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Aguilera-Verdugo, J. J., Driencourt-Mangin, F., Hernandez-Pinto, R. J., Plenter, J., Ramirez-Uribe, S., Renteria-Olivo, A. E., et al. (2020). Open Loop Amplitudes and Causality to All Orders and Powers from the Loop-Tree Duality. Phys. Rev. Lett., 124(21), 211602–6pp.
Abstract: Multiloop scattering amplitudes describing the quantum fluctuations at high-energy scattering processes are the main bottleneck in perturbative quantum field theory. The loop-tree duality is a novel method aimed at overcoming this bottleneck by opening the loop amplitudes into trees and combining them at integrand level with the real-emission matrix elements. In this Letter, we generalize the loop-tree duality to all orders in the perturbative expansion by using the complex Lorentz-covariant prescription of the original one-loop formulation. We introduce a series of mutiloop topologies with arbitrary internal configurations and derive very compact and factorizable expressions of their open-to-trees representation in the loop-tree duality formalism. Furthermore, these expressions are entirely independent at integrand level of the initial assignments of momentum flows in the Feynman representation and remarkably free of noncausal singularities. These properties, that we conjecture to hold to other topologies at all orders, provide integrand representations of scattering amplitudes that exhibit manifest causal singular structures and better numerical stability than in other representations.
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Gnendiger, C., Signer, A., Stockinger, D., Broggio, A., Cherchiglia, A. L., Driencourt-Mangin, F., et al. (2017). To d, or not to d: recent developments and comparisons of regularization schemes. Eur. Phys. J. C, 77(7), 471–39pp.
Abstract: 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.
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Foffa, S., Sturani, R., & Torres Bobadilla, W. J. (2021). Efficient resummation of high post-Newtonian contributions to the binding energy. J. High Energy Phys., 02(2), 165–18pp.
Abstract: A factorisation property of Feynman diagrams in the context the Effective Field Theory approach to the compact binary problem has been recently employed to efficiently determine the static sector of the potential at fifth post-Newtonian (5PN) order. We extend this procedure to the case of non-static diagrams and we use it to fix, by means of elementary algebraic manipulations, the value of more than one thousand diagrams at 5PN order, that is a substantial fraction of the diagrams needed to fully determine the dynamics at 5PN. This procedure addresses the redundancy problem that plagues the computation of the binding energy with respect to more “efficient” observables like the scattering angle, thus making the EFT approach in harmonic gauge at least as scalable as the others methods.
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Driencourt-Mangin, F., Rodrigo, G., Sborlini, G. F. R., & Torres Bobadilla, W. J. (2019). Universal four-dimensional representation of H -> gamma gamma at two loops through the Loop-Tree Duality. J. High Energy Phys., 02(2), 143–39pp.
Abstract: We extend useful properties of the H unintegrated dual amplitudes from one- to two-loop level, using the Loop-Tree Duality formalism. In particular, we show that the universality of the functional form regardless of the nature of the internal particle still holds at this order. We also present an algorithmic way to renormalise two-loop amplitudes, by locally cancelling the ultraviolet singularities at integrand level, thus allowing a full four-dimensional numerical implementation of the method. Our results are compared with analytic expressions already available in the literature, finding a perfect numerical agreement. The success of this computation plays a crucial role for the development of a fully local four-dimensional framework to compute physical observables at Next-to-Next-to Leading order and beyond.
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Driencourt-Mangin, F., Rodrigo, G., Sborlini, G. F. R., & Torres Bobadilla, W. J. (2022). Interplay between the loop-tree duality and helicity amplitudes. Phys. Rev. D, 105(1), 016012–13pp.
Abstract: The spinor-helicity formalism has proven to be very efficient in the calculation of scattering amplitudes in quantum field theory, while the loop-tree duality (LTD) representation of multiloop integrals exhibits appealing and interesting advantages with respect to other approaches. In view of the most recent developments in LTD, we exploit the synergies with the spinor-helicity formalism to analyze illustrative one- and two-loop scattering processes. We focus our discussion on the local UV renormalization of IR and UV finite helicity amplitudes and present a fully automated numerical implementation that provides efficient expressions, which are integrable directly in four space-time dimensions.
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