1. 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.

2. Vertex Reconstruction FermiLab, October 2000 Physics @ 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

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

4. Vertex Reconstruction FermiLab, October 2000 Zeus Central Tracking Detector 205 cm long, 18.2<R<79.4. Magnetic field 1.43 T. 24192 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)

5. 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)

6. Vertex Reconstruction FermiLab, October 2000 Ghost hits

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

8. 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

9. Vertex Reconstruction FermiLab, October 2000 Arc Identification Network Follow the primary visual system Input 100000 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 

10. 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

11. 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.

12. 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.

13. 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.

14. Vertex Reconstruction FermiLab, October 2000 z-location resolution

15. Vertex Reconstruction FermiLab, October 2000 Number of track found

16. 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.

17. 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

18. 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)

19. 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”.