· FeynCalc

Name: Xiu-Lei Ren Date: 12/26/16-07:02:25 PM Z

Dear Vladyslav,

Thanks. As your suggestion, I have updated Package-X to the latest version (2.0.3).

Before reply the last email, I want to report a bug when converting the PaVe coefficient function from Feyncalc to Package-X.

Take A0(mN^2) for example:

$LoadAddOns = {“FeynHelpers”};
«FeynCalc`
PaXEvaluate[A0[mN^2]] // Expand // Simplify

The output is not right, ‘-Log(\pi)’ should be ‘Log(4\pi)’.

It seems that the substitution (Eq.(6) in arXiv:1611.06793)
\frac{1}{\epsilon} -> \frac{1}{\epsilon} - \gamma_E + \log(4*\pi)
works as
\frac{1}{\epsilon} -> \frac{1}{\epsilon} - \gamma_E - \log(\pi)

Then,
1. At before, I peform the 1/mN expansion after PaXEvaluate. As you noticed that, there have some suspicous terms. Then, I perform the numerical evaluation, it will produce the weird terms
such as, PaXDiLog[Complex[-1,-6],-0.2].

SPD[p4, p4] = mN^2;
XC0 = C0[SPD[p4], SPD[q], SPD[p4 + q], mN^2, mpi^2, mpi^2] //
ExpandScalarProduct;
XC0Re00 = PaXEvaluate[XC0, PaXC0Expand -> True] // Normal;
Series[XC0Re00, {mN, \[Infinity], 0}] // Normal // Simplify
%/.{mN -> 0.94, mpi -> 0.14, SPD[p4, q] -> 0.03, SPD[q] -> 0.04}

2. If I want to evaluate C0 with Dimension=4, such as,

SP[p4x, p4x] = mN^2;
XC04 = C0[SP[p4x], SP[qx], SP[p4x + qx], mN^2, mpi^2, mpi^2] //
  ExpandScalarProduct;
XC04x = PaXEvaluate[XC04, PaXC0Expand -> True,
    PaXSeries -> , PaXAnalytic -> True] // Normal //
   Simplify
The final result is the same as D dimensions. I want to know that it is a safe way to use Package-X or not?

Looking forward to your reply. Happy holidays!

Cheers,
Xiu-Lei