1naustin@mail.cern.ch 1

Endcap C SCT Endcap C SCT Efficiency Efficiency

Calculation Calculation UpdateUpdate

Nicholas AustinNicholas AustinUniversity of University of

LiverpoolLiverpoolOperations Operations

MeetingMeetingJune 2007June 2007

2

• Want to calculate the efficiency of the SCT modules in the endcap C.

• Need to optimise the road width to be used in this calculation.

• Original plan to extrapolate TRT tracks into SCT and compare positions

with hit RDO strips

SCT Endcap C Module Efficiency Calculation… Original Plans

3

• Discovered that internal back tracking tool was not suited for this task

• Bad resolution of TRT measurements give great errors when fitting the track. • Only tracks with many SCT space points are reconstructed well, however,

• In order to remove biases from efficiency calculation, SP’s in active disk have to be removed and tracks refitted. This causes more problems with bad reconstruction and low statistics.

• Basically the backtracking is a black box which we do not understand.

• It has been decided to abandon this method in favour of one that does not use tracks or backtracking at all.

SCT Endcap C Module Efficiency Calculation…

Problems with Original Plans

4

No track cuts!!! (we don’t understand backtracking so don’t want to use it.

Require 2 or more space points

Loop over

disks/sides

Loop over

SP’s

Find and count all SP’s NOT in active disk, and

Store their global positions and corresponding disk numbers

Require 2 or more space points not in active disk

Loop over all

modules in

the active

disk

Loop over

pairs of SP’s

not in active

disk

Take one SP as starting position, obtain

direction from their relative positions,

extrapolate to every module in the active disk.

If extrapolation is fiducial predictedhit = true

Loop over

RDO’s

Find RDO strip hits in active

module.

If RDO strip passes through

predicted area of predicted hit,

efficient = true for active

module

efficient = false

predictedhit = false disks

SP’s

New Method – Extrapolate SCT Space Point Pairs

5

Loop over

disks/sides

Loop over

SP’s

Find and count all SP’s NOT in active disk, and

Store their global positions and corresponding disk numbers

Require 2 or more space points not in active disk

Loop over all

modules in

the active

disk

Loop over

pairs of SP’s

not in active

disk

Take one SP as starting position, obtain

direction from their relative positions,

extrapolate to every module in the active disk.

If extrapolation is fiducial predictedhit = true

Loop over

RDO’s

Find RDO strip hits in active

module.

If RDO strip passes through

predicted area of predicted hit,

efficient = true for active

module

active disk

efficient = false

predictedhit = false

New Method – Extrapolate Space Point Pairs, continued.

6

Loop over

disks/sides

Loop over

SP’s

Find and count all SP’s NOT in active disk, and

Store their global positions and corresponding disk numbers

Require 2 or more space points not in active disk

Loop over all

modules in

the active

disk

Loop over

pairs of SP’s

not in active

disk

Take one SP as starting position, obtain

direction from their relative positions,

extrapolate to every module in the active disk.

If extrapolation is fiducial predictedhit = true

Loop over

RDO’s

Find RDO strip hits in active

module.

If RDO strip passes through

predicted area of predicted hit,

efficient = true for active

module

efficient = false

predictedhit = false

New Method – Extrapolate Space Point Pairs, continued.

7

Loop over

disks/sides

Loop over

SP’s

Find and count all SP’s NOT in active disk, and

Store their global positions and corresponding disk numbers

Require 2 or more space points not in active disk

Loop over all

modules in

the active

disk

Loop over

pairs of SP’s

not in active

disk

Take one SP as starting position, obtain

direction from their relative positions,

extrapolate to every module in the active disk.

If extrapolation is fiducial predictedhit = true

Loop over

RDO’s

efficient = false

predictedhit = false

Find RDO strip hits in active

module.

If RDO strip passes through

predicted area of predicted hit,

efficient = true for active

module

New Method – Extrapolate Space Point Pairs, continued.

8

SCT Efficiency Road Width Calculation – Method Summary and Geometry correction

• Extrapolate straight lines through space point pairs into the ‘active disk’.

• Compare intersect positions of the extrapolated lines and the SCT modules, with ‘RDO hits’.

• Plot distance/residual between the extrapolated positions and the ‘hit strips’

• ‘dist’ is the correct distance that we need to measure.

Extrapolated ‘Predicted Position at (xextrap,yextrap)

RDO hit = centre of a strip that has detected the

cosmic particle, (xrdo,0)

Using similar triangles: W = (Wmax + Wmin) / 2 r = W*L / (Wmax – Wmin) dist = Xrdo * (1 + Yextrap/r) - Xextrap

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Efficiency Method (A) to calculate efficiency for each disk and side

ij =

N(predicted hits with rdo strip hits near by, in disk i, side j)

N(predicted hits in disk i, side j)

=

N(predictedhit + efficient)

N(predictedhit)

For each layer (disk, side)…

• Count the number of times there is a predicted hit (denominator).

