Fuchsia : A tool for reducing differential equations for Feynman master integrals to epsilon form

Gituliar, Oleksandr; Magerya, Vitaly

doi:10.1016/j.cpc.2017.05.004

Preprint

PUBDB-2017-11208

Fuchsia : A tool for reducing differential equations for Feynman master integrals to epsilon form

Gituliar, O. (Corresponding author) ; Magerya, V.

2017
North Holland Publ. Co. Amsterdam

Computer physics communications 219, 329 - 338 (2017) [10.1016/j.cpc.2017.05.004]

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Please use a persistent id in citations: doi:10.1016/j.cpc.2017.05.004 doi:10.3204/PUBDB-2017-11208

Abstract: We present Fuchsia — an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients $∂_xJ(x,ε)=\mathbb{A}(x,ε)J(x,ε)$ finds a basis transformation $\mathbb{T}(x,ε),i.e., J(x,ε)= \mathbb{T}(x,ε)J′(x,ε)$, such that the system turns into the epsilon form: $∂_x J′(x,ε)=ε \mathbb{S}(x)J′(x,ε)$, where $\mathbb{S}(x)$, where is a Fuchsian matrix. A system of this form can be trivially solved in terms of polylogarithms as a Laurent series in the dimensional regulator. That makes the construction of the transformation $\mathbb{T}(x,ε)$ crucial for obtaining solutions of the initial system.In principle, Fuchsia can deal with any regular systems, however its primary task is to reduce differential equations for Feynman master integrals. It ensures that solutions contain only regular singularities due to the properties of Feynman integrals.

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