Dear Luka,
so far I don't see a problem with your result. For
res = (PaVe[1, 2, {p10, p12, p20}, {m02, m12, m22}] -
PaVe[1, 2, {p20, p12, p10}, {m02, m22, m12}]) //
PaVeReduce // Simplify
I obtain
((m02 - m12) B0[0, m02, m12] + (-m02 + m22) B0[0, m02,
m22] + (m12 - m22) B0[0, m12, m22])/(p10^2 + (p12 - p20)^2 -
2 p10 (p12 + p20))
Inserting explicit results for B0's
sols = {B0[0, m02, m12] ->
1/(16 Epsilon \[Pi]^4) + (-m02 Log[m02/
m12] + (m02 - m12) (1 + Log[ScaleMu^2/m12]))/(
16 (m02 - m12) \[Pi]^4),
B0[0, m02, m22] ->
1/(16 Epsilon \[Pi]^4) + (-m02 Log[m02/
m22] + (m02 - m22) (1 + Log[ScaleMu^2/m22]))/(
16 (m02 - m22) \[Pi]^4),
B0[0, m12, m22] ->
1/(16 Epsilon \[Pi]^4) + (-m12 Log[m12/
m22] + (m12 - m22) (1 + Log[ScaleMu^2/m22]))/(
16 (m12 - m22) \[Pi]^4)};
via (res/.sols)//PowerExpand//Simplify
I indeed get 0, as it should be. Please let me know, if you get
something else.
Cheers,
Vladyslav
Am 11.06.2015 um 08:37 schrieb Luka Popov:
> I am a little bit confused with the results I get using PaVeReduce. Naimely, one should expect the Passarino-Veltman function C_{12} to be symmetric with respect to the replacement p1 <-> p2 and m1 <-> m2, according to its definition.
>
> However, I don't get this result when evaluating it with PaVeReduce:
>
> PaVe[1, 2, {p10, p12, p20}, {m02, m12, m22}] -
> PaVe[1, 2, {p20, p12, p10}, {m02, m22, m12}] // PaVeReduce
>
> The result of the above line is given by B0 functions and it does not equals zero, even when B0 is exactly calculated and inserted in the result.
>
> Can you please tell me if I am doing something wrong? Thank you.
>
> With regards,
> Luka Popov
>
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