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Local integrands for the five-point amplitude in planar N=4 SYM up to five loops.

Ambrosio, Raquel G. and Eden, Burkhard and Goddard, Timothy and Heslop, Paul and Taylor, Charles (2015) 'Local integrands for the five-point amplitude in planar N=4 SYM up to five loops.', Journal of high energy physics., 2015 (1). p. 116.


Integrands for colour ordered scattering amplitudes in planar N=4 SYM are dual to those of correlation functions of the energy-momentum multiplet of the theory. The construction can relate amplitudes with different numbers of legs. By graph theory methods the integrand of the four-point function of energy-momentum multiplets has been constructed up to six loops in previous work. In this article we extend this analysis to seven loops and use it to construct the full integrand of the five-point amplitude up to five loops, and in the parity even sector to six loops. All results, both parity even and parity odd, are obtained in a concise local form in dual momentum space and can be displayed efficiently through graphs. We have verified agreement with other local formulae both in terms of supertwistors and scalar momentum integrals as well as BCJ forms where those exist in the literature, i.e. up to three loops. Finally we note that the four-point correlation function can be extracted directly from the four-point amplitude and so this uncovers a direct link from four- to five-point amplitudes.

Item Type:Article
Additional Information:Published on behalf of the International School for Advanced Studies (SISSA).
Full text:(NA) Not Applicable
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Date accepted:15 December 2014
Date deposited:18 February 2015
Date of first online publication:13 January 2015
Date first made open access:No date available

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