Hough Map Improvement 2016-7-14

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

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

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

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

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

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

2.Track width determination ρ 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

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

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

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

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