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Filipuzzi, A. (2011). Universality Violation In Leptonic W Decays: An Effective Field Theory Approach. Acta Physica Polonica B, 42(11), 2453–2459.
Abstract: We analyse the deviation from universality in leptonic W decays suggested by current PDG data within a general effective field theory approach. Considering the constraints to the New Physics effects coming from Electroweak precision observables we are able to set limits on the amount of universality violation that can be accounted for in a broad class of New Physics models. Our approach starts from a usual Single Operator analysis and extends up to considering the interplay of all the effective operators defined by our EFT.
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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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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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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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Casas, F., Oteo, J. A., & Ros, J. (2012). Unitary transformations depending on a small parameter. Proc. R. Soc. A, 468(2139), 685–700.
Abstract: We formulate a unitary perturbation theory for quantum mechanics inspired by the Lie-Deprit formulation of canonical transformations. The original Hamiltonian is converted into a solvable one by a transformation obtained through a Magnus expansion. This ensures unitarity at every order in a small parameter. A comparison with the standard perturbation theory is provided. We work out the scheme up to order ten with some simple examples.
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