilla, On the Four-Dimensional Formulation of Dimensionally Regulated Amplitudes, Eur. Phys. J. C 74 (2014) 3197 [arXiv:1404.4783] [INSPIRE].
S. Catani, D. de Florian and G. Rodrigo, Space-like (versus time-like) collinear limits in QCD: Is factorization violated?, JHEP 07 (2012) 026 [arXiv:1112.4405] [INSPIRE].
S. Becker, C. Reuschle and S. Weinzierl, Numerical NLO QCD calculations, JHEP 12 (2010) 013 [arXiv:1010.4187] [INSPIRE].
G. Rodrigo et al., IFIC/15-73 in preparation.
G.F.R. Sborlini, Loop-tree duality and quantum field theory in four dimensions, PoS(RADCOR2015)082 [arXiv:1601.04634] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1506.04617
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Hernández-Pinto, R.J., Sborlini, G.F.R. & Rodrigo, G. Towards gauge theories in four dimensions. J. High Energ. Phys. 2016, 44 (2016). https://doi.org/10.1007/JHEP02(2016)044
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2016)044