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

DOI10.1016/J.NUCLPHYSB.2016.04.013zbMATH Open1336.81038arXiv1602.01481OpenAlexW2336585037MaRDI QIDQ288417

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Publication date: 26 May 2016

Published in: (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1602.01481

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