Torres Bobadilla, W. J. et al, Driencourt-Mangin, F., & Rodrigo, G. (2021). May the four be with you: novel IR-subtraction methods to tackle NNLO calculations. Eur. Phys. J. C, 81(3), 250–61pp.
Abstract: 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.
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Ramirez-Uribe, S., Hernandez-Pinto, R. J., Rodrigo, G., Sborlini, G. F. R., & Torres Bobadilla, W. J. (2021). Universal opening of four-loop scattering amplitudes to trees. J. High Energy Phys., 04(4), 129–22pp.
Abstract: The perturbative approach to quantum field theories has made it possible to obtain incredibly accurate theoretical predictions in high-energy physics. Although various techniques have been developed to boost the efficiency of these calculations, some ingredients remain specially challenging. This is the case of multiloop scattering amplitudes that constitute a hard bottleneck to solve. In this paper, we delve into the application of a disruptive technique based on the loop-tree duality theorem, which is aimed at an efficient computation of such objects by opening the loops to nondisjoint trees. We study the multiloop topologies that first appear at four loops and assemble them in a clever and general expression, the (NMLT)-M-4 universal topology. This general expression enables to open any scattering amplitude of up to four loops, and also describes a subset of higher order configurations to all orders. These results confirm the conjecture of a factorized opening in terms of simpler known subtopologies, which also determines how the causal structure of the entire loop amplitude is characterized by the causal structure of its subtopologies. In addition, we confirm that the loop-tree duality representation of the (NMLT)-M-4 universal topology is manifestly free of noncausal thresholds, thus pointing towards a remarkably more stable numerical implementation of multiloop scattering amplitudes.
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Llanes Jurado, J., Rodrigo, G., & Torres Bobadilla, W. J. (2017). From Jacobi off-shell currents to integral relations. J. High Energy Phys., 12(12), 122–22pp.
Abstract: In this paper, we study off-shell currents built from the Jacobi identity of the kinematic numerators of gg -> X with X = ss, q (q) over bar, gg. We find that these currents can be schematically written in terms of three-point interaction Feynman rules. This representation allows for a straightforward understanding of the Colour-Kinematics duality as well as for the construction of the building blocks for the generation of higher-multiplicity tree-level and multi-loop numerators. We also provide one-loop integral relations through the Loop-Tree duality formalism with potential applications and advantages for the computation of relevant physical processes at the Large Hadron Collider. We illustrate these integral relations with the explicit examples of QCD one-loop numerators of gg -> ss.
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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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