• Count the number of times there is a predicted hit with a strip hit near (numerator).

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Method usually works quite well...

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... But some don’t work…

Predicted hits where there blatantly shouldn’t be predicted hits!

12

Problems arise when there are extrapolations to multiple modules in the

same disk. This is usually as a result of having >1 SP in a disk.

Possible fixes:

Only except extrapolations in a particular angle range.

Only except extrapolations that pass through both trigger counters.

New Efficiency Method:

Look at the ratio of single to double hits. This would give efficiencies for

each disk without using extrapolations that have no nearby strip hit.

13

Define efficiency of hit on one side of particular disk =

Then, for each disk…

Count Ratio: R = N(double sided hits) / N(single + double hits)

=0

000

or orP

(

P

( ) = (1-) + (1-) + 2 = (2-)

= 2

R = /(2-) , and calculate the disk efficiency

= 2R/(1+R)

1

111

Error in , d = (de/dR) dR

= {-2R/(1+R)2 + 2/(1+R)} dR

(where dR = binomial error of Ratio)

XXXXXX

XX )

New Ratio Method (B) to calculate efficiency for each disk

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Only gives 'side efficiencies' for each disk (i = efficiency of one

side of disk i).

but automatically only uses ‘good’ extrapolations to modules where there should be hits.

New Ratio Method (B) to calculate efficiency for each disk…

Advantages

15

Also (simple fix), to really clean up the dataset and remove many fake

extrapolations, remove all events where there is more than one space

point on any particular disk.

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Results from Last Time...

Previously did not understand

the weird bumps in the

distribution.

These bumps appear on the left

of the peak for side 0, and the

right for side 1.

Turned out to be times when I

was comparing strip hits on the

correct side of the module with

extrapolated positions on the

wrong side of the module.

Stereo angle between sides

explains the periodic nature, and

the ~2mm shift of the bumps.

This has been fixed, also a

couple of double counting

issues!!!

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Results after fix... Residuals for Disk 1

inner

> outer

WHY???

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Sigma of Residuals Plots

Why is disk 2 so

large?

Why are the sides

so different?

Especially the

Errors?

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Disk Side Num Den Eff

0 0 3446 4091 0.84234

0 1 3454 4100 0.84244

1 0 5102 6007 0.84934

1 1 5091 6028 0.84456

2 0 6256 7053 0.88700

2 1 6239 7070 0.88246

3 0 3584 4186 0.85619

3 1 3570 4201 0.84980

4 0 2330 2882 0.80847

4 1 2305 2869 0.80342

5 0 294 558 0.52688

5 1 292 556 0.52518

6 0 0 139 0.00000

6 1 0 139 0.00000

7 0 0 94 0.00000

7 1 0 93 0.00000

Efficiencies, Method A

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Disk Efficiency

0 0.8919

1 0.8938

2 0.9242

3 0.9363

4 0.9411

5 0.9283

6 0.0000

7 0.0000

Efficiencies, Method B

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Looping over SP pairs means multiple extrapolations to each layer per

event.

This gives a strange predicted area.

Not the best definition for efficiency.

Want to use all space points outside the active layer to fit one single

straight line that is to be extrapolated to the active layer and compared to

RDO hits.

Perform a minimisation of the sum of the squares of the residuals

(distances between the space point positions and the fitted track).

Introducing a Least Square Fit Extrapolation Method

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Require 2 or more space points and no more than one space point in any one disk

Loop over

disksLoop over

SP’s

Find and count all SP’s NOT in active disk, and

Store their global positions and corresponding disk numbers

Require 2 or more space points not in active disk…

Perform least squares fit on SP’s not in active disk x0[3] (arbitrary starting point on fitted line)

dir[3] (direction of fitted line).

Loop over

sidesLoop over

all modules

in the active

layer

Extrapolate least square SP fit to active module.

