1. Update of pattern recognition
2011/8/25
Ryohji Akimoto

2. Update of pattern recognition
Pattern recognition : grouping hit clusters which are supposed to be from an identical track.
Pattern recognition in the current code starts from a cluster on the first sublayer, then search clusters on the next sublayer around projection point calculated by already grouped clusters (or collision vertex).
The projection point at the next sublayer is calculated by straight projection.
But, if more than 3 clusters are grouped, bending angle can be calculated.
makes search area narrow and therefore makes fake track rate decrease.

3. Quick pT calculation
The calculation of bending angle in pattern recognition is enough to estimate roughly but should be done quickly.
Circle fit in XY-plane is proper, but iteration is necessary if more than 4 clusters are fitted due to non-linearity of chi-square.
There are some ways of circle fit without iteration.
Conformal mapping : circle passing the origin transformed to line
Riemann fit

4. Riemann fit
transform XY-plane to the Riemann sphere in 3D-space by the following transformation
Any points on a circle in XY-plane are transformed both on the Riemann sphere and on a plane in 3D-space.
Transformed points are fitted by plane in 3D-space ( ) with the least chi-square method.

5. Riemann fit v.s. iterative fit
0.3 GeV/c
0.5 GeV/c
1 GeV/c
5 GeV/c
10 GeV/c
iterative fit
Riemann fit
Checked with single track simulation.
At low pT (< 1GeV/c), pT reconstructed by Riemann fit is comparable to that by iterative fit.
But at high pT (> 5GeV/c), pT reconstructed by Riemann fit is worse than that by iterative fit.

6. phi - projected phi phi difference : 0.3 GeV/c 0.5 GeV/c 1 GeV/c
real hit
5 GeV/c
10 GeV/c
projected hit
Rhit
Rdiff
collision vertex
phi difference :

7. Reconstruction efficiency
± 0.05 rad
± 0.1 rad
300 MeV/c
97.66%
99.31%
500 MeV/c
98.81%
99.60%
1 GeV/c
99.25%
99.84%
5 GeV/c
99.53%
99.66%
10 GeV/c
99.57%
99.78%
efficiency : (real hit is within the area in phi) / (tracks reconstructed by the current code with more than 4 clusters)

8. Time consumption Simulation event : generated with HIJING (100 event)
Time consumption at svxreco.C
with circle projection (cut : 0.05 rad)
SvxStandAloneReco::process_event() : sec. / 100 events
Total : sec. / 100 event
with line projection (current code)
SvxStandAloneReco::process_event() : sec. / 100 events
Total : sec. / 100 event
~20 % improved in total

9. Reconstructed tracks
with circle projection (cut : 0.05 rad) : 475,252 segments / 100 events
with line projection (current code) : 140,110 segments / 100 events
quality cut : < -5
# of segments with circle projection is larger than that with line projection.
outlook : check fake track rate with mixed event
comes from “track-related” fake track (radiation or etc..) ?