1. TRACK DICTIONARY (UPDATE) RESOLUTION, EFFICIENCY AND L – R AMBIGUITY SOLUTION Claudio Chiri MEG meeting, 21 Jan 2004

2. Several tracks with similar kinematics producing a single hit pattern Hit pattern Single and unique string (i.e. a dictionary key) Average (over the set) track parameters The dictionary concept Several tracks with similar kinematics producing a single hit pattern Several tracks with similar kinematics producing a single hit pattern Several tracks with similar kinematics producing a single hit pattern

3. The track dictionary is a ordered list of records: Key (hit pattern)  average track parameters + rms The track dictionary exploits the “digital” response of the spectrometer NO Tdrift used NO z measurements used yet

4. MC sample used to build the dictionary: Positrons from Michel decay; Unpolarized muons; Generator level cuts:  0.08 < |cosθ| < 0.35;  -60° < φ < 60°.

5. Start with 50000 independent events The resulting dictionary consists of ~6500 different patterns Efficiency check on 10000 independent tracks produce: Efficiency = 86%

6. 250000 generated events  12900 patterns; efficiency = 95% 100000 generated events  9000 patterns; efficiency = 91% Next steps for the dictionary update gives:

7. Where are located the tracks populating the dictionary ? Not uniform spectrometer illumination  dictionary completeness does not grow linearly with generated statistics Sector N Wire N

8. The actual dictionary is obtained with 250k independent MC tracks and consists of about 12900 different patterns The population of the patterns is not uniform: 40% has 1 entry 43% has 2 ÷ 10 entries 13% has 11 ÷ 50 entries 4% more than 50 entries Number of events in a dictionary record

9. All events e + Momentum components at the vertex Events in the dictionary Track first turn has hits in at least three sectors The spectrometer acceptance defines the e + kinematics

10. All events Other e + kinematics variables Events in the dictionary Track first turn has hits in at least three sectors

11. How do the distributions of the average track parameters in the dictionary compare with the actual parameter distributions ?

12. Momentum components for events in the dictionary Event by event distributions Average in each Dictionary record Track first turn has hits in at least three sectors Px / MeV Py / MeV Pz / MeV LEFT RIGHT

13. The comparison of the distributions of an average parameter in the dictionary with the actual parameter distribution shows: Px and Py have similar shapes; Pz a hit pattern in the spectrometer cannot tell the sign of Pz; the shape of the distribution of |Pz| is not well reproduced  poor |Pz| resolution of the dictionary.

14. What is the dictionary “resolution” for all parameters ? p MC - σ Generate a sample of independent events For tracks in the dictionary acceptance (Nsectors > 2) find the dictionary key compare; Px with (key); normalize to RMS vertex X vertex Y vertex Z Px Py Pz

15. Starting from digit ID and drift time, in each sector we have 4 possible solution (4 tangent segments) Digitization of the MC hit from x,y,z to: number of sector (1-17), number of chamber (1-2) number of wire (1-9) D.C.A(digit) smearing of 200  m  Tdrift (const V drift ) Z(digit) smearing of 300  m First reconstruction step drift circle LEFT – RIGHT AMBIGUITY SOLUTION

16. P Q T The assumption: track ~ circle with centre in C if PT and QT are straight segments tangent to C and intersecting in point T, then α = α´ The strategy: select the right tangents in two consecutive sectors by choosing the pair giving the minimum  ´ Intrinsic limitations: non uniform B implies that tracks are not exactly circles drift distance resolution ‘ C  ’’

17. The plot shows the distribution of   for 1000 tracks All possible combinations (23097) Exact combinations (3778) We need to define a cut on  which allows to keep high efficiency for correct left-right choices and to reject wrong combinations  rad rejects 57% of the incorrect solutions

18. Efficiency vs  efficiency With Δα = 0.24 rad we reach 90% of total efficiency in L – R solution. By definition, the total efficiency comes from two terms: -Tracks where the L – R ambigurity is solved in each sector (60%); -Tracks where the L – R ambigurity isn’t solved only in 1 sector (30%)  cut

19. To be done dictionary: Optimize stats. given by 1 – eff. ~ 10 -3 - 10 -4 and by looking at RMS vs stats. (intrinsic resolution of method); Add noise hits; Add inefficiency of Drift Chamber; Add drift time; Superimpose tracks.

20. To be done L – R ambiguity solving: improve efficiency, evaluate timing; study the effect of resolution varying with the impact parameter use the “calibrated” digits, (i.e. x,y.z as estimated after left-right ambiguity resolution) as starting points for F. Cei’s algorithm estimating track parameters.

21. A long term plan once a fit algorithm is defined Get dictionary output –if the hit pattern corresponds to a key –when/if the resolution is appropriate for the fit (save computing time) go to the track fit Solve left-right ambiguity –if the track is not found in the dictionary –if the hit pattern gives ambiguous track parameters (high combinatorial calculations only when needed) go to the track fit else