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Dhani, P. K., Rodrigo, G., & Sborlini, G. F. R. (2023). Triple-collinear splittings with massive particles. J. High Energy Phys., 12(12), 188–20pp.
Abstract: We analyze in detail the most singular behaviour of processes involving triple-collinear splittings with massive particles in the quasi-collinear limit, and present compact expressions for the splitting amplitudes and the corresponding splitting kernels at the squared-amplitude level. Our expressions fully agree with well-known triple-collinear splittings in the massless limit, which are used as a guide to achieve the final expressions. These results are important to quantify dominant mass effects in many observables, and constitute an essential ingredient of current high-precision computational frameworks for collider phenomenology.
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de Florian, D., Sborlini, G. F. R., & Rodrigo, G. (2016). Two-loop QED corrections to the Altarelli-Parisi splitting functions. J. High Energy Phys., 10(10), 056–16pp.
Abstract: We compute the two-loop QED corrections to the Altarelli-Parisi (AP) splitting functions by using a deconstructive algorithmic Abelianization of the well-known NLO QCD corrections. We present explicit results for the full set of splitting kernels in a basis that includes the leptonic distribution functions that, starting from this order in the QED coupling, couple to the partonic densities. Finally, we perform a phenomenological analysis of the impact of these corrections in the splitting functions.
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Driencourt-Mangin, F., Rodrigo, G., & Sborlini, G. F. R. (2018). Universal dual amplitudes and asymptotic expansions for gg -> H and H -> gamma gamma in four dimensions. Eur. Phys. J. C, 78(3), 231–7pp.
Abstract: Though the one-loop amplitudes of the Higgs boson to massless gauge bosons are finite because there is no direct interaction at tree level in the Standard Model, a well-defined regularization scheme is still required for their correct evaluation. We reanalyze these amplitudes in the framework of the four-dimensional unsubtraction and the loop-tree duality (EDU/LTD), and show how a local renormalization solves potential regularization ambiguities. The Higgs boson interactions are also used to illustrate new additional advantages of this formalism. We show that LTD naturally leads to very compact integrand expressions in four space-time dimensions of the one-loop amplitude with virtual electroweak gauge bosons. They exhibit the same functional form as the amplitudes with top quarks and charged scalars, thus opening further possibilities for simplifications in higher-order computations. Another outstanding application is the straightforward implementation of asymptotic expansions by using dual amplitudes. One of the main benefits of the LTD representation is that it is supported in a Euclidean space. This characteristic feature naturally leads to simpler asymptotic expansions.
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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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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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Clemente, G., Crippa, A., Jansen, K., Ramirez-Uribe, S., Renteria-Olivo, A. E., Rodrigo, G., et al. (2023). Variational quantum eigensolver for causal loop Feynman diagrams and directed acyclic graphs. Phys. Rev. D, 108(9), 096035–19pp.
Abstract: We present a variational quantum eigensolver (VQE) algorithm for the efficient bootstrapping of the causal representation of multiloop Feynman diagrams in the loop-tree duality or, equivalently, the selection of acyclic configurations in directed graphs. A loop Hamiltonian based on the adjacency matrix describing a multiloop topology, and whose different energy levels correspond to the number of cycles, is minimized by VQE to identify the causal or acyclic configurations. The algorithm has been adapted to select multiple degenerated minima and thus achieves higher detection rates. A performance comparison with a Grover's based algorithm is discussed in detail. The VQE approach requires, in general, fewer qubits and shorter circuits for its implementation, albeit with lesser success rates.
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