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Leading singularities and off-shell conformal integrals.

Drummond, James and Duhr, Claude and Eden, Burkhard and Heslop, Paul and Pennington, Jeffrey and Smirnov, Vladimir A. (2013) 'Leading singularities and off-shell conformal integrals.', Journal of high energy physics., 2013 (8). p. 133.


The three-loop four-point function of stress-tensor multiplets in N = 4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In this paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol — with an appropriate ansatz for its structure — as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certain limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. The techniques we develop can be applied more generally, and we illustrate this by analytically evaluating one of the integrals contributing to the same four-point function at four loops. This example shows a connection between the leading singularities and the entries of the symbol.

Item Type:Article
Additional Information:Published on behalf of SISSA, the International School for Advanced Studies.
Keywords:Supersymmetric gauge theory, Scattering amplitudes, Extended supersymmetry.
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Publisher statement:This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Date accepted:No date available
Date deposited:14 January 2014
Date of first online publication:August 2013
Date first made open access:No date available

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