Vertex Reconstructing Neural Networks at the ZEUS Central Tracking Detector FermiLab, October 2000 Erez Etzion 1, Gideon Dror 2, David Horn 1, Halina Abramowicz 1 1. Tel-Aviv University, Tel Aviv, Israel. 2. The Academic College of Tel-Aviv-Yaffo, Tel Aviv, Israel.

Vertex Reconstruction FermiLab, October 2000 HERA High energy e – p scattering probe deep inside the proton in order to study its constituents structure Study substructure of quarks, electrons, N and C current procesesss, tests of QCD and search fo new particles Ee=27.5 GeV, Ep=820GeV

Vertex Reconstruction FermiLab, October 2000 ZEUS 3 level trigger Collision every 96 nsec (10MHz), FLT ~ 1MHz, SLT<100Khz

Vertex Reconstruction FermiLab, October 2000 Zeus Central Tracking Detector 205 cm long, 18.2<R<79.4. Magnetic field 1.43 T wires, 4608 signal wires, 9 superlayers (8 wire layer each) Axial wires Superlayer 1,3,5,7,9, Stereo (+/- 50) 2,4,6,8. 1,3,5 – z meas. (+/- 4cm)

Vertex Reconstruction FermiLab, October 2000 Input Data The Input SLT data: Xy position of superlayers 1,3,5,7,9 Z-by-timing in 1,3,5 (red)

Vertex Reconstruction FermiLab, October 2000 Ghost hits

Vertex Reconstruction FermiLab, October 2000 Z measurement uncertinties Example of z Meas. Uncertainty Left – single track in xy; Right – z vs r

Vertex Reconstruction FermiLab, October 2000 The Network Based on step-wise changes in the data representation: input points ->local line segments- >global arcs. Two parallel networks: 1.Construct arcs & correctly find some of the tracks 2.Evaluate z location of the interaction point

Vertex Reconstruction FermiLab, October 2000 Arc Identification Network Follow the primary visual system Input neurons (the retina like) cover 5000cm 2 Neuron fire when hitted in its receptive field. (xy) Second layer – line segment detector (XY  ). An active 2ed layer=line segment centered at XY with angle 

Vertex Reconstruction FermiLab, October 2000 Receptive fields of line segment neuron A line segment centered about the central black dot with orientation parallel to the oblique line is connected to the input neurons(squares) with weight: pink +1 Blue=-1 Yellow=0

Vertex Reconstruction FermiLab, October 2000 Third layer Network A track from the IP project into circle in r-  Transform the representation of local line segments into arc segments. A neuron is labled by  I (curvature, slope and ring). Mapping = winner take all.

Vertex Reconstruction FermiLab, October 2000 Arc Identification last stage Neurons are global arc detectors. Detect tracks projected in z=0 plane. Each active neuron  is equivalent in the xy plane to one arc in the plot.

Vertex Reconstruction FermiLab, October 2000 z Location Network Similar architecture to the first net A first layer input from the receptive field as its corresponding neuron in the first net. Get the mean of the z values of the points within the receptieve field. Second layer compute the mean value of the z of the first layer. The z averaging procedure is similary propagated to the third layer. Last layer evaluate the z value of the origin of each arc identified by the first network by simple linear extrapolation. The final z estimate of the vertex is calculated by averaging the output of all active fourth layer neurons.

Vertex Reconstruction FermiLab, October 2000 z-location resolution

Vertex Reconstruction FermiLab, October 2000 Number of track found

Vertex Reconstruction FermiLab, October 2000 Network Performance Study performed with 324 Networks Sigma vs number of neurons Small correlation -.26 The classical histogram method width ~8.5 cm.

Vertex Reconstruction FermiLab, October 2000 Network Performance (2) The network output width as a function of N1 and N2 N1=# neurons in the first layer N2=#neurons in the third layer

Vertex Reconstruction FermiLab, October 2000 New developments and cross- checks Form lateral connection between 1 st layer, which enabled us to reduce threshold still with good signal to noise - > reduce network size. Study network size –> x10 reduction. parameters: size and shape of receptive fields in 1 st layer, resolution in k-theta space, range of k- values (loosing tracks with r<45 cm)

Vertex Reconstruction FermiLab, October 2000 Summary FF double NN for pattern identification, selecting a subset of which is simple to derive the answer. Fixed architecture – can be implemented in HW. 1 st NN partial tracking in xy. The 2ed NN handles z-values of the trajectories estimating the z arcs origin. Performance is better than the “clasical method”.