CSC Cluster Studies Woochun Park (Thanks to David Adams for the help) @Muon Reconstruction 5/3/2007 5/3/2007 CSC Cluster Studies 1
Introduction ϕ Resolution of cluster position is � estimated as = ⊕ ⋅ ϕ σ σ σ tan tot 0 φ σ φ is expected to be � where h is cathode-anode spacing (2.54mm) σ L and <Q L > are the rms and the mean charge distribution of the Landau distribution. (0.44), that is 0.635mm. CSC is inclined by 11.59 o and the � average track from the IP will have normal incidence but φ ranges -4 o ~ 4 o . ATLAS Inter Note MUON-NO-055 http://www.usatlas.bnl.gov/~wpark/cscval/muon-94-055.pdf 5/3/2007 CSC Cluster Studies 2
Estimate σ 0 and σ φ We can measure σ 0 and σ φ from the fit on σ tot -tan φ or σ 2 tot -tan 2 φ. � � Fitting function is first-order polynomial as = + 2 2 σ A Btan φ tot � Square of residual rms is used as σ 2 tot with mean of residual is 0. � σ 0 = sqrt(A) and σ φ = 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* � σ 0 = 39.5 ± 0.3 µ m � σ φ = 0.524 ± 0.015 mm tot σ 2 tan 2 φ 5/3/2007 CSC Cluster Studies 3
Estimate charge error We use fixed charge error δ Q for each strip charge (4300e for the plot) � If we divide the formula by calculated error as � 2 2 2 σ A tan φ tan φ = + ′ = + tot B 2 pull A B 2 2 2 σ σ σ 2 σ est est est est est ~ δ Q σ 2 � sqrt(A’) is scale factor for the given δ Q to get a proper charge error. � σ φ = sqrt(B). � Scale factor is 1.039 ± 0.009. � δ Q should be 4468e ± 39e. � σ φ = 0.545 ± 0.013 mm which is close � 2 σ to the value in previous page. tot 2 σ est 2 tan φ 5/3/2007 CSC Cluster Studies 4 2 σ est
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. � σ 0 , σ φ and δ Q are good parameters � Validate MC simulation � Compare MC to real data � MC shows much more precise than cosmic data (See Kostas’s talk). � δ Q (e) σ 0 (µ m ) σ φ (µ m ) 5 GeV/c 39.5 ± 0.3 545 ± 13 4468 ± 39 10 GeV/c 38.5 ± 0.4 569 ± 12 4312 ± 40 50 GeV/c 38.5 ± 0.3 567 ± 11 4308 ± 38 100 GeV/c 37.6 ± 0.4 567 ± 13 4262 ± 40 Cosmic data 88.4 693 (parabola fit) 5/3/2007 CSC Cluster Studies 5
Error Estimate 1.268 � 1.004 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 σ φ =0.635 mm in 5GeV/c single muon MC � sample. 5/3/2007 CSC Cluster Studies 6
Pull Width on Eta without angular term with angular term Pull width Pseudo-rapidity Pseudo-rapidity η= 2.28 for normal incident track. 5/3/2007 CSC Cluster Studies 7
Pull Width vs Calculated Position Error with angular term without angular term Pull width σ calc (mm) σ calc (mm) 5/3/2007 CSC Cluster Studies 8
Pull Width vs Peak Strip Charge with angular term without angular term Pull width Q Peak Q Peak 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 9
Pull Width vs Strip Position with angular term without angular term Pull width Cluster Postion in strip Cluster Postion in strip 0 means “center of strip”, -1 is for “left” and +1 is for “right” 5/3/2007 CSC Cluster Studies 10
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 11
Conclusion � We study how to estimate error appropriately considering angular dependence: � σ 0 and σ φ from the fit with = + 2 2 σ A Btan φ tot and these are about 40 microns and 0.56 mm. 2 tan φ ′ � Charge error can be estimated from the fit with = + 2 pull A B 2 σ and it’s about 4300e. est � Adding angular error term in quadratic improves pull distribution and remove correlations. � σ 0 , σ φ , 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. 5/3/2007 CSC Cluster Studies 12
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