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Ramirez-Uribe, S., Hernandez-Pinto, R. J., Rodrigo, G., & Sborlini, G. F. R. (2022). From Five-Loop Scattering Amplitudes to Open Trees with the Loop-Tree Duality. Symmetry-Basel, 14(12), 2571–14pp.
Abstract: Characterizing multiloop topologies is an important step towards developing novel methods at high perturbative orders in quantum field theory. In this article, we exploit the Loop-Tree Duality (LTD) formalism to analyse multiloop topologies that appear for the first time at five loops. Explicitly, we open the loops into connected trees and group them according to their topological properties. Then, we identify a kernel generator, the so-called N7MLT universal topology, that allows us to describe any scattering amplitude of up to five loops. Furthermore, we provide factorization and recursion relations that enable us to write these multiloop topologies in terms of simpler subtopologies, including several subsets of Feynman diagrams with an arbitrary number of loops. Our approach takes advantage of many symmetries present in the graphical description of the original fundamental five-loop topologies. The results obtained in this article might shed light into a more efficient determination of higher-order corrections to the running couplings, which are crucial in the current and future precision physics program.
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Renteria-Estrada, D. F., Hernandez-Pinto, R. J., & Sborlini, G. F. R. (2021). Analysis of the Internal Structure of Hadrons Using Direct Photon Production. Symmetry-Basel, 13(6), 942–10pp.
Abstract: Achieving a precise description of the internal structure of hadrons is crucial for deciphering the hidden properties and symmetries of fundamental particles. It is a hard task since there are several bottlenecks in obtaining theoretical predictions starting from first principles. In order to complement highly accurate experiments, it is necessary to use ingenious strategies to impose constraints from the theory side. In this article, we describe how photons can be used to unveil the internal structure of hadrons. We explore how to describe NLO QCD plus LO QED corrections to hadron plus photon production at colliders and discuss the impact of these effects on the experimental measurements.
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Aguilera-Verdugo, J. D., Driencourt-Mangin, F., Hernandez-Pinto, R. J., Plenter, J., Prisco, R. M., Ramirez-Uribe, N. S., et al. (2021). A Stroll through the Loop-Tree Duality. Symmetry-Basel, 13(6), 1029–37pp.
Abstract: The Loop-Tree Duality (LTD) theorem is an innovative technique to deal with multi-loop scattering amplitudes, leading to integrand-level representations over a Euclidean space. In this article, we review the last developments concerning this framework, focusing on the manifestly causal representation of multi-loop Feynman integrals and scattering amplitudes, and the definition of dual local counter-terms to cancel infrared singularities.
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Aguilera-Verdugo, J. J., Hernandez-Pinto, R. J., Rodrigo, G., Sborlini, G. F. R., & Torres Bobadilla, W. J. (2021). Mathematical properties of nested residues and their application to multi-loop scattering amplitudes. J. High Energy Phys., 02(2), 112–42pp.
Abstract: The computation of multi-loop multi-leg scattering amplitudes plays a key role to improve the precision of theoretical predictions for particle physics at high-energy colliders. In this work, we focus on the mathematical properties of the novel integrand-level representation of Feynman integrals, which is based on the Loop-Tree Duality (LTD). We explore the behaviour of the multi-loop iterated residues and explicitly show, by developing a general compact and elegant proof, that contributions associated to displaced poles are cancelled out. The remaining residues, called nested residues as originally introduced in ref. [1], encode the relevant physical information and are naturally mapped onto physical configurations associated to nondisjoint on-shell states. By going further on the mathematical structure of the nested residues, we prove that unphysical singularities vanish, and show how the final expressions can be written by using only causal denominators. In this way, we provide a mathematical proof for the all-loop formulae presented in ref. [2].
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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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