If extrapolation is fiducial (will only happen once per

disk/side) predictedhit = trueLoop over

RDO’s

Find RDO strip hits in active module. If RDO

strip passes through predicted area of predicted

hit…

bool efficient = false

bool predictedhit = false

What the code looks like now – Two efficiency methods and a Least Squares Fit

bool hitonside0 = falsebool hitonside1 = false

efficient = true for active module.if(side==0) hitonside0 = true;if(side==1) hitonside1= true;

if(predictedhit) Fill m_EfficiencyHistTot for disk, side.if(efficient) Fill m_EfficiencyHistEff for disk, side.if(hitonside0 || hitonside1) Fill m_singlehitcount for disk.

if(hitonside0 && hitonside1) Fill m_doublehitcount for disk.

disks

SP’s x

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Want to minimise the squares of the differences between data points and the fit in two

projections:

Minimise S = i (z

i - (p

1x

i + p

2))2 +

i(z

i – (q

1y

i+q

2))2

p1 = n

ix

iz

i –

ix

i

iz

i

nix

i2 - (

ix

i)2

q1 = n

iy

iz

i –

iy

i

iz

i

niy

i2 - (

iy

i)2

q2 = 1/n (

iz

i - q

1

iy

i)p

2 = 1/n (

iz

i - p

1

ix

i)

Choose 2 arbitrary z points and calculate x and y. Use one of the points as a ‘starting

position’ and the relative position of one w.r.t. the other as a ‘direction’ for the extrapolation.

z = p1x + p

2 ==> x = (z - p

2)/p

1

z = q1y + q

2 ==> y = (z - q

2)/q

1

The Least Squares Fit of Space Points not in the Active Layer… How is it done?

==>

24

Residuals from Least Square Fit Method

Cuts: 2+ SP's in event and no more than one SP in any disk.

inner

> outer

WHY???

25

Mean of Residuals from Least Square Fit Method

Cuts: 2+ SP's in event and no more than one SP in any disk.

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Sigma of Residuals from Least Square Fit Method

Cuts: 2+ SP's in event and no more than one SP in any disk.

Again... why are the

two sides so

different???

Especially the

errors?

Need to look into

this!!!

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Disk Side Num Den Eff

0 0 3346 3943 0.84859

0 1 3337 3939 0.84717

1 0 4926 5837 0.84393

1 1 4918 5861 0.83911

2 0 6119 6971 0.87778

2 1 6099 7000 0.87129

3 0 3474 4045 0.85884

3 1 3463 4059 0.85317

4 0 2256 2727 0.82728

4 1 2240 2715 0.82505

5 0 285 459 0.62092

5 1 287 456 0.62939

6 0 0 64 0.00000

6 1 0 64 0.00000

7 0 0 38 0.00000

7 1 0 38 0.00000

Efficiencies (Method A) from Least Square Fit Method

Cuts: 2+ SP's in event and no more than one SP in any disk.

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Disk Efficiency

0 0.8927

1 0.8911

2 0.9249

3 0.9367

4 0.9395

5 0.9336

6 0.0000

7 0.0000

Efficiencies (Method B) from Least Square Fit Method

Cuts: 2+ SP's in event and no more than one SP in any disk.

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Comparison between two extrapolation methods (same cuts), Efficiency

Method A.

Disk, Side SP Pair Method Efficiency

Least Square Fit Method Efficiency

0,0 0.84234 0.84859

0,1 0.84244 0.84717

1,0 0.84934 0.84393

1,1 0.84456 0.83911

2,0 0.88700 0.87778

2,1 0.88246 0.87129

3,0 0.85619 0.85884

3,1 0.84980 0.85317

4,0 0.80847 0.82728

4,1 0.80342 0.82505

5,0 0.52688 0.62092

5,1 0.52518 0.62939

6,0 0.00000 0.00000

6,1 0.00000 0.00000

7,0 0.00000 0.00000

7,1 0.00000 0.00000

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Comparison between two extrapolation methods (same cuts), Efficiency

Method B.

Disk SP Pair Method Efficiency

Least Square Fit Method Efficiency

0 0.8918 0.8927

1 0.8938 0.8911

2 0.9242 0.9249

3 0.9363 0.9367

4 0.9411 0.9305

5 0.9283 0.9336

6 0.0000 0.0000

7 0.0000 0.0000

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Comparison between two extrapolation methods (same cuts).

• Not much between the efficiencies derived from both extrapolation methods.

• The least square fit extrapolation does seem to improve the efficiencies ever so slightly.

• The least square fit extrapolation gives a much more definitive definition of efficiency (only one extrapolation per ‘experiment’.

• The least square fit extrapolation removes a loop from the code and makes it much simpler.

• Decided to discard the space point pair method in favour of the least square fit

extrapolation.

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Summary so far…

• The code is now very straight forward and both efficiency methods are well defined due to the single extrapolation achieved with a least squares fit.

• However, the efficiencies still seem to be rather low.

• The code no longer uses track information, only Space Points. As we cannot cut on the number of space points without biasing the results I am limited in how much I can clean up the sample.

• I need to look at other explanations as to why my efficiencies are low.

Method A Method B

33

Discussion with Helen, Sergey and Andy…

• Do we have low energy muons scattering off silicon surfaces?

• Look at the energy and transverse momentum of the truth muon

• Look at the incident angles of the truth muon and the extrapolated track at module surfaces.

• Where does the truth muon go when the SP extrapolation is not efficient?

