Name: Vladyslav Shtabovenko (email_not_shown)
Date: 07/25/17-12:35:33 PM Z


Hi,

the reason is that your expression is a mixture of 4- and D-dimensional
quantities. So when you want to compute the trace, the given expression
is illegal in the Naive Dimensional Regularization (NDR) scheme, where
everything must be D-dimensional.

So either you ensure that your expression is purely D-dimensional

f1 = coef0 Pair[Momentum[Polarization[k2, I], D],
     LorentzIndex[\[Mu], D]] SpinorUBarD[k1,
      0].GAD[\[Mu]].QuarkPropagator[{k1 + k2, 0},
      Explicit -> True].GAD[\[Nu]].SpinorUD[p1,
      0] (-MTD[\[Nu], \[Alpha]] +
      FVD[k1 + k2 - p1, \[Nu]] FVD[k1 + k2 - p1, \[Alpha]]/
        mW^2) FAD[{k1 + k2 - p1, mW}] SpinorVBarD[p2,
      0].GAD[\[Alpha]].(1 - GA5).SpinorUD[p3, m] // FCI

(or 4-dimensional, if it's tree level) or you switch to the
t'Hooft-Veltman scheme via

$BreitMaison=True;

where traces may contain 4- and D-dimensional objects. However, if your
input expression has any inconsistencies w.r.t the dimensions, the trace
will of course be also inconsistent.

Cheers,
Vladyslav

Am 24.07.2017 um 11:24 schrieb Maksym:
> Hi! I'm experiencing an issue when trying to calculate the squared amplitude.
>
> The code is
>
> FCClearScalarProducts[];
> {coef0 = u Sqrt[\[Alpha]] g/2, coef1 = 1/(32 Pi s)};
> {ScalarProduct[k1, k1] = ScalarProduct[k2, k2] = 0,
> ScalarProduct[p1, p1] = ScalarProduct[p2, p2] = 0,
> ScalarProduct[p3, p3] = m^2,
> ScalarProduct[k1, k2] = s/2, ScalarProduct[k1, p1] = -t1/2,
> ScalarProduct[k1, p2] = (s1 + t1 - t2)/2,
> ScalarProduct[k1, p3] = (s - s1 + t2)/2,
> ScalarProduct[k2, p1] = (s - s2 + t1)/2,
> ScalarProduct[k2, p2] = (s2 + t2 - t1 - m^2)/2,
> ScalarProduct[k3, p3] = (m^2 - t2)/2, ScalarProduct[p1, p2] = s1/2,
> ScalarProduct[p1, p3] = (s - s1 - s2)/2,
> ScalarProduct[p2, p3] = (s2 - m^2)};
> f1 = coef0 PolarizationVector[
> k2, \[Mu]] SpinorUBar[k1,
> 0].GA[\[Mu]].QuarkPropagator[{k1 + k2, 0},
> Explicit -> True].GA[\[Nu]].SpinorU[p1,
> 0] (-MetricTensor[\[Nu], \[Alpha]] +
> FourVector[
> k1 + k2 - p1, \[Nu]] FourVector[k1 + k2 - p1, \[Alpha]]/
> mW^2) PropagatorDenominator[k1 + k2 - p1,
> mW] SpinorVBar[p2, 0].GA[\[Alpha]].(1 - GA5). SpinorU[p3, m] // FCI
> f1star = ComplexConjugate[f1]
> m11 = DoPolarizationSums[f1 f1star, k2, 0]
> m22 = FermionSpinSum[m11] /. DiracTrace -> TR // Contract // Simplify
> Mfinal = m22
> dsigbardz = coef1 Mfinal
>
> It displays the amplitude correctly and evaluates its complex conjugation, but faols when calculating the fermion polarization sum with the error
> "Error! DiracTrick has encountered a fatal problem and must abort the computation. The problem reads: Incorrect combination of dimensions and g^5 scheme!"
>
> What is the reason for this?
>



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