CSC Cluster Studies Woochun Park (Thanks to David Adams for the - - PowerPoint PPT Presentation

5/3/2007 CSC Cluster Studies 1

CSC Cluster Studies

Woochun Park (Thanks to David Adams for the help) @Muon Reconstruction 5/3/2007

5/3/2007 CSC Cluster Studies 2

Introduction

• Resolution of cluster position is

estimated as

• σφ is expected to be

where h is cathode-anode spacing (2.54mm) σL and <QL> are the rms and the mean charge distribution

• f the Landau distribution. (0.44),

that is 0.635mm.

• CSC is inclined by 11.59o and the

average track from the IP will have normal incidence but φ ranges

• 4o ~ 4o.

ϕ tan σ σ σ

φ tot

⋅ ⊕ =

ATLAS Inter Note MUON-NO-055 http://www.usatlas.bnl.gov/~wpark/cscval/muon-94-055.pdf

ϕ

5/3/2007 CSC Cluster Studies 3

Estimate σ0 and σφ

• We can measure σ0 and σφ from the fit on σtot-tanφ or σ2

tot-tan2φ.

Fitting function is first-order polynomial as Square of residual rms is used as σ2

tot with mean of residual is 0.

σ0 = sqrt(A) and σφ=sqrt(B).

• Fitting result is from 5GeV/c single muon MC (20k).
• /castor/cern.ch/user/m/muonprod/1203

/digit/mc12.csc120.007205.digit.mu*

σ0 = 39.5 ± 0.3 µm σφ = 0.524 ± 0.015 mm

φ Btan A σ

2 2 tot

+ =

tan2φ σ2

tot

5/3/2007 CSC Cluster Studies 4

Estimate charge error

• We use fixed charge error δQ for each strip charge (4300e for the plot)
• If we divide the formula by calculated error as
• σ2

est ~ δQ

• sqrt(A’) is scale factor for the given δQ to get a proper charge error.
• σφ=sqrt(B).
• Scale factor is 1.039 ± 0.009.
• δQ should be 4468e ± 39e.
• σφ = 0.545 ± 0.013 mm which is close

to the value in previous page.

2 est 2 2 est 2 est 2 tot

σ φ tan B σ A σ σ + =

2 est 2 2

σ φ tan B A pull + ′ =

2 est 2 tot

σ σ

2 est 2

σ φ tan

5/3/2007 CSC Cluster Studies 5

Momentum Dependence

• There is a momentum dependence.
• Resolution for normal incident track get a little better in higher

momentum.

• Angular resolution is a little worse in higher momentum.
• Charge error is less in higer momentum.
• σ0, σφ and δQ are good parameters
• Validate MC simulation
• Compare MC to real data
• MC shows much more precise than cosmic data (See Kostas’s talk).

4312 ± 40 569 ± 12 38.5 ± 0.4 10 GeV/c 4308 ± 38 567 ± 11 38.5 ± 0.3 50 GeV/c 4262 ± 40 567 ± 13 37.6 ± 0.4 100 GeV/c 693 88.4 Cosmic data (parabola fit) 4468 ± 39 545 ± 13 39.5 ± 0.3 5 GeV/c δQ (e) σφ (µm) σ0 (µm)

5/3/2007 CSC Cluster Studies 6

Error Estimate

• Charge error is estimated about 4300e.
• Angular dependence was not considered in position error

calculation.

• It makes pull width is correlated with pseudo-rapidity, total

charge, etc.

• Adding angular term in quadratic improve pull width correlation.
• In following page, we add σφ=0.635mm in 5GeV/c single muon MC

sample. 1.268 1.004

5/3/2007 CSC Cluster Studies 7

Pull Width on Eta

without angular term with angular term η= 2.28 for normal incident track. Pseudo-rapidity Pseudo-rapidity Pull width

5/3/2007 CSC Cluster Studies 8

Pull Width vs Calculated Position Error

without angular term with angular term

σcalc (mm)

Pull width

σcalc (mm)

5/3/2007 CSC Cluster Studies 9

Pull Width vs Peak Strip Charge

QPeak

without angular term with angular term Pull width

QPeak

The more charge deposit in strip, the smaller error becomes because charge error is fixed. So, pull width becomes larger.

5/3/2007 CSC Cluster Studies 10

Pull Width vs Strip Position

0 means “center of strip”, -1 is for “left” and +1 is for “right” without angular term with angular term Pull width Cluster Postion in strip Cluster Postion in strip

5/3/2007 CSC Cluster Studies 11

Charge Correlation in MC (5GeV/c muon)

X-Y strip charges are

correlated.

Line Fit:

F(Qx)=13.1+1.059*Qx

[Qy-F(Qx)]/1000

5/3/2007 CSC Cluster Studies 12

Conclusion

We study how to estimate error appropriately

considering angular dependence:

σ0 and σφ from the fit with

and these are about 40 microns and 0.56 mm.

Charge error can be estimated from the fit with

and it’s about 4300e.

Adding angular error term in quadratic improves pull distribution

and remove correlations.

σ0 , σφ , and charge error are good parameter to validate new rel

13.0.X MC and compare it to real data.

More validations need to be done.

Check the cluster performance with adding angular error term

and new charge error for different samples (Zmumu,etc).

Compare with cosmic data in more detail. X-Y strip charge correlation study will be done.

φ Btan A σ

2 2 tot

+ =

2 est 2 2

σ φ tan B A pull + ′ =