• Compare the number of times a muon has single and double sided hits with that for the truth muon.

• Do we have nasty showers or scattering from the detector material. Should this be happening in Monte Carlo?

• Plot the number of space points and tracks per event.

• Also I need to understand why the residuals for the inner modules are so much wider than those for the outer and middle?

• Need to run over SR1 data.

• May be a good idea to also look at beam halo and gas Monte Carlo. This will require upgrade to v.13. Upgrading would be a good idea anyway! I am the only person in ATLAS using v.12.0.3-COS!!!

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Latest Progress…

• I have added the truth information

• A starting position (vertex) and a direction (momentum) for the truth muon can be obtained from the McEventCollection.

• The truth muon can then be extrapolated in the same way as the least square space point fit to each disk.

• Residuals and efficiencies for both methods have been calculated using the extrapolation of the truth muon.

• Properties of the truth muon have been compared with those of the extrapolated track, including direction and incident angles at surfaces.

35

Residuals: SP Extrap vs RDO Hits and Truth Muon Extrap vs RDO Hits

Disk 0, Side 0

Disk 0, Side 1

Disk 1, Side 0

Disk 1, Side 1

Outer Middle Inner

All distance scales are in mm

36

Residuals: SP Extrap vs RDO Hits and Truth Muon Extrap vs RDO Hits

Outer Middle Inner

Disk 2, Side 0

Disk 2, Side 1

Disk 3, Side 0

Disk 3, Side 1

37

Residuals: SP Extrap vs RDO Hits and Truth Muon Extrap vs RDO Hits

Outer Middle

Disk 4, Side 0

Disk 4, Side 1

38

Residuals: SP Extrap vs RDO Hits and Truth Muon Extrap vs RDO Hits

• Truth muon residuals are all nice gaussian peaks centred at zero and all have small widths.

• SP extrapolation residuals are not so good. Especially for inner disks.

• Notice sign of shift of SP Extrap residual is periodic with disk number.

39

Sigma of Residuals… Truth Muon and S.P. Extrapolation

40

Efficiencies for Method A… Truth Muon and S.P. Extrapolation

41

Efficiencies for Method B… Truth Muon and S.P. Extrapolation

42

Efficiencies for Methods A and B… Truth Muon and S.P. Extrapolation

A B

43

Event Statistics

• Each event in the MC sample only has one truth particle… a muon.

• However, each event has multiple tracks.

• These tracks must either come from noise (?) or low energy muon scattering.

44

• As expected, more muons with low energies than higher energies.

• But there has obviously been a cut at 80GeV.

• Are these energies low enough for scatter effects?

Kinematics of the Truth Muon

45

Comparisons between the directions of the truth muon and the S.P. extrap.

N.B. There are more entries for the S.P. Extrapolation as each collection of space points undergoes multiple extrapolations to each disk.

46

Comparisons between the directions of the truth muon and the S.P. extrap.

47

Hit positions of Efficient and Inefficient S.P extrapolated hits.

Seems to be a concentration of inefficient hits at the tops of modules. Need to look closer at “zcol” plots to really look at this.

48

Hit positions of Truth muon extrapolated hits.

Here the red dots correspond to times when the S.P. Extrapolation is inefficient, not the truth muon extrapolation!

49

“Relative” Residuals of Efficient S.P. Extrapolations.

50

“Relative” Residuals of Inefficient S.P. Extrapolations.

51

Angular distribution of Efficient and Inefficient S.P extrapolated hits.

52

Angular distribution of Truth muon extrapolated hits.

Here the red dots correspond to times when the S.P. Extrapolation is inefficient, not the truth muon extrapolation!

53

Angular Residuals of Efficient S.P. Extrapolations.

54

Angular Residuals of Inefficient S.P. Extrapolations.

55

Cutting on the number of Space Points.

• When I was extrapolating TRT tracks in order to calculate the efficiencies I was able to clean up the data set by cutting on the quality of the track.

• The current version of the code only uses SCT space points.

• The only thing to cut on is the number of SCT space points.

• It is obvious that cutting on this will bias the results (since extrapolations are compared to RDO hits… two of which form a space point).

• However, by accident I ran with a cut requiring an event to have 3 or more space points.

• Of course this has increased the efficiencies.

• Could this be counted as a good track cut?

56

Sigma of Residuals… Truth Muon and S.P. Extrapolation (NSP>2 cut)

57

Method A Efficiencies… Truth Muon and S.P. Extrapolation (NSP>2 cut)

58

Method B Efficiencies… Truth Muon and S.P. Extrapolation (NSP>2 cut)

59

Efficiencies (Method A and B)… Truth Muon and S.P. Extrapolation (NSP>2

cut)

60

Still to do…

61