Leading singularities and off-shell conformal integrals

Drummond, James; Duhr, Claude; Eden, Burkhard; Heslop, Paul; Pennington, Jeffrey; Smirnov, Vladimir A.

Abstract

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.

Citation

Drummond, J., Duhr, C., Eden, B., Heslop, P., Pennington, J., & Smirnov, V. A. (2013). Leading singularities and off-shell conformal integrals. Journal of High Energy Physics, 2013(8), Article 133. https://doi.org/10.1007/jhep08%282013%29133

• Journal Article Type: Article
• Publication Date: Aug 29, 2013
• Deposit Date: Nov 21, 2013
• Publicly Available Date: Jan 14, 2014
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2013
• Issue: 8
• Article Number: 133
• DOI: https://doi.org/10.1007/jhep08%282013%29133
• Keywords: Supersymmetric gauge theory, Scattering amplitudes, Extended supersymmetry.
• Public URL: https://durham-repository.worktribe.com/output/1444340