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

By Ettore Remiddi, L. Tancredi. 2016

158 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d3a95a161066f7e53cde192cb4f42c1d67d13116

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In Astronomy and Astrophysics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph (2017, background): “The entries of this matrix were determined for the first time in [25] by studying the imaginary part of the graph.”