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Bierenbaum, I., Buchta, S., Draggiotis, P., Malamos, I., & Rodrigo, G. (2013). Tree-loop duality relation beyond single poles. J. High Energy Phys., 03(3), 025–24pp.
Abstract: We develop the Tree-Loop Duality Relation for two- and three-loop integrals with multiple identical propagators (multiple poles). This is the extension of the Duality Relation for single poles and multi-loop integrals derived in previous publications. We prove a generalization of the formula for single poles to multiple poles and we develop a strategy for dealing with higher-order pole integrals by reducing them to single pole integrals using Integration By Parts.
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Bierenbaum, I., Catani, S., Draggiotis, P., & Rodrigo, G. (2010). A tree-loop duality relation at two loops and beyond. J. High Energy Phys., 10(10), 073–22pp.
Abstract: The duality relation between one-loop integrals and phase-space integrals, developed in a previous work, is extended to higher-order loops. The duality relation is realized by a modification of the customary +i0 prescription of the Feynman propagators, which compensates for the absence of the multiple-cut contributions that appear in the Feynman tree theorem. We rederive the duality theorem at one-loop order in a form that is more suitable for its iterative extension to higher-loop orders. We explicitly show its application to two-and three-loop scalar master integrals, and we discuss the structure of the occurring cuts and the ensuing results in detail.
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Buchta, S., Chachamis, G., Draggiotis, P., Malamos, I., & Rodrigo, G. (2014). On the singular behaviour of scattering amplitudes in quantum field theory. J. High Energy Phys., 11(11), 014–13pp.
Abstract: We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop-tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.
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Campanario, F., Kerner, M., Ninh, L. D., & Rosario, I. (2020). Diphoton production in vector-boson scattering at the LHC at next-to-leading order QCD. J. High Energy Phys., 06(6), 072–25pp.
Abstract: In this paper, we present results at next-to-leading order (NLO) QCD for photon pair production in association with two jets via vector boson scattering within the Standard Model (SM), and also in an effective field theory framework with anomalous gauge coupling effects via bosonic dimension-6 and 8 operators. We observe that, com- pared to other processes in the class of two electroweak (EW) vector boson production in association with two jets, more exclusive cuts are needed in order to suppress the SM QCD-induced background channel. As expected, the NLO QCD corrections reduce the scale uncertainties considerably. Using a well-motivated dynamical scale choice, we find moderate K -factors for the EW-induced process while the QCD-induced channel receives much larger corrections. Furthermore, we observe that applying a cut of Delta phi(cut)(j2 gamma 1) <2.5 for the second hardest jet and the hardest photon helps to increase the signal significance and reduces the impact of higher-order QCD corrections.
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Campanario, F., Kerner, M., Ninh, D. L., & Zeppenfeld, D. (2014). Next-to-leading order QCD corrections to ZZ production in association with two jets. J. High Energy Phys., 07(7), 148–14pp.
Abstract: We present a calculation of next-to-leading order QCD corrections to QCD-induced ZZ production in association with two jets at hadron colliders. Both Z bosons decay leptonically with all off-shell effects, virtual photon contributions and spin-correlation effects fully taken into account. This process is an important background to weak boson scattering and to searches for signals of new physics beyond the Standard Model. As expected, the next-to-leading order corrections reduce significantly the scale uncertainty and show a non-trivial phase space dependence in kinematic distributions. Our code will be publicly available as part of the parton level Monte Carlo program VBFNLO.
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