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Campanario, F., Kerner, M., & Zeppenfeld, D. (2018). Z gamma production in vector-boson scattering at next-to-leading order QCD. J. High Energy Phys., 01(1), 160–19pp.
Abstract: Cross sections and differential distributions for Z gamma production in association with two jets via vector boson fusion are presented at next-to-leading order in QCD. The leptonic decays of the Z boson with full off-shell effects and spin correlations are taken into account. The uncertainties due to different scale choices and pdf sets are studied. Furthermore, we analyze the effect of including anomalous quartic gauge couplings at NLO QCD.
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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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Sborlini, G. F. R., de Florian, D., & Rodrigo, G. (2014). Triple collinear splitting functions at NLO for scattering processes with photons. J. High Energy Phys., 10(10), 161–29pp.
Abstract: We present splitting functions in the triple collinear limit at next-to-leading order. The computation was performed in the context of massless QCD+QED, considering only processes which include at least one photon. Through the comparison of the IR divergent structure of splitting amplitudes with the expected known behavior, we were able to check our results. Besides that we implemented some consistency checks based on symmetry arguments and cross-checked the results among them. Studying photon-started processes, we obtained very compact results.
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Bierenbaum, I., Buchta, S., Draggiotis, P., Malamos, I., & Rodrigo, G. (2013). Tree-loop duality relation beyond single poles. J. High Energy Phys., 03(3), 025–24pp.
Abstract: We develop the Tree-Loop Duality Relation for two- and three-loop integrals with multiple identical propagators (multiple poles). This is the extension of the Duality Relation for single poles and multi-loop integrals derived in previous publications. We prove a generalization of the formula for single poles to multiple poles and we develop a strategy for dealing with higher-order pole integrals by reducing them to single pole integrals using Integration By Parts.
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Hernandez-Pinto, R. J., Sborlini, G. F. R., & Rodrigo, G. (2016). Towards gauge theories in four dimensions. J. High Energy Phys., 02(2), 044–14pp.
Abstract: The abundance of infrared singularities in gauge theories due to unresolved emission of massless particles (soft and collinear) represents the main difficulty in perturbative calculations. They are typically regularized in dimensional regularization, and their subtraction is usually achieved independently for virtual and real corrections. In this paper, we introduce a new method based on the loop-tree duality (LTD) theorem to accomplish the summation over degenerate infrared states directly at the integrand level such that the cancellation of the infrared divergences is achieved simultaneously, and apply it to reference examples as a proof of concept. Ultraviolet divergences, which are the consequence of the point-like nature of the theory, are also reinterpreted physically in this framework. The proposed method opens the intriguing possibility of carrying out purely four-dimensional implementations of higher-order perturbative calculations at next-to-leading order (NLO) and beyond free of soft and final-state collinear subtractions.
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Catani, S., de Florian, D., & Rodrigo, G. (2012). Space-like (vs. time-like) collinear limits in QCD: is factorization violated? J. High Energy Phys., 07(7), 026–88pp.
Abstract: We consider the singular behaviour of QCD scattering amplitudes in kinematical configurations where two or more momenta of the external partons become collinear. At the tree level, this behaviour is known to be controlled by factorization formulae in which the singular collinear factor is universal (process independent). We show that this strict (process-independent) factorization is not valid at one-loop and higher-loop orders in the case of the collinear limit in space-like regions (e. g., collinear radiation from initial-state partons). We introduce a generalized version of all-order collinear factorization, in which the space-like singular factors retain some dependence on the momentum and colour charge of the non-collinear partons. We present explicit results on one-loop and two-loop amplitudes for both the two-parton and multiparton collinear limits. At the level of squared amplitudes and, more generally, cross sections in hadron-hadron collisions, the violation of strict collinear factorization has implications on the non-abelian structure of logarithmically-enhanced terms in perturbative calculations (starting from the next-to-next-to-leading order) and on various factorization issues of mass singularities (starting from the next-to-next-to-next-to-leading order).
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Chachamis, G., Deak, M., Hentschinski, M., Rodrigo, G., & Sabio Vera, A. (2015). Single bottom quark production in kT-factorisation. J. High Energy Phys., 09(9), 123–17pp.
Abstract: We present a study within the k(T)-factorisation scheme on single bottom quark production at the LHC. In particular, we calculate the rapidity and transverse momentum differential distributions for single bottom quark/anti-quark production. In our setup, the unintegrated gluon density is obtained from the NLx BFKL Green function whereas we included mass effects to the Lx heavy quark jet vertex. We compare our results to the corresponding distributions predicted by the usual collinear factorisation scheme. The latter were produced with Pythia 8.1.
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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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Mateu, V., & Rodrigo, G. (2013). Oriented event shapes at (NLL)-L-3 + O(alpha(2)(S)). J. High Energy Phys., 11(11), 030–29pp.
Abstract: We analyze oriented event-shapes in the context of Soft-Collinear Effective Theory (SCET) and in fixed-order perturbation theory. Oriented event-shapes are distributions of event-shape variables which are differential on the angle theta(T) that the thrust axis forms with the electron-positron beam. We show that at any order in perturbation theory and for any event shape, only two angular structures can appear: F-0 = 3/8 (1+cos(2) theta(T)) and F-1 = (1 – 3 cos(2) theta(T)). When integrating over theta(T) to recover the more familiar event-shape distributions, only F-0 survives. The validity of our proof goes beyond perturbation theory, and hence only these two structures are present at the hadron level. The proof also carries over massive particles. Using SCET techniques we show that singular terms can only arise in the F-0 term. Since only the hard function is sensitive to the orientation of the thrust axis, this statement applies also for recoil-sensitive variables such as Jet Broadening. We show how to carry out resummation of the singular terms at (NLL)-L-3 for Thrust, Heavy-Jet Mass, the sum of the Hemisphere Masses and C-parameter by using existing computations in SCET. We also compute the fixed-order distributions for these event-shapes at O(alpha(S)) analytically and at O(alpha(2)(S)) with the program Event2.
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Buchta, S., Chachamis, G., Draggiotis, P., Malamos, I., & Rodrigo, G. (2014). On the singular behaviour of scattering amplitudes in quantum field theory. J. High Energy Phys., 11(11), 014–13pp.
Abstract: We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop-tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.
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