LToolsImplicitPrefactor
is an option for
LToolsEvaluate
. It specifies a prefactor that does not show
up explicitly in the input expression, but is understood to appear in
front of every Passarino-Veltman function. The default value is
1
.
You may want to use
LToolsImplicitPrefactor->1/(2Pi)^D
when working with
1-loop amplitudes, if no explicit prefactor has been introduced from the
very beginning.
[] LToolsLoadLibrary
(* ====================================================
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.
====================================================*)
Here the prefactor arises from the conversion of to
[FAD[{q, m}], q, InitialSubstitutions -> {m -> 5}] LToolsEvaluate
[FAD[{q, m}], q, InitialSubstitutions -> {m -> 5}, Head -> keep] LToolsEvaluate
This recovers the textbook prefactor
[FAD[{q, m}], q, InitialSubstitutions -> {m -> 5}, LToolsImplicitPrefactor -> 1/(2 Pi)^(4 - 2 Epsilon)] LToolsEvaluate
[FAD[{q, m}], q, PaXImplicitPrefactor -> 1/(2 Pi)^(4 - 2 Epsilon)] /. {m -> 5, ScaleMu^2 -> 1}) // N (PaXEvaluate
If the input expression contains both loop and non-loop terms, only
the terms containing a PaVe
-function will be multiplied by
the implicit prefactor
[extra + FAD[{q, m}], q, InitialSubstitutions -> {m -> 2}, LToolsExpandInEpsilon -> False] LToolsEvaluate