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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ArXiv ePrint: 1206.4180
Supported by REA Grant Agreement PITN-GA-2010-264564 (LHCPhenoNet), by the MICINN Grants FPA2007-60323, FPA2011-23778 and Consolider-Ingenio 2010 Programme CSD2007-00042 (CPAN). (Ioannis Malamos)
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Kleiss, R.H.P., Malamos, I., Papadopoulos, C.G. et al. Counting to one: reducibility of one- and two-loop amplitudes at the integrand level. J. High Energ. Phys. 2012, 38 (2012). https://doi.org/10.1007/JHEP12(2012)038
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DOI: https://doi.org/10.1007/JHEP12(2012)038