Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral
High Energy Physics - Phenomenology
2017-01-23 v3
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.
Keywords
Cite
@article{arxiv.1602.01481,
title = {Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral},
author = {Ettore Remiddi and Lorenzo Tancredi},
journal= {arXiv preprint arXiv:1602.01481},
year = {2017}
}
Comments
36 pages, v3 fixed a typo in Eq.(5.5)