SIMULATION AND STUDY OF THE CMS

ENDCAP MUON ALIGNMENT SCHEME

A Thesis

Submitted to the Faculty

of

Purdue University

by

Robert H. Lee

In Partial Fulfillment of the

Requirements for the Degree

of

Doctor of Philosophy

May 2002

Dedicated to my wife, Angela

**ACKNOWLEDGMENTS**

I have been very fortunate to have both started and completed this
journey with the guidance of Laszlo Gutay and David Eartly. They created
the opportunity for me to succeed early on and continued to offer their
assistance and guidance when it was needed most. Likewise, I owe Kaori
Maeshima a tremendous debt of gratitude, as she has spent the past
several years carefully monitoring my progress and providing me with the
advice and daily counsel needed to complete this thesis. I would have
been lost without her. I am lucky to count Laszlo, David, and Kaori as
good friends.

I am also very fortunate that Hans Wenzel was kind enough to make a
significant effort to help me understand the physics reconstruction
software as well as provide me with the special computing resources
required to run it quickly. His help was invaluable. I would also like
to acknowledge the support of Fermilab and the Department of Energy for
providing me with the resources to work in the USCMS Collaboration and
complete my thesis.

My brother Ryan and my closest friends Ricardo, Denis, David, Todd,
Kevin, Susan, Heather, Josh, Missy, Jess, Jeff, and the Hu family
deserve thanks for their many years of friendship and for reminding me
not to take things too seriously.

Finally, I am most grateful to Angela, who has made of all my endeavors
much easier than they would have been without her, and to my parents,
who gave me everything I needed to complete this work.

