LToolsExpandInEpsilon is an option for
LToolsEvaluate. When set to True (default),
the result returned by LoopTools and multiplied with proper conversion
factors will be expanded around \varepsilon =
0 to \mathcal{O}(\varepsilon^0).
The \varepsilon-dependent conversion
factors arise from the differences in the normalization between
Passarino-Veltman functions in FeynCalc and LoopTools. In addition to
that, the prefactor specified via LToolsImplicitPrefactor
may also depend on \varepsilon.
Setting this option to False will leave the prefactors
unexpanded, which might sometimes be useful when examining the obtained
results.
Overview, LToolsEvaluate, LToolsImplicitPrefactor.
LToolsLoadLibrary[]\text{LoopTools library loaded.}
(* ====================================================
FF 2.0, a package to evaluate one-loop integrals
written by G. J. van Oldenborgh, NIKHEF-H, Amsterdam
====================================================
for the algorithms used see preprint NIKHEF-H 89/17,
'New Algorithms for One-loop Integrals', by G.J. van
Oldenborgh and J.A.M. Vermaseren, published in
Zeitschrift fuer Physik C46(1990)425.
====================================================*)The default behavior of LToolsEvaluate is to do the
\varepsilon-expansion automatically
LToolsEvaluate[FAD[q, q - p], q, InitialSubstitutions -> {SPD[p] -> 1}]\frac{0.\, +9.8696 i}{\varepsilon }-(31.0063\, -2.74429 i)
This can be disabled by setting LToolsExpandInEpsilon to
False
LToolsEvaluate[FAD[q, q - p], q, InitialSubstitutions -> {SPD[p] -> 1}, LToolsExpandInEpsilon -> False]\frac{(0.\, +1. i) \pi ^{2-\varepsilon } \Gamma (1-\varepsilon )^2 \Gamma (\varepsilon +1)}{\varepsilon \Gamma (1-2 \varepsilon )}-\frac{(3.14159\, -2. i) \pi ^{2-\varepsilon } \Gamma (1-\varepsilon )^2 \Gamma (\varepsilon +1)}{\Gamma (1-2 \varepsilon )}