Picard-Fuchs equations for Feynman integrals
High Energy Physics - Phenomenology
2015-06-12 v2 Mathematical Physics
Algebraic Geometry
math.MP
Abstract
We present a systematic method to derive an ordinary differential equation for any Feynman integral, where the differentiation is with respect to an external variable. The resulting differential equation is of Fuchsian type. The method can be used within fixed integer space-time dimensions as well as within dimensional regularisation. We show that finding the differential equation is equivalent to solving a linear system of equations. We observe interesting factorisation properties of the D-dimensional Picard-Fuchs operator when D is specialised to integer dimensions.
Cite
@article{arxiv.1212.4389,
title = {Picard-Fuchs equations for Feynman integrals},
author = {Stefan Müller-Stach and Stefan Weinzierl and Raphael Zayadeh},
journal= {arXiv preprint arXiv:1212.4389},
year = {2015}
}
Comments
15 pages, version to be published