FTPC Conformal Mapping Tracker

Markus D. OldenburgMax-Planck-Institut für Physik, München24.02.2000

Overview

IntroductionAlgorithm

Conformal Mapping Data organization Track finding

PerformanceFirst ResultsOutlook

Introduction

Global tracking algorithms treat all clusters equally

Local tracking algorithms try to extend given track by adding a

new cluster look for the next point in the expected

direction

Conformal Mapping I

Assumption: Particles follow helical trajectories. circular path in the bending plane straight line in (s, z) space, with:

s: length of track in 3-dimensional spacez: coordinate along magnetic field

Conformal Mapping II

Fitting of straight lines is easier and faster than fitting cirlces.

transform x, y coordinates of a cluster to x‘, y‘ with: x‘ = (x - xt) / r2

y‘ = (yt - y) / r2

r2 = (x - xt)2 + (y - yt)2

Data organization I

Clusters are organized in sub-volumes.Sub-volumes are obtained by segmenting

the tracking volume into cubes in (r, ) with r = row, = azimuthal angle, and = pseudorapidity.

The origin of this coordinate system is the main vertex.

Data organization II

Each volume is identified by three indexes (ir, i, i).

Each cluster is uniquely associated with one sub-volume.

Track finding

Program starts with outermost padrows and proceeds

towards inner most ones clusters with smaller

uncrowded regions are searched first

Where to look for the next cluster?

If cluster k is located in sub-volume (kr, k, k) only look for the next cluster on this track in sub-volume (jr, j, j) with kr - Nr jr kr - 1

k - N j k + N

k - N j k + N

parameters Nr, N, N

Tracklet search: build track segments

link a cluster k to its closest unused cluster j

distance d |kr - jr| (|k - j| + |k - j|)iterate until tracklet consists of a

certain number of clusters N

Tracklet extension to tracks

if # clusters on track is N:fit clusters to straight lines in

conformal space for bending plane tracklength s vs. z: s(z)

iterate until: no additional cluster found track ends here all found clusters exceeds cut(s)

track ended before maximal amount of clusters attained

Vertex constraint on/off

tracking is done twice with (main) vertex constraint

(conformal mapping transformation includes main vertex: xt, yt = 0)

without vertex constraint (first cluster on track gives xt, yt)

Parameters

General: # of segments in (r, )Different settings for main vertex tracks

and tracks without vertex constraint # of clusters to perform tracklet search N minimal # of clusters on a track # of row segm. to look into for clusters Nr

for tracklet extensionfor track extension

# of segm. to look into for clusters N, N

Cuts to reject new clusters

Different cuts for main vertex tracks and tracks without vertex constraint maximal angle for tracklets maximal angle for tracks maximal distance from circle fit maximal distance from length fit

Outlook

Track Evaluator has to be completed to be able to understand current

problems to be able to compare different track

algorithmsCuts have to be refined by looking

into simulated data