Aguilera-Verdugo, J. J., Hernandez-Pinto, R. J., Rodrigo, G., Sborlini, G. F. R., & Torres Bobadilla, W. J. (2021). Causal representation of multi-loop Feynman integrands within the loop-tree duality. J. High Energy Phys., 01(1), 69–26pp.
Abstract: The numerical evaluation of multi-loop scattering amplitudes in the Feynman representation usually requires to deal with both physical (causal) and unphysical (non-causal) singularities. The loop-tree duality (LTD) offers a powerful framework to easily characterise and distinguish these two types of singularities, and then simplify analytically the underling expressions. In this paper, we work explicitly on the dual representation of multi-loop Feynman integrals generated from three parent topologies, which we refer to as Maximal, Next-to-Maximal and Next-to-Next-to-Maximal loop topologies. In particular, we aim at expressing these dual contributions, independently of the number of loops and internal configurations, in terms of causal propagators only. Thus, providing very compact and causal integrand representations to all orders. In order to do so, we reconstruct their analytic expressions from numerical evaluation over finite fields. This procedure implicitly cancels out all unphysical singularities. We also interpret the result in terms of entangled causal thresholds. In view of the simple structure of the dual expressions, we integrate them numerically up to four loops in integer space-time dimensions, taking advantage of their smooth behaviour at integrand level.
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Aguilera-Verdugo, J. J., Hernandez-Pinto, R. J., Rodrigo, G., Sborlini, G. F. R., & Torres Bobadilla, W. J. (2021). Mathematical properties of nested residues and their application to multi-loop scattering amplitudes. J. High Energy Phys., 02(2), 112–42pp.
Abstract: The computation of multi-loop multi-leg scattering amplitudes plays a key role to improve the precision of theoretical predictions for particle physics at high-energy colliders. In this work, we focus on the mathematical properties of the novel integrand-level representation of Feynman integrals, which is based on the Loop-Tree Duality (LTD). We explore the behaviour of the multi-loop iterated residues and explicitly show, by developing a general compact and elegant proof, that contributions associated to displaced poles are cancelled out. The remaining residues, called nested residues as originally introduced in ref. [1], encode the relevant physical information and are naturally mapped onto physical configurations associated to nondisjoint on-shell states. By going further on the mathematical structure of the nested residues, we prove that unphysical singularities vanish, and show how the final expressions can be written by using only causal denominators. In this way, we provide a mathematical proof for the all-loop formulae presented in ref. [2].
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ATLAS Collaboration(Aad, G. et al), Cabrera Urban, S., Castillo Gimenez, V., Costa, M. J., Fassi, F., Ferrer, A., et al. (2013). Search for dark matter candidates and large extra dimensions in events with a jet and missing transverse momentum with the ATLAS detector. J. High Energy Phys., 04(4), 075–51pp.
Abstract: A search for new phenomena in events with a high-energy jet and large missing transverse momentum is performed using data from proton-proton collisions at root s = 7 TeV with the ATLAS experiment at the Large flatiron Collider. Four kinematic regions are explored using a dataset corresponding to an integrated luminosity of 4.7 fb(-1). No excess of events beyond expectations from Standard Model processes is observed, and limits are set on large extra dimensions and the pair production of dark matter particles.
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ATLAS Collaboration(Aad, G. et al), Cabrera Urban, S., Castillo Gimenez, V., Costa, M. J., Fassi, F., Ferrer, A., et al. (2012). Search for R-parity-violating supersymmetry in events with four or more leptons in root s=7 TeV pp collisions with the ATLAS detector. J. High Energy Phys., 12(12), 124–36pp.
Abstract: A search for new phenomena in final states with four or more leptons (electrons or muons) is presented. The analysis is based on 4.7 fb(-1) of root s = 7TeV proton-proton collisions delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in two signal regions: one that requires moderate values of missing transverse momentum and another that requires large effective mass. The results are interpreted in a simplified model of R-parity-violating supersymmetry in which a 95% CL exclusion region is set for charged wino masses up to 540GeV. In an R-parity-violating MSUGRA/CMSSM model, values of m(1/2) up to 820GeV are excluded for 10 < tan beta < 40.
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ATLAS Collaboration(Aad, G. et al), Cabrera Urban, S., Castillo Gimenez, V., Costa, M. J., Fassi, F., Ferrer, A., et al. (2012). Search for anomalous production of prompt like-sign lepton pairs at root s=7 TeV with the ATLAS detector. J. High Energy Phys., 12(12), 007–41pp.
Abstract: An inclusive search for anomalous production of two prompt, isolated leptons with the same electric charge is presented. The search is performed in a data sample corresponding to 4.7 fb(-1) of integrated luminosity collected in 2011 at root s = 7TeV with the ATLAS detector at the LHC. Pairs of leptons (e(+/-)e(+/-), e(+/-)mu(+/-), and mu(+/-)mu(+/-)) with large transverse momentum are selected, and the dilepton invariant mass distribution is examined for any deviation from the Standard Model expectation. No excess is found, and upper limits on the production cross section of like-sign lepton pairs from physics processes beyond the Standard Model are placed as a function of the dilepton invariant mass within a fiducial region close to the experimental selection criteria. The 95% confidence level upper limits on the cross section of anomalous e(+/-)e(+/-), e(+/-)mu(+/-), or mu(+/-)mu(+/-) production range between 1.7 fb and 64 fb depending on the dilepton mass and flavour combination.
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