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de Florian, D., Sborlini, G. F. R., & Rodrigo, G. (2016). QED corrections to the Altarelli-Parisi splitting functions. Eur. Phys. J. C, 76(5), 282–6pp.
Abstract: We discuss the combined effect of QED and QCD corrections to the evolution of parton distributions. We extend the available knowledge of the Altarelli-Parisi splitting functions to one order higher in QED, and we provide explicit expressions for the splitting kernels up to O(alpha alpha(S)). The results presented in this article allow one to perform a parton distribution function analysis reaching full NLO QCD-QED combined precision.
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Sborlini, G. F. R., de Florian, D., & Rodrigo, G. (2015). Polarized triple-collinear splitting functions at NLO for processes with photons. J. High Energy Phys., 03(3), 021–30pp.
Abstract: We compute the polarized splitting functions in the triple collinear limit at next-to-leading order accuracy (NLO) in the strong coupling alpha(S), for the splitting processes gamma -> qq gamma, gamma -> qqg and g -> qq gamma. The divergent structure of each splitting function was compared to the predicted behaviour according to Catani's formula. The results obtained in this paper are compatible with the unpolarized splitting functions computed in a previous article. Explicit results for NLO corrections are presented in the context of conventional dimensional regularization (CDR).
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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). 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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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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