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Campanario, F., Czyz, H., Gluza, J., Jelinski, T., Rodrigo, G., Tracz, S., et al. (2019). Standard model radiative corrections in the pion form factor measurements do not explain the a(mu) anomaly. Phys. Rev. D, 100(7), 076004–5pp.
Abstract: In this paper, we address the question of whether the almost four standard deviations difference between theory and experiment for the muon anomalous magnetic moment a(mu) can be explained as a higher-order Standard Model perturbation effect in the pion form factor measurements. This question has, until now, remained open, obscuring the source of discrepancies between the measurements. We calculate the last radiative corrections for the extraction of the pion form factor, which were believed to be potentially substantial enough to explain the data within the Standard Model. We find that the corrections are too small to diminish existing discrepancies in the determination of the pion form factor for different kinematical configurations of low-energy BABAR, BES-III and KLOE experiments. Consequently, they cannot noticeably change the previous predictions for a(mu) and decrease the deviations between theory and direct measurements. To solve the above issues, new data and better understanding of low-energy experimental setups are needed, especially as new direct a(mu) measurements at Fermilab and J-PARC will provide new insights and substantially shrink the experimental error.
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Aguilera-Verdugo, J. J., Driencourt-Mangin, F., Plenter, J., Ramirez-Uribe, S., Rodrigo, G., Sborlini, G. F. R., et al. (2019). Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders. J. High Energy Phys., 12(12), 163–12pp.
Abstract: 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.
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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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Aguilera-Verdugo, J. J., Hernandez-Pinto, R. J., Rodrigo, G., Sborlini, G. F. R., & Torres Bobadilla, W. J. (2021). Causal representation of multi-loop Feynman integrands within the loop-tree duality. J. High Energy Phys., 01(1), 69–26pp.
Abstract: The numerical evaluation of multi-loop scattering amplitudes in the Feynman representation usually requires to deal with both physical (causal) and unphysical (non-causal) singularities. The loop-tree duality (LTD) offers a powerful framework to easily characterise and distinguish these two types of singularities, and then simplify analytically the underling expressions. In this paper, we work explicitly on the dual representation of multi-loop Feynman integrals generated from three parent topologies, which we refer to as Maximal, Next-to-Maximal and Next-to-Next-to-Maximal loop topologies. In particular, we aim at expressing these dual contributions, independently of the number of loops and internal configurations, in terms of causal propagators only. Thus, providing very compact and causal integrand representations to all orders. In order to do so, we reconstruct their analytic expressions from numerical evaluation over finite fields. This procedure implicitly cancels out all unphysical singularities. We also interpret the result in terms of entangled causal thresholds. In view of the simple structure of the dual expressions, we integrate them numerically up to four loops in integer space-time dimensions, taking advantage of their smooth behaviour at integrand level.
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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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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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Plenter, J., & Rodrigo, G. (2021). Asymptotic expansions through the loop-tree duality. Eur. Phys. J. C, 81(4), 320–13pp.
Abstract: Asymptotic expansions of Feynman amplitudes in the loop-tree duality formalism are implemented at integrand-level in the Euclidean space of the loop three-momentum, where the hierarchies among internal and external scales are well-defined. The ultraviolet behaviour of the individual contributions to the asymptotic expansion emerges only in the first terms of the expansion and is renormalized locally in four space-time dimensions. These two properties represent an advantage over the method of Expansion by Regions. We explore different approaches in different kinematical limits, and derive explicit asymptotic expressions for several benchmark configurations.
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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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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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