Integration by parts identities in integer numbers of dimensions. A criterion for decoupling systems of differential equations
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Date
2015-12
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Publisher
Elsevier
Abstract
Integration by parts identities (IBPs) can be used to express large numbers of apparently different
d-dimensional Feynman Integrals in terms of a small subset of so-called master integrals (MIs). Using
the IBPs one can moreover show that the MIs fulfil linear systems of coupled differential equations in the
external invariants. With the increase in number of loops and external legs, one is left in general with an
increasing number of MIs and consequently also with an increasing number of coupled differential equations,
which can turn out to be very difficult to solve. In this paper we show how studying the IBPs in fixed
integer numbers of dimension d = n with n ∈ N one can extract the information useful to determine a new
basis of MIs, whose differential equations decouple as d → n and can therefore be more easily solved as
Laurent expansion in (d − n)
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Keywords
Differential equations, Integrals
Citation
Nuclear Physics B 901 (2015) 282-317