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