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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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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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Deak, M. (2013). Estimation of saturation and coherence effects in the KGBJS equation – a non-linear CCFM equation. J. High Energy Phys., 07(7), 087–18pp.
Abstract: We solve the modified non-linear extension of the CCFM equation – KGBJS equation – numerically for certain initial conditions and compare the resulting dipole amplitudes with those obtained front solving the original CCFM equation and the BFKL and BK equations for the same initial conditions. We improve the low transversal momentum behaviour of the KGBJS equation by a small modification.
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Greynat, D., de Rafael, E., & Vulvert, G. (2014). Asymptotic behaviour of pion-pion total cross-sections. J. High Energy Phys., 03(3), 107–21pp.
Abstract: We derive a sum rule which shows that the Froissart-Martin bound for the asymptotic behaviour of the pi pi total cross sections at high energies, if modulated by the Lukaszuk-Martin coefficient of the leading log(2)s behaviour, cannot be an optimal bound in QCD. We next compute the total cross sections for pi(+)pi(-), pi(+/-)pi(0) and pi(0)pi(0) scattering within the framework of the constituent chiral quark model (C chi QM) in the limit of a large number of colours N-c and discuss their asymptotic behaviours. The same pi pi cross sections are also discussed within the general framework of Large-N-c QCD and we show that it is possible to make an Ansatz for the isospin I = 1 and I = 0 spectrum which satisfy the Froissart-Martin bound with coefficients which, contrary to the Lukaszuk-Martin coefficient, are not singular in the chiral limit and have the correct Large-N-c counting. We finally propose a simple phenomenological model which matches the low energy behaviours of the sigma(total)(pi +/-pi 0)(s) cross section predicted by the CxQM with the high energy behaviour predicted by the Large-N-c Ansatz. The magnitude of these cross sections at very high energies is of the order of those observed for the pp and pp scattering total cross sections.
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Campanario, F., & Kubocz, M. (2014). Higgs boson CP-properties of the gluonic contributions in Higgs plus three jet production via gluon fusion at the LHC. J. High Energy Phys., 10(10), 173–16pp.
Abstract: in high energy hadronic collisions, a general CP-violating Higgs boson Phi with accompanying jets can be efficiently produced via gluon fusion, which is mediated by heavy quark loops. In this article, we study the dominant sub-channel gg -> ggg Phi of the gluon fusion production process with triple real emission corrections at order alpha(5)(s). We go beyond the heavy top-quark approximation and include the full mass dependence of the top- and bottom-quark contributions. Furthermore, in a specific model we demonstrate the features of our program and show the impact of bottom-quark loop contributions in combination with large values of tan beta on differential distributions sensitive to CP-rneasurements of the Higgs boson.
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