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Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders. (English) Zbl 1431.81156
Summary: We present the first comprehensive analysis of the unitarity thresholds and anomalous thresholds of scattering amplitudes at two loops and beyond based on the loop-tree duality, and show how non-causal unphysical thresholds are locally cancelled in an efficient way when the forest of all the dual on-shell cuts is considered as one. We also prove that soft and collinear singularities at two loops and beyond are restricted to a compact region of the loop three-momenta, which is a necessary condition for implementing a local cancellation of loop infrared singularities with the ones appearing in real emission; without relying on a subtraction formalism.

81U05 \(2\)-body potential quantum scattering theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81V05 Strong interaction, including quantum chromodynamics
81T50 Anomalies in quantum field theory
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[1] S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett.B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].
[2] T. Becher and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett.102 (2009) 162001 [Erratum ibid.111 (2013) 199905] [arXiv:0901.0722] [INSPIRE].
[3] Cutkosky, Re, Singularities and discontinuities of Feynman amplitudes, J. Math. Phys., 1, 429 (1960) · Zbl 0122.22605
[4] Mandelstam, S., Unitarity condition below physical thresholds in the normal and anomalous cases, Phys. Rev. Lett., 4, 84 (1960) · Zbl 0089.21603
[5] Landau, Ld, On analytic properties of vertex parts in quantum field theory, Nucl. Phys., 13, 181 (1959) · Zbl 0088.22004
[6] Cutkosky, Re, Anomalous thresholds, Rev. Mod. Phys., 33, 448 (1961) · Zbl 0108.42506
[7] Coleman, S.; Norton, Re, Singularities in the physical region, Nuovo Cim., 38, 438 (1965)
[8] Kershaw, D., Algebraic factorization of scattering amplitudes at physical Landau singularities, Phys. Rev., D 5, 1976 (1972)
[9] Deshpande, Ng; Margolis, B.; Trottier, Hd, Gluon mediated rare decays of the top quark: Anomalous threshold and its phenomenological consequences, Phys. Rev., D 45, 178 (1992)
[10] A. Frink, J.G. Korner and J.B. Tausk, Massive two loop integrals and Higgs physics, hep-ph/9709490 [INSPIRE].
[11] Goria, S.; Passarino, G., Anomalous threshold as the pivot of Feynman amplitudes, Nucl. Phys. Proc. Suppl., 183, 320 (2008)
[12] Dennen, T., Landau singularities from the amplituhedron, JHEP, 06, 152 (2017) · Zbl 1380.81397
[13] Chin, P.; Tomboulis, Et, Nonlocal vertices and analyticity: Landau equations and general Cutkosky rule, JHEP, 06, 014 (2018) · Zbl 1395.83105
[14] G. Passarino, Peaks and cusps: anomalous thresholds and LHC physics, arXiv:1807.00503 [INSPIRE].
[15] C. Gómez and R. Letschka, Masses and electric charges: gauge anomalies and anomalous thresholds, arXiv:1903.01311 [INSPIRE].
[16] Catani, S., From loops to trees by-passing Feynman’s theorem, JHEP, 09, 065 (2008) · Zbl 1245.81117
[17] Bierenbaum, I.; Catani, S.; Draggiotis, P.; Rodrigo, G., A tree-loop duality relation at two loops and beyond, JHEP, 10, 073 (2010) · Zbl 1291.81381
[18] Bierenbaum, I., Tree-loop duality relation beyond simple poles, JHEP, 03, 025 (2013)
[19] Buchta, S., On the singular behaviour of scattering amplitudes in quantum field theory, JHEP, 11, 014 (2014) · Zbl 1333.81149
[20] Buchta, S.; Chachamis, G.; Draggiotis, P.; Rodrigo, G., Numerical implementation of the loop-tree duality method, Eur. Phys. J., C 77, 274 (2017)
[21] Driencourt-Mangin, F.; Rodrigo, G.; Sborlini, Gfr, Universal dual amplitudes and asymptotic expansions for gg → H and H → γγ in four dimensions, Eur. Phys. J., C 78, 231 (2018)
[22] Driencourt-Mangin, F.; Rodrigo, G.; Sborlini, Gfr; Torres Bobadilla, Wj, Universal four-dimensional representation of H → γγ at two loops through the Loop-Tree Duality, JHEP, 02, 143 (2019)
[23] Baadsgaard, C., New representations of the perturbative S-matrix, Phys. Rev. Lett., 116, 061601 (2016) · Zbl 1356.81208
[24] Caron-Huot, S., Loops and trees, JHEP, 05, 080 (2011) · Zbl 1296.81128
[25] Hernandez-Pinto, Rj; Sborlini, Gfr; Rodrigo, G., Towards gauge theories in four dimensions, JHEP, 02, 044 (2016) · Zbl 1388.81329
[26] Sborlini, Gfr; Driencourt-Mangin, F.; Hernandez-Pinto, R.; Rodrigo, G., Four-dimensional unsubtraction from the loop-tree duality, JHEP, 08, 160 (2016)
[27] Sborlini, Gfr; Driencourt-Mangin, F.; Rodrigo, G., Four-dimensional unsubtraction with massive particles, JHEP, 10, 162 (2016)
[28] Tomboulis, Et, Causality and unitarity via the tree-loop duality relation, JHEP, 05, 148 (2017) · Zbl 1396.81184
[29] Feynman, Rp, Quantum theory of gravitation, Acta Phys. Polon., 24, 697 (1963)
[30] R. Runkel, Z. Szor, J.P. Vesga and S. Weinzierl, Causality and loop-tree duality at higher loops, Phys. Rev. Lett.122 (2019) 111603 [Erratum ibid.123 (2019) 059902] [arXiv:1902.02135] [INSPIRE].
[31] Capatti, Z.; Hirschi, V.; Kermanschah, D.; Ruijl, B., Loop-tree duality for multiloop numerical integration, Phys. Rev. Lett., 123, 151602 (2019)
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