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FTPC Conformal Mapping Tracker Markus D. Oldenburg Max-Planck-Institut für Physik, München

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Overview zIntroduction zAlgorithm yConformal Mapping yData organization yTrack finding zPerformance zFirst Results zOutlook

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Introduction zGlobal tracking algorithms ytreat all clusters equally zLocal tracking algorithms ytry to extend given track by adding a new cluster ylook for the next point in the expected direction

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Conformal Mapping I zAssumption: Particles follow helical trajectories. y circular path in the bending plane y straight line in (s, z) space, with: xs: length of track in 3-dimensional space xz: coordinate along magnetic field

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Conformal Mapping II zFitting of straight lines is easier and faster than fitting cirlces. z transform x, y coordinates of a cluster to x, y with: yx = (x - x t ) / r 2 yy = (y t - y) / r 2 yr 2 = (x - x t ) 2 + (y - y t ) 2

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Data organization I zClusters are organized in sub-volumes. zSub-volumes are obtained by segmenting the tracking volume into cubes in (r, ) with yr = row, y = azimuthal angle, and y = pseudorapidity. zThe origin of this coordinate system is the main vertex.

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Data organization II zEach volume is identified by three indexes (i r, i, i ). zEach cluster is uniquely associated with one sub-volume.

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Track finding zProgram starts with youtermost padrows and proceeds towards inner most ones yclusters with smaller z uncrowded regions are searched first

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Where to look for the next cluster? zIf cluster k is located in sub-volume (k r, k, k ) only look for the next cluster on this track in sub-volume (j r, j, j ) with yk r - N r j r k r - 1 yk - N j k + N z parameters N r, N, N

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Tracklet search: build track segments zlink a cluster k to its closest unused cluster j zdistance d |k r - j r | (| k - j | + | k - j |) ziterate until tracklet consists of a certain number of clusters N

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Tracklet extension to tracks zif # clusters on track is N: zfit clusters to straight lines in yconformal space for bending plane ytracklength s vs. z: s(z) ziterate until: yno additional cluster found track ends here yall found clusters exceeds cut(s) track ended before ymaximal amount of clusters attained

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Vertex constraint on/off ztracking is done twice ywith (main) vertex constraint (conformal mapping transformation includes main vertex: x t, y t = 0) ywithout vertex constraint (first cluster on track gives x t, y t )

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Parameters zGeneral: # of segments in (r, ) zDifferent settings for main vertex tracks and tracks without vertex constraint y# of clusters to perform tracklet search N yminimal # of clusters on a track y# of row segm. to look into for clusters N r xfor tracklet extension xfor track extension y# of segm. to look into for clusters N, N

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Cuts to reject new clusters zDifferent cuts for main vertex tracks and tracks without vertex constraint ymaximal angle for tracklets ymaximal angle for tracks ymaximal distance from circle fit ymaximal distance from length fit

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Outlook zTrack Evaluator has to be completed yto be able to understand current problems yto be able to compare different track algorithms zCuts have to be refined by looking into simulated data

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