1. Hough Map Improvement

2. Outline Distinguish (+ - ) charge of track on Hough space
Study the track width on Hough space

3. 1.Improved method on Hough space
In the first step , only use axial hits to fill Hough space
Imformation of slant of sin curve ->split a hole circle to 2 half circle
From mathematical derivation , we can distinguish a hit on which side of the circle by (sign of slant) *(sign of ρ) ρ
A pi- event
Hits on 1st half and 2nd half have different sign of slant when there appears a track θ

4. Improved method on Hough space
select 1st half hits on track -> get hits of clockwise -> get a candidate track of negative charge
select 2nd half hits on track -> get hits of anticlockwise -> get a candidate track of negative charge
So split a HoughMap into two charge
- charge map
+ charge map

5. Determine whether from same track
Algorithm Procedure
HoughHitList
HoughMap -
HoughMap +
Peak finding
Peak finding
Determine track
Determine track
Determine whether from same track

6. Why Solve Back to back events for high pt
For low pt , decay and energy lose of the 2nd hits spoil the circle finding
Not focus one area

7. 2.Track width determination
Different kinds of hits
Noise hit
Hit on decayed track
Hit from delta e
2nd half hits on a track circle
1st half hits on single turn track
To study the width of the track
No decay & delta e track
No background
Single turn track
Only take 1st half hits into consider

8. 2.Track width determinationρ
Only use axial hits ->more focused area
My suppose
Method
Find the most focused area
Cut HoughMap to as many bins( 500*500)
The highest bin (ρ, θ) should be the parameter of the track θ
Parameters (ρ, θ) explain the parameter of track on BESIII x-y space
Compare the peak with the track par from MC truth
500 single curve events (no decay and delta e)
ρ - ρTruth
θ - θ Truth
ρ -> 1/r , θ->angle on x-y plane
The highest bin on HoughMap can similar express the track

9. Track width determination
Method
Extend the size bin by bin from two directions around the highest bin
confirm the size of peak at least include 70% hits of the track
For one event , the size of the peak is recorded by (thetaNum,rhoNum)
500 single curve events (no decay and delta e)
thetaNum:peak need to combine number of bins along theta axias
rhoNum:peak need to combine number of bins along rho axias
If we use cut peak width by (4,4)
84% events has collected more than 70% useful hits
ThetabinNum
rhobinNum

10. Track width determination procedure
Cut HoughMap to 500*500 (as small)
Look for the highest bin
If (collected hits>70% of all hits)
Yes No
thetaNum++
Or rhoNum++
Combine highest bin with bins around it
Record theta/rho binNum

11. Hit tracking efficiency
hits proportion
50%
60%
70%
80%
90%
100%
Efficiency
94.2%
89.7%
83.5%
64.5%
39.5%
21%
Means 94.2% events find more than 50% useful hits

12. Track width varied with ρ
The track width should be some distribution in HoughMap
Along θ direction track are no difference
Along ρ direction , has some difference ,but not clear
Under studying