$LimitTo4
is a variable with default setting False
. If set to True
, the limit Dimension -> 4
is performed after tensor integral decomposition.
$LimitTo4 is a global variable that determines whether UV-divergent Passarino-Veltman functions are simplified by taking the limit .
A generic IR-finite Passarino-Veltman function can be written as , with being the prefactor of the pole and being the finite part. Therefore, products of such functions with coefficients that are rational functions of with can be simplified to , whenever such products appear in the reduction.
This relation is correct only if the Passarino-Veltman functions have no IR divergences, or if such divergences are regulated without using dimensional regularization.
For this reason, even when $LimitTo4 is set to True
, the simplifications are applied only to and functions. Although functions can exhibit an IR divergence, such integrals are zero in dimensional regularization, so that no mixing of -terms from IR and UV can occur.
The default value of $LimitTo4
is False
. Notice that even when the switch is set to True
, it will essentially affect only the Passarino-Veltman reduction via PaVeReduce
.
The modern and more flexible way to simplify amplitudes involving IR-finite PaVe
functions is to use the special routine PaVeLimitTo4
.
Overview, PaVe, PaVeReduce, OneLoop, $LimitTo4IRUnsafe, PaVeLimitTo4.
$LimitTo4