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Differential equations for multi-loop integrals and two-dimensional kinematics

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Abstract

In this paper we consider multi-loop integrals appearing in MHV scattering amplitudes of planar \( \mathcal{N}=4 \) SYM. Through particular differential operators which reduce the loop order by one, we present explicit equations for the two-loop eight-point finite diagrams which relate them to massive hexagons. After the reduction to two-dimensional kinematics, we solve them using symbol technology. The terms invisible to the symbols are found through boundary conditions coming from double soft limits. These equations are valid at all-loop order for double pentaladders and allow to solve iteratively loop integrals given lower-loop information. Comments are made about multi-leg and multi-loop integrals which can appear in this special kinematics. The main motivation of this investigation is to get a deeper understanding of these tools in this configuration, as well as for their application in general four-dimensional kinematics and to less supersymmetric theories.

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  1. Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489, Berlin, Germany

    L. Ferro

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ArXiv ePrint: 1204.1031

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Ferro, L. Differential equations for multi-loop integrals and two-dimensional kinematics. J. High Energ. Phys. 2013, 160 (2013). https://doi.org/10.1007/JHEP04(2013)160

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  • DOI: https://doi.org/10.1007/JHEP04(2013)160

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