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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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Ramirez-Uribe, S., Renteria-Olivo, A. E., Rodrigo, G., Sborlini, G. F. R., & Vale Silva, L. (2022). Quantum algorithm for Feynman loop integrals. J. High Energy Phys., 05(5), 100–32pp.
Abstract: We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal singular configurations of multiloop Feynman diagrams. To identify such configurations, we exploit Grover's algorithm for querying multiple solutions over unstructured datasets, which presents a quadratic speed-up over classical algorithms when the number of solutions is much smaller than the number of possible configurations. A suitable modification is introduced to deal with topologies in which the number of causal states to be identified is nearly half of the total number of states. The output of the quantum algorithm in IBM Quantum and QUTE Testbed simulators is used to bootstrap the causal representation in the loop-tree duality of representative multiloop topologies. The algorithm may also find application and interest in graph theory to solve problems involving directed acyclic graphs.
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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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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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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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