Hub and Spoke Algorithm: 1 Electron, 2 Electron, Red Electron, Blue Electron

1. Hub and Spoke Algorithm: 1 Electron, 2 Electron, Red Electron, Blue Electron Presentation by David Miller, SUNY-Stony Brook REU ’08 Mentor: Professor Thomas Hemmick

2. Algorithm Ideas • Old: Clustering • Clusters could grow to any size or shape • Fails with scintillation • New: Hub and Spoke (HnS) • - Reconstructed electron location is used as center for search region • Hub: multiple-pad sum at center • Spoke: multiple-pad sum at some R and phi away from center

3. Two Possible Pad Sizes: 3 vs 7 - Two options that are presently coded

4. Definition Spoke Radius (SR) • Spoke Radius: The number of hexagon centers away from the hub, the algorithm will search for a spoke. • Defined slightly differently for 3-tuple vs 7-tuple (See following diagrams)

5. Three-tuple definition of SR

6. Seven-tuple definition of SR

7. Basic Algorithm Parameters • Size of Hub • 3-tuple or 7 tuple? Or some other geometry? • Size of Spoke • Area of search region - What spoke radius to use?

8. Size of Hub\spoke • Small Hub (3-tuple) - Less collected scintillation -> less variation due to scintillation - Lose some Cherenkov response. On average lose 92% of response (see next diagram) • Large Hub (7-tuple) - Never miss Cherenkov response - Large Scintillation. 3-tuple seems preferred for this reason.

10. 3 vs 7 tuple; Size of Spoke • Three-tuple vs seven-tuple • Three-tuple seems preferred due to less scintillation • Three-tuple’s smallest possible spoke radius (without overlap with hub) is 2, vs the seven-tuple’s 3. (See slides 5&6) • Size of Spoke • As presently coded, sizes of hub and spoke are equal • Could imagine a 7-tuple hub and 3-tuple spoke

11. Spoke Radius • Largeradius • Pick up false physical electron or large noise fluctuation • Single electron events will be misclassified as double • Small radius • Miss true Dalitz partner (see next diagram) • Dalitz decays will be misclassified as single

12. Opening Angle Distribution In Spoke Radius Terms

13. Ingredients • Pi0 Dalitz Conversions: Read from file created by Exodus, realistic momentum distribution. • Single (Signal) electrons: Read from same file, but only one electron from a decay is kept • Scintillation: Spread uniformly across HBD, ranges from 0.0 – 2.0 scintillation photon per pad • Hadrons: No ionizations, but hadrons were spread uniformly and their locations were used as a response to “zero” electrons

14. Note: 100 Cherenkov photons used to help to train the intuition.

20. Doubles Spoke Radius = 2 Doubles Spoke Radius = 5

21. Singles Spoke Radius = 2 Singles Spoke Radius = 5

22. Hadrons Spoke Radius = 2 Hadrons Spoke Radius = 5

23. Singles Doubles

24. Spoke Radius: Discriminator?

25. How to make decisions • One possible way - TMVA: Hub, spoke, and central-electron-to-spoke distance may be put in as a training tree into this multivariate analysis package • For a given hub, spoke, and spoke distance TMVA will output a number from -1 to 1 indicating signal-like or background-like • Cut is made on this classifier at some desired signal survival rate