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Kleiss, R. H. P., Malamos, I., Papadopoulos, C. G., & Verheyen, R. (2012). Counting to one: reducibility of one- and two-loop amplitudes at the integrand level. J. High Energy Phys., 12(12), 038–24pp.
Abstract: Calculation of amplitudes in perturbative quantum field theory involve large loop integrals. The complexity of those integrals, in combination with the large number of Feynman diagrams, make the calculations very difficult. Reduction methods proved to be very helpful, lowering the number of integrals that need to be actually calculated. Especially reduction at the integrand level improves the speed and set-up of these calculations. In this article we demonstrate, by counting the numbers of tensor structures and independent coefficients, how to write such relations at the integrand level for one-and two-loop amplitudes. We clarify their connection to the so-called spurious terms at one loop and discuss their structure in the two-loop case. This method is also applicable to higher loops, and the results obtained apply to both planar and non-planar diagrams.
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Jueid, A., Kip, J., Ruiz de Austri, R., & Skands, P. (2024). The Strong Force meets the Dark Sector: a robust estimate of QCD uncertainties for anti-matter dark matter searches. J. High Energy Phys., 02(2), 119–48pp.
Abstract: In dark-matter annihilation channels to hadronic final states, stable particles – such as positrons, photons, antiprotons, and antineutrinos – are produced via complex sequences of phenomena including QED/QCD radiation, hadronisation, and hadron decays. These processes are normally modelled by Monte Carlo (MC) event generators whose limited accuracy imply intrinsic QCD uncertainties on the predictions for indirect-detection experiments like Fermi-LAT, Pamela, IceCube or Ams-02. In this article, we perform a comprehensive analysis of QCD uncertainties, meaning both perturbative and nonperturbative sources of uncertainty are included – estimated via variations of MC renormalization-scale and fragmentation-function parameters, respectively – in antimatter spectra from dark-matter annihilation, based on parametric variations of the Pythia 8 event generator. After performing several retunings of light-quark fragmentation functions, we define a set of variations that span a conservative estimate of the QCD uncertainties. We estimate the effects on antimatter spectra for various annihilation channels and final-state particle species, and discuss their impact on fitted values for the dark-matter mass and thermally-averaged annihilation cross section. We find dramatic impacts which can go up to O(10%) for the annihilation cross section. We provide the spectra in tabulated form including QCD uncertainties and code snippets to perform fast dark-matter fits, in this github repository.
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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). Dynamics of isolated-photon plus jet production in pp collisions at root s=7 TeV with the ATLAS detector. Nucl. Phys. B, 875(3), 483–535.
Abstract: The dynamics of isolated-photon plus jet production in pp collisions at a centre-of-mass energy of 7 TeV has been studied with the ATLAS detector at the LHC using an integrated luminosity of 37 pb(-1). Measurements of isolated-photon plus jet bin-averaged cross sections are presented as functions of photon transverse energy, jet transverse momentum and jet rapidity. In addition, the bin-averaged cross sections as functions of the difference between the azimuthal angles of the photon and the jet, the photon jet invariant mass and the scattering angle in the photon jet centre-of-mass frame have been measured. Next-to-leading-order QCD calculations are compared to the measurements and provide a good description of the data, except for the case of the azimuthal opening angle.
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