track dictionary (update) resolution, efficiency and l – r ambiguity solution claudio chiri meg...
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TRACK DICTIONARY (UPDATE)
RESOLUTION,EFFICIENCY
AND L – R AMBIGUITY SOLUTION
Claudio ChiriMEG meeting, 21 Jan 2004
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
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 usedNO z measurements used yet
MC sample used to build the dictionary:
• Positrons from Michel decay;
• Unpolarized muons;
• Generator level cuts: 0.08 < |cosθ| < 0.35;-60° < φ < 60° .
Start with 50000 independent events
The resulting dictionary consists of ~6500 different patterns
Efficiency check on 10000 independent tracks produce:
Efficiency = 86%
250000 generated events 12900 patterns; efficiency = 95%
100000 generated events 9000 patterns; efficiency = 91%
Next steps for the dictionary updategives:
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
The actual dictionary is obtained with250k 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
All events
e+ Momentum components at the vertex
Events in thedictionary
Track first turn has hits in at least three sectors
The spectrometer acceptance defines the e+ kinematics
All events
Other e+ kinematics variables
Events in thedictionary
Track first turn has hits in at least three sectors
How do the distributions of the average track parameters
in the dictionary compare with the actual parameter distributions ?
Momentum componentsfor events in the dictionary
Event by eventdistributions
Average in eachDictionary record
Track first turn has hits in at least three sectors
Px / MeV Px / MeV
Py / MeV Py / MeV
Pz / MeV Pz / MeV
LEFT RIGHT
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.
What is the dictionary “resolution” for all parameters ?
pMC - < pdict > σ
Generate a sample of independent events
For tracks in the dictionary acceptance (Nsectors > 2)
find the dictionary keycompare;
Px with <Px>(key);normalize to RMS<Px>
vertex X
vertex Y
vertex Z
Px
Py
Pz
Starting from digit ID and drift time, in each sector we have 4 possiblesolution (4 tangent segments)
Digitization of the MC hitfrom 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 200m Tdrift (const Vdrift) Z(digit) smearing of 300m
First reconstruction stepdrift circle
LEFT – RIGHT AMBIGUITY SOLUTION
P
Q
T
The assumption: track ~ circle with centre in Cif 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
’
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 rejects57% of the incorrect
solutions
Efficiency vs
efficiency
With Δα = 0.24 rad we reach90% 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
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.
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.
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