Name: Nikita Belyaev (email_not_shown)
Date: 08/08/15-02:25:32 AM Z


Dear Vladyslav,

Sorry for such a late reply, we've been investigating the problem in much more details.

Looks like it is some kind of a general problem.

The most illustrating example is the following.
To calculate the multiplication of traces of gamma matrices we can use one useful formula. Let's write it in the following way:

Tr[A.GA[a].GS[k].GA[b].(1-GA[5])].Tr[B.GA[b].GS[p].GA[a].(1-GA[5])]=4*Tr[A.GS[p].(1-GA[5])]*Tr[B.GS[k].(1-GA[5])],

where A and B are any possible combinations of gamma matrices, p and k - Feynman slashed 4-vectors.
The proof of the general case can be founded in special literature, but we've proved this formula for the cases when both A and B are sets of three and one gamma matrices (for example, A=GA[a].GA[b].GA[c] and A=GA[a] respectively).

We've checked this formula in FeynCalc and calculated the difference between left and right part of this equation and we got zero answer for the case when A and B contains only one gamma matrix.
Then we've checked the same for the case when A and B are sets of three gamma matrices. In this case we got the imaginary answer which looks the same as the imaginary part in our previous trace calculation. Real part was zero.

According to our calculation of u^3 terms we also have done some checks. Our initial general calculation, as you know, contains the imaginary terms proportional to u^3.
But when we simplified the related expressions by hand and reduced the amount of gamma matrices by using few mathematical tricks the result no longer contains the imaginary part.
We can provide you a working example of that if you are going to re-check this.

So the problem should be hidden somewhere here, calculation of long chain of gamma matrices causes this bug.

Should we contact the FORM developers or you have some better ideas?

Best Regards,
Nikita Belyaev



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