Dirac matrices in dimensional regularization, get correct order epsilon

Let us work in dimension $D = 4-2epsilon$.

In 4-dimension, we can write $text{Tr}[A B]$, where $A$ and $B$ are string of gamma matrices, as

$sum_m text{Tr}[A~Gamma^m]text{Tr}[B~Gamma^m]$, where $Gamma^m = {1,gamma_5,gamma^mu,gamma_5gamma^mu,sigma_{munu}}$ are complete set of gamma matrices spanning the dirac space in 4-dim.

As it is well-known, generalizing this to non-integer $D$ dimension causes difficulties since $gamma_5$ (defined as $gamma_5= igamma^0gamma^1gamma^2gamma^3$ in 4-dim.) cannot be well-defined.

One often does not need to work with the explicit form of $gamma_5$, but uses the two relations to evaluate the trace:

i)$~{gamma_5,gamma^mu}=0,,$

ii)$~text{Tr}[gamma_5gamma^{mu}gamma^{nu}gamma^{rho}gamma^{sigma}]=-4iepsilon_{munurhosigma},.$

However, in $D$ dimension, the two relations cannot be satisfied simultaneously; and people use different $gamma_5$-schemes to treat $gamma_5$ in $D$-dimension.

However, when you evaluate both of the traces $text{Tr}[A B]$ and $sum_m text{Tr}[A~Gamma^m]text{Tr}[B~Gamma^m]$ in $D$-dimension by using different $gamma_5$-schemes they do not necessarily agree.

As an example,

take $A = (gammacdot p_1)gamma^alpha(gammacdot p_2)$ and $B =gamma^beta(gammacdot p_1)(gammacdot p_2)$.

Then evaluation of $sum_m text{Tr}[A~Gamma^m]text{Tr}[B~Gamma^m]$ requires $gamma_5$ scheme choice.

Then
$text{Tr}[A B] = -4~(D-2)~(2~(p_1cdot p_2)^2 – p_1^2~ p_2^2)$

$left(sum_m text{Tr}[A~Gamma^m]text{Tr}[B~Gamma^m]right)_{text{t’Hooft-Veltman}} = -4~(D-2)~left((D-2)~(p_1cdot p_2)^2 – (D-3)p_1^2~ p_2^2right)$

$left(sum_m text{Tr}[A~Gamma^m]text{Tr}[B~Gamma^m]right)_{text{NDR}} = -4D~(p_1cdot p_2)^2 + 8p_1^2~ p_2^2$

where ‘NDR’ is naive dimensional regularization scheme and ‘t’Hooft-Veltman’ is t’Hooft-Veltman-scheme.

All three results agree when $D$ is taken to be 4, but do not agree in $epsilon$ terms. Is there a way to ensure agreement down to $epsilon$ piece?