$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 D-4 \to 0.
A generic IR-finite Passarino-Veltman function X can be written as X = \frac{a}{D-4} + b + \mathcal{O}(\varepsilon), with a being the prefactor of the pole and b being the finite part. Therefore, products of such functions with coefficients that are rational functions of D with f(D) = f(4) + (D-4) f'(4) + \mathcal{O}(\varepsilon^2) can be simplified to f(D) X = f(4) X + a f'(4) + \mathcal{O}(\varepsilon), 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 A
and B functions. Although B functions can exhibit an IR divergence,
such integrals are zero in dimensional regularization, so that no mixing
of \varepsilon-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\text{False}