ACD Recon update, effects on background rejection

Using new ACD merit variables in background rejection

 Current background rejection

Prefilters:

ClassificationTree:

 Using New Variables

 AcdTkr1VetoSigmaHit and VetoHit1

AcdTkr1VetoSigmaHit is an estimator of the "best" hit vetoing the track, expressed in "sigma".   This is the sum in quadrature of contributions from the miss distance between the track and the tile or ribbon and the signal size being less that 1 MIP.  For MIP-like signals along the track projection both terms are 0, so this variable is 0.  If the track missed the tile  this variable is postive, likewise if the signal is less than 1 MIP.

 
Same plot, but with the X-axis remapped with log10( AcdTkr1VetoSigmaHit + 0.01)

Note the small peak in the signal distribution around 7-9 is from low energy deposits in the tile pointed to by the track.
For completeness here is a plot of  AcdTkr1VetoSigmaHit v. AcdTkr1ActiveDist

 
VetoHit1 is the same variable, including the tracker SSDVeto. 
VetoHit1 = sqrt(Acd2Tkr1VetoSigmaHit*Acd2Tkr1VetoSigmaHit+1.5*Tkr1SSDVeto*Tkr1SSDVeto)
Here is a plot of VetoHit1 

Same plot, but the X-axis remapped with log10(VetoHit1+0.01)

 
Again, note the small peak in the signal distribution around 7-9 is from low energy deposits in the tile pointed to by the track. 
 

  AcdTkr1VetoSigmaGap and VetoGap1

 AcdTkr1VetoSigmaGap is an estimator of the track passing through a gap in the ACD, expressed in "sigma".   This is the sum in quadrature of two contributions: the geometrical       calculations of the track going in the gap and the chance of seeing no signal from the gap.  For high energy tracks that pass into the corner gaps of the ACD it is 0.  For tracks going into ribbons it is 1.5 (which represents the fact that we do expect some signal from the ribbons, albiet a small one).

 Here is a plot of the low end of AcdTkr1VetoSigmaGap for all events:

 For comparison, here is a plot of AcdTkr1VetoSigmaGap v. AcdTkr1RibbonDist:

In analogy with VetoHit1 above we can define VetoGap1 to take into account the Trk1SSDVeto:
   VetoGap1 = sqrt(Acd2Tkr1VetoSigmaGap*Acd2Tkr1VetoSigmaGap+1.5*Tkr1SSDVeto*Tkr1SSDVeto)
 
Here is a plot of the low end of VetoGap1 for all events. 

If we look at only those events that pass weren't vetoed because of a track tile association or b/c of excess energy in the ACD we see this:
 

For Comparison, here is a plot of VetoGap1 v. AcdTkr1RibbonDist for the same set of events.

AcdTkrVetoSigmaHit and VetoHit

We can also select the best association by looping over all tracks instead of just using the best track.
Here is a plot of that variable, AcdTkrVetoSigmaHit: 

 
In analogy to VetoHit1 we can make VetoHit from  AcdTkrVetoSigmaHit. 
Here is a plot of that:
 

 
Then if we only look at events that weren't rejected because of VetoHit1 or excess energy:

 
So, we could consider cutting very loose on this and rejecting some event with a high probablity match.
 

Reproducing Existing Performance with simple cuts 

Some other useful new Variables, (for Classification Tree)

 Another type of variable we consider is the scaled energy in a cone around the track.  We have three variables that reflect 15, 30 and 45 degreee cones.

With these variables (and some familiar ones) we can make a Classification Tree.

This plot show the performance of the CT (in red) relative to the pass 6 cuts (3 black circles).  The prefilter performances are also shown.
For comparison the CT performance without any prefilters is also show (in blue). 
 
Just to give some numbers, here are numbers for 3 different values of cutting on the CT output. 

 Basically, these numbers correspond to either 15% reduction in residual background at given signal efficiency or 3-4% increase in signal efficiency at given background.