Problem 2010

Created attachment 473 [details]
Chi2 for the same tracks rotated around the y-axis with and without this fix

In the muon g-2 experiment, we made the (non-judicious) choice of placing our detector planes close to the z-axis.  This highlighted a bug that doesn't show up if they're in x or y (as is presumably the case for most collider geometry with the beam along z).

The mistake is in error_propagation/src/G4ErrorFreeTrajState.cc. Line 255 reads:
  G4double sinpPostInv = 1./std::sin( vpPreNorm.theta() );
whereas I think it should be:
  G4double sinpPostInv = 1./std::sin( vpPostNorm.theta() );

It looks like this is a simple typo (given the variable name).

To verify that this is indeed correct, I took the a set of tracks and "measurements" in a vacuum world and rotated them around the y-axis - this should be invariant in terms of the chi2 of my fit track.  The attached plots show the chi2 rising close to the z-axis (my phi_z is theta) in the pre-fix version and uniform in the post-fix version.

In addition, one other small fix to the same file is to add in:
  if( 1. - std::fabs(vpPreNorm.z()) < kCarTolerance ) return 4;
alongside line 252:
  if( 1. - std::fabs(vpPostNorm.z()) < kCarTolerance ) return 4;
In tracking calculations, an inverse is normally taken and when sinpPre is tiny, this can cause big precision problems.  Given we're already not able to track along a postStep of Z, it doesn't seem a big deal to catch the preStep too.