1. Inner Detector Alignment :Residue and Clustering Algorithm
Tun Sheng Tan, Muhammad Firdaus Mohd Soberi
Sept
UW Analysis Meeting Autumn 2014

2. Content Part1: Overview Introduction Motivation/Project Background
Objective
Part2: Analysis and Algorithms
Algorithm
Plan/Current Progress-Issues -Results
Future Progress/Outlook
Summary/Conclusion

3. Part 1: Overview

4. The ATLAS Detector

5. Introduction ATLAS inner detector structure (layers)
Pixels Detector (4 layers: 3 older b-layers + recently-added IBL)
Semiconductor Tracker (SCT)-4 layers
Transition Radiation Tracker (TRT)- 72 layers ~50k straw- gaseous drift tubes
Entire tracking system is embedded in super conducting solenoidal coil of 2T B-field
ATLAS pixel detector is the innermost substructure of the inner detector and largest pixel-based system at LHC.
About 80 million pixels
Covered from 12cm to 5cm from to interaction point
IBL is added at radius about ~3cm,

6. Inner Detector with end caps-Side View

7. Motivation /Project Background
IBL (Insertible B-Layer) added. What’s IBL?
There are 3 layers in pixel detector and IBL is the fourth
Improvement (after IBL):
Performance consolidation (improved b-tagging)
Mitigate radiation damage to the previous innermost b-layer at 5 cm
Planar sensor + 3D sensor technology
Innermost and fourth layer of pixel detector
Resulted in tiny cylinder about 3cm radius, 70 cm long. Innovatively small but added 12 million more detection channels
-LS1 shutdown Started Jan 2013
-Installation tool 10m long and require ‘big opening’+ lifting up muon wheels to surface for insertion

8. What is alignment and why?
When reconstructing the event, the detector positions used in the reconstruction algorithm often does not correspond to the actual relative position of the installed detector.
Spatial misalignment of the detector affect track parameters which then leads to incorrect physics results (eg. invariant mass)
Spatial misalignment also leads to decreased resolution accuracy and quality

9. What is alignment and why?
The process of determining the precise position of the active modules (that makes up the detector layers) for most accurate tracking is called alignment.
6 degree-of-freedoms (DOFs) called alignment parameters
Tx, Ty, Tz ( translations about center of object) and Rx, Ry, Rz (around Cartesian axis)
Uniquely determined position and orientation of modules is space-treat as rigid body
5 track parameters (for helixical trajectories)
𝑑 ° , 𝑧 ° , ∅ ° , 𝜃, 𝑞/𝑝

10. IBL Algorithm Levels 3 levels of alignment procedure levels
To mimic precisely the detector alignment DOFs
Each module is given 6 alignment parameters or DOFs
Difference in treatment of the structure as multiple or combined bodies leads to the extra DOFS

11. Detail overview of the 3 alignment procedure levels

12. Our Objective
Minor:
Complete IBL alignment and reproduce results for preparation of next run
To study the basic monitoring and output residual plots
To test and compare different pixel clustering method residual plots
Digital-worst resolution, depends on same weight of charge for different sails in the cluster
Analog-better resolution, depends on weighted charge distribution for clustering
Neuron Network(NN) – A specific type of machine learning algorithm. Specify all the parameters and let it decide which method give best resolution.
To compare the residual plots of iterated alignment after convergence and misaligned geometry as well as to nominal geometry
To compare residual plots as function of detector phi for collision data vs cosmic data

13. Part 2: Analysis and Algorithms

14. Alignment Algorithm
There are two track based alignment algorithms that are being implemented:
Global  2
Local  2
In general, we define:
 2 = ℎ𝑖𝑡𝑠 𝑖 𝑚 𝑖 − ℎ 𝑖 𝜎 𝑖 2
Where 𝑚 𝑖 is the measured position, ℎ 𝑖 is the predicted position, 𝜎 𝑖 is the standard deviation.
By finding an  , alignment parameter such that 𝑑  2 𝑑 =0 will gives the minimum of  2 and so giving the true alignment.

15. Using Newton-Raphson method to find :
∆ 𝛼 𝑖 = 𝛼 𝑖 −  0 =− 𝑑 2  2 𝑑𝛼 2 −1 𝛼=𝛼 0 𝑑  2 𝛼 0 𝑑𝛼
This calculation is repeated until a convergence criteria is achieved.
𝑑  2 𝑑 is an N vector matrix. 𝑑 2  2 𝑑𝛼 2 is an NxN dimensional matrix.
To solve the large NxN matrix, one uses diagonalization or matrix inversion method.
Inversion method:
𝑑 2  2 𝑑𝛼 2 𝛼=𝛼 0 ∆ 𝛼 𝑖 =− 𝑑  2 𝛼 0 𝑑𝛼
∆ 𝛼 𝑖 = 𝑗 𝑢 𝑗 ∗− 𝑑  2 𝛼 0 𝑑𝛼 𝑑 𝑗 𝑢 𝑖 𝑗
With 𝑢 𝑗 being the eigenvectors and 𝑑 𝑖 being the eigenvalues of 𝑑 2  2 𝑑𝛼 2 =UD U T , 𝐷 𝑖𝑗 = 𝑑 𝑖 𝛿 𝑖𝑗 .
The uncertainties on the alignment parameters is given by the covariance matrix 𝐶= 𝐴 −1 :
𝐶 𝑖𝑗 = 𝑙 𝑢 𝑖 𝑙 𝑢 𝑗 𝑙 𝑑 𝑙

16. Example of Weak Modes
From :

17. Global  2 vs Local  2 Method
Global  2 method is unpractical for very large number of degrees of freedom (DoF).
Local  2 method is similar to Global method but the matrix being inverted is smaller and requires more iterations
𝑑 2  2 𝑑𝛼 2 is being broken down into separate systems of equations.

18. Comparisons between residual clustering algorithms (Rel19)
Digital seems
to have better
performance
than analog
The Pixel local x and y unbiased residual distributions for the example of a multi-muon simulated sample.

19. The Pixel local x and y unbiased residual distributions for the example of a multi-muon simulated sample.
Observation: The performance of analog and digital are almost identical in all of the pixel barrel layers except for IBL layer

20. Issues
Monitoring options for alignment jobs is False by default as opposed to “True” that is being stated on the tutorial page.
Will edit the page.
Alignment jobs for Rel17 give segmentation fault when turning on monitoring option. Monitoring package seems to have some problem (by Pierfrancesco).
Will rebuild the package.

21. Outlook
To figure out how to change the geometry settings for alignment jobs
To setup the cosmic muon data set for alignment jobs
To rebuild monitoring package for rel17
To create an organized document of the background knowledge required. (optional)

22. Conclusion Rel19(completed): Rel17(in progress):
Neuron Network clustering has the best performance.
Analog and Digital are about the same in performance in most cases but digital seems to be just slightly better.
Rel17(in progress):
The monitoring package seems to have problems when we run it.

23. References Slides and Documents df
Cool animation on the ATLAS detector structure and how each works!