**TABLE OF CONTENTS**

**Page**

**LIST OF TABLES** [7](#list-of-tables)

**TABLE OF FIGURES** [13](#list-of-figures)

**ABSTRACT** [22](#abstract)

**1** **INTRODUCTION** 1

1.1 The Higgs Boson 1

1.2 LHC and role of the CMS Detector 4

1.2.1 Inner Tracking and Calorimetry in CMS 5

1.2.2 Muon System 6

1.2.2.1 Barrel Muon 7

1.2.2.2 Endcap Muon 8

1.2.3 Expected Behavior of SM Higgs at the LHC 9

1.2.4 Discovery Potential for Standard Model Higgs at CMS 12

1.2.4.1 H b bbar (Z, W± b bbar) Events 13

1.2.4.2 H γγ Events 14

1.2.4.3 H W^+^W^-^ 2 lepton 2 neutrino Events 15

1.2.4.4 H ZZ 4 lepton Events 16

1.3 Endcap Muon Position Monitoring System (EMPMS) 16

1.3.1 The Need for an Endcap Muon Position Monitoring System 17

1.3.1.1 Level 1 Trigger Requirements in the CMS Endcap 18

1.3.1.2 Endcap Track Reconstruction Requirements 21

1.3.1.3 Design Requirements for the Endcap Alignment System 22

1.3.2 Design of the Endcap Alignment System 23

1.3.2.1 Straight Line Monitoring and CSC Tracking in ME ±234 25

1.3.2.2 Straight Line Monitoring and CSC Tracking in ME ±1 27

1.3.2.3 Locations of Off-SLM CSC Chambers 30

**2** **EMU ALIGNMENT SIMULATION AND RECONSTRUCTION** 31

2.1 COCOA Software Description and Fit Methodology 31

2.2 Reconstruction of a Prototype EMU Alignment System Using COCOA 33

2.2.1 Endcap Muon Position Monitoring System (EMPMS) Reconstruction at
CERN ISR Test Hall 34

2.3 Implementation of COCOA for EMPMS ISR Testing 36

2.4 Determination of ISR Dowel Positions from Survey Information 37

2.5 COCOA Reconstruction of ISR Test Setup 40

2.5.1 COCOA Reconstruction with References et2, et3, and es10 41

2.5.1.1 July/August Results 42

2.5.1.2 September Results 44

2.5.1.3 Discussion of et2, et3, and es10 Reference Sensor Reconstruction
46

2.5.2 COCOA Reconstruction with References et2, et3, and es9 50

2.5.2.1 July/August Results 50

2.5.2.2 September Results 52

2.5.2.3 Discussion of et2, et3, and es9 Reference Sensor Reconstruction
54

2.5.2.4 Conclusions 58

2.6 Limitations of the COCOA ISR Reconstruction 61

2.6.1 Determination of Angular Orientations 61

2.6.2 Reference et2 MAB Motions 62

2.6.3 Calibration of DCOPS Sensors 62

2.6.4 Calibration of Transfer Plate 63

2.6.5 Additional Fit Parameters (Shadowing, Poor Centroids) 64

2.6.6 Redundancy of Second Measurements in SLM Line 65

2.6.7 First Level Analysis of CCD Data 65

**3** **SIMULATION OF THE FULL EMU ALIGNMENT SCHEME** 67

3.1 Construction and Extraction of Simulation Parameters and Objects 67

3.2 Final Simulation Script Geometry Compared to Theoretical Placement
69

3.3 Estimation of Uncertainties Used in EMU Simulations 71

3.3.1 Digital CCD Optical Position Sensor (DCOPS) Sensors 71

3.3.1.1 Uncertainties in Direct Calibration of First Pixel Position 71

3.3.1.2 Uncertainties in Pixel Array Orientation and Length 72

3.3.1.3 Uncertainty of CCD Array and Packaging Positioning 72

3.3.1.4 Uncertainty of CCD Package Orientation inside DCOPS Window Frame
74

3.3.1.5 Final Estimation of Uncertainty in CCD Pixel - DCOPS Reference
Pin Calibration 74

3.3.2 CSC Active Center - DCOPS Reference Pin Calibration 75

3.3.2.1 CSC Panel Definition 76

3.3.2.2 Assembly of Final Chamber from Multiple Panels 78

3.3.2.3 Alignment Mounting Hardware 79

3.3.2.4 Deformation of Chambers and Chamber Components 80

3.3.2.5 Angular/Rotational Uncertainties 80

3.3.2.6 Final Estimation of DCOPS - CSC Active Center Uncertainties 81

3.3.3 Estimation of Other Simulation Parameters and Uncertainties 83

3.4 Simulation Results (Idealized EMU System) 84

3.4.1 Comparison of Large Simulations vs. Small Simulations 85

3.4.2 Simulation of the Idealized System 86

3.4.3 Relationships and Correlations Between EMU Components 89

3.4.3.1 Correlations Between 'Unknown' Quantities 90

3.4.3.2 Correlations Between 'Known' and 'Unknown' Quantities 92

3.4.3.3 LINK Interface to EMU Alignment System 93

3.4.3.4 DCOPS-Reference Center Tolerance 95

3.4.3.5 DCOPS Pixel Resolution 96

3.4.3.6 ME 1/2 Inclinometer Resolution 98

3.5 Conclusions 99

**4** **PHYSICS PERFORMANCE OF THE ENDCAP MUON DETECTOR** 100

4.1 Overview of Measurement of Momenta in the CMS Endcap 100

4.1.1 Overview of Muon Track Formation 102

4.1.2 Characterization of Momentum Resolution 103

4.2 Limiting Factors For Measurement of Momenta in the CMS Endcap 104

4.2.1 Physical Constraints Affecting Momenta Measurement 104

4.2.1.1 Multiple Coulomb Scattering 104

4.2.1.2 Energy Loss 106

4.2.1.3 Detector Design Constraints Affecting Momenta Measurement 109

4.2.2 Intrinsic CSC Resolution 109

4.2.3 Level 1 Triggering 111

4.2.3.1 Offline Spatial Resolution 112

4.2.3.2 Hit and Track Formation Efficiency 113

4.2.4 The Magnetic Field 114

4.3 Simulated Performance of the Endcap Muon System Using CMSIM 117

4.3.1 CMSIM Description 117

4.3.2 Summary of CMSIM Results 118

4.4 Simulated Muon System Performance with ORCA 121

4.4.1 Endcap Studies in ORCA 123

4.4.1.1 Intrinsic Detector Response (Perfect Alignment) 124

4.4.1.2 Effect of Multiple Scattering 128

**5** **EFFECT OF CSC CHAMBER MISALIGNMENT** 133

5.1 Effect of Random CSC Misalignment on Muon p~t~ Reconstruction 134

5.1.1 Effect of Random CSC Misalignment on L3 Reconstruction 134

5.1.2 Effect of Random CSC Misalignment L2 Reconstruction 143

5.2 Effect of ME Station Misalignment on Muon p~t~ Reconstruction 152

5.2.1 Effect of ME Disk Misalignment (Constant Shift) on L3
Reconstruction 152

5.2.2 Effect of ME Disk Misalignment (Constant Shift) on L2
Reconstruction 155

5.3 Effect of Misalignment on the L1 Endcap Muon Trigger 160

5.4 Impact of Elevated Single Muon p~t~ Trigger Thresholds on H→ ZZ
→2μ^+^μ^-^ Events 165

5.5 Summary and Discussion of Results 167

**LIST OF REFERENCES** 168

**APPENDIX**

A.1 Definition of Chamber Labeling Scheme in CMS 171

A.1.1 Local Definition of Cathode Strip and Anode Wire Planes 173

A.1.2 Global Orientation of Cathode Strip and Anode Wire Planes 174

A.2 Development of COCOA Simulation and Definition of Simulated Objects
175

A.2.1 Digital CCD Optical Position Sensor (DCOPS) Sensors 176

A.2.2 CSC Chambers 178

A.2.3 ME 2, 3, 4 Straight Line Monitoring (SLM) Line Layout 180

A.2.4 Muon Endcap Station 1 (ME 1) Layout 184

A.2.5 Transfer Lines 187

A.2.6 Script Labeling Conventions 191

A.2.7 Final Scripts Compared to Theoretical Placement 192

**VITA** 193

# **LIST OF TABLES** {#list-of-tables .unnumbered}

**Table** **Page**

1.  Key parameters of the CMS Electromagnetic Calorimeter. Resolution is
    given as a function of incident photon energy while
    ![](media/image1.wmf){width="0.18055555555555555in"
    height="0.19375in"} denotes the terms add in quadrature \[adapted
    from 1.3\]. 6

2.  Key parameters of the CMS Hadronic Calorimeter. Resolution is given
    as a function of incident single particle energy while
    ![](media/image1.wmf){width="0.18055555555555555in"
    height="0.19375in"} denotes the terms add in quadrature \[adapted
    from