Update on vernier scan note/analysis

 A reasonably recent draft pdf is included at the bottom.

 

 

I've been working on a new way of measuring the nongaussianity of the vernier scan profiles, since the original method proved not to work well with the BHT3coin trigger.

 

Old method:

Compare the cross section from the fit using all data points to the cross section when only the few points around the peak are included.  This gave reasonable values for a fake vernier scan filled with perfect values, as well as for the BHT3 data.  When applied to the BHT3coin data, it didn't improve despite the clearly improved shape that could be seen by eye.

 

Twogaus  method:

Replace our assumption of a single-gaussian beam profile with a double-gaussian, a wide, low-integral gaussian superimposed over a larger, narrower one.  By choosing parameters carefully, we can read the fraction of the beams that are in the narrow gaussian directly from the fit results.  These values were seemingly reasonable, with the idea that perfect > BHT3coin > BHT3.  

However, the original fit did not perform well, converging without attempting to fit the first half of the vernier scan profile in each case.  Adding additional constraints helped that, but the fit remains frustratingly unstable.  For any particular setup, it still does seem to preserve the idea that the heirarchy of the three samples should remain perfect, BHT3coin, BHT3.

 

Jan's suggestion:

An hour ago Jan suggested a very tempting shortcut which I will explore tomorrow, making a few relatively easy assumptions about the relationship between chisquared and the shape.  It might double-count the statistical uncertainty.

 

 

None of these features affect the raw numebrs for the luminosities, which are also attached below.