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arXiv · 1602.01481

Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral

Ettore Remiddi·Lorenzo Tancredi
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Abstract

It is shown that the study of the imaginary part and of the corresponding dispersion relations of Feynman graph amplitudes within the differential equations method can provide a powerful tool for the solution of the equations, especially in the massive case. The main features of the approach are illustrated by discussing the simple cases of the 1-loop self-mass and of a particular vertex amplitude, and then used for the evaluation of the two-loop massive sunrise and the QED kite graph (the problem studied by Sabry in 1962), up to first order in the (d-4) expansion.

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Ettore Remiddi, Lorenzo Tancredi. 2017-01-20. Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral. https://doi.org/10.1016/j.nuclphysb.2016.04.013

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