My collaborators and I are constructing the experiments of gamma-ray
polarization introduced by Compton scattering in 10--1000 keV energy
range with Genat 4, and found that the polarization angle of scattered
photons is not as we predicted.
We compared the polarization angle of scattered photons in Geant 4
with that in EGS 4, and found that the angle is different.
In general, the polarization angle has a one-to-one relation with the
scattering direction in the classical limit.
However, the polarization angle in Geant 4 is randomly distributed in
some angle range.

I read the source code "G4LowEnergyPolarizedCompton.cc" and found the
description that I cannot understand.
The following is the part where the polarization angle is calculated.
Since the angle of cosBeta is randomly distributed, the polarization
angle is also randomized.

  G4double xParallel = normalisation*cosBeta;
  G4double yParallel = -(sinSqrTh*cosPhi*sinPhi)*cosBeta/normalisation;
  G4double zParallel = -(costheta*sinTheta*cosPhi)*cosBeta/normalisation;
  G4double xPerpendicular = 0.;
  G4double yPerpendicular = (costheta)*sinBeta/normalisation;
  G4double zPerpendicular = -(sinTheta*sinPhi)*sinBeta/normalisation;

  G4double xTotal = (xParallel + xPerpendicular);
  G4double yTotal = (yParallel + yPerpendicular);
  G4double zTotal = (zParallel + zPerpendicular);

  gammaPolarization1.setX(xTotal);
  gammaPolarization1.setY(yTotal);
  gammaPolarization1.setZ(zTotal);


I tried to modify as follows, the result is in good agreement with
that of EGS 4.

  xTotal = normalisation;
  yTotal = -(sinSqrTh*cosPhi*sinPhi)/normalisation;
  zTotal = -(costheta*sinTheta*cosPhi)/normalisation;

  gammaPolarization1.setX(xTotal);
  gammaPolarization1.setY(yTotal);
  gammaPolarization1.setZ(zTotal);

Although I did not know the correct formula of polarization angle in
the Klein-Nishina regime,
the above formula agrees with the classical limit derived from the
Lienard-Wiechart potential.
This part is not changed over the Geant 4 version 4.1--6.0.