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Sborlini, G. F. R., Driencourt-Mangin, F., Hernandez-Pinto, R. J., & Rodrigo, G. (2016). Four-dimensional unsubtraction from the loop-tree duality. J. High Energy Phys., 08(8), 160–42pp.
Abstract: We present a new algorithm to construct a purely four dimensional representation of higher-order perturbative corrections to physical cross-sections at next-to-leading order (NLO). The algorithm is based on the loop-tree duality (LTD), and it is implemented by introducing a suitable mapping between the external and loop momenta of the virtual scattering amplitudes, and the external momenta of the real emission corrections. In this way, the sum over degenerate infrared states is performed at integrand level and the cancellation of infrared divergences occurs locally without introducing subtraction counter-terms to deal with soft and final-state collinear singularities. The dual representation of ultraviolet counter-terms is also discussed in detail, in particular for self-energy contributions. The method is first illustrated with the scalar three-point function, before proceeding with the calculation of the physical cross-section for gamma* -> q (q) over bar (g), and its generalisation to multi-leg processes. The extension to next-to-next-to-leading order (NNLO) is briefly commented.
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Sborlini, G. F. R., Driencourt-Mangin, F., & Rodrigo, G. (2016). Four-dimensional unsubtraction with massive particles. J. High Energy Phys., 10(10), 162–34pp.
Abstract: We extend the four-dimensional unsubtraction method, which is based on the loop-tree duality (LTD), to deal with processes involving heavy particles. The method allows to perform the summation over degenerate IR configurations directly at integrand level in such a way that NLO corrections can be implemented directly in four space-time dimensions. We define a general momentum mapping between the real and virtual kinematics that accounts properly for the quasi-collinear configurations, and leads to an smooth massless limit. We illustrate the method first with a scalar toy example, and then analyse the case of the decay of a scalar or vector boson into a pair of massive quarks. The results presented in this paper are suitable for the application of the method to any multipartonic process.
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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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Gnendiger, C., Signer, A., Stockinger, D., Broggio, A., Cherchiglia, A. L., Driencourt-Mangin, F., et al. (2017). To d, or not to d: recent developments and comparisons of regularization schemes. Eur. Phys. J. C, 77(7), 471–39pp.
Abstract: We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the computation of simple quantities in the various schemes, we point out similarities and differences between them.
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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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