Name: Karl Date: 08/14/19-04:06:33 PM Z
Hi,
i am calculating the tree level process e+ e- -> t t~ only with an Z
exchange, so no photon is involved. After the calculation i took this
squared element and wanted to check whether it fits numerically for a
specific phase space point
by comparing it for example with MadGraph. It turns out that both
values differ, so i calculated this process by hand and i see that i
obtain a different result than FeynCalc does and my result fits with
the result from MadGraph. The difference can be traced back to the contraction of the Levi Civita tensors occurring due to the gamma5 in the vertices. Your implementation seems to use the opposite sign in comparison to the usual definitions and this sign difference causes
the result to be wrong. You can see it for example in the help menu when you enter “Levi Civita” in the search field. There you find the following example:
In[7]:= t1 =
LeviCivita[\[Alpha], \[Beta], \[Gamma],
\[Rho]].LeviCivita[\[Alpha], \
\[Beta], \[Gamma], \[Rho]]
In[8]:= Contract[t1]
Out[8]= -D^4+6 D^3-11 D^2+6 D
Setting D->4 in the result leads to -24, contrary to the usual definition of 24. In the calculation one obtains:
In[150]:=
LeviCivita[\[Mu], \[Mu]C, \[Nu],
\[Rho]]*
LeviCivita[\[Mu], \[Mu]C, \[Alpha],
\[Beta]] // Contract
Out[150]= 2 Overscript[g, _]^(\[Alpha]\[Rho]) Overscript[g, _]^(\[Beta]\[Nu])-2 Overscript[g, _]^(\[Alpha]\[Nu]) Overscript[g, _]^(\[Beta]\[Rho])
where the sign is again different to the usual definition. Is it possible to cure this different sign such that i obtain a correct result? Ultimately, i would like to calculate processes like e+ e- -> t t~ g or with another gluon in the final state. By the way your result is the same as in FORM.
Thank you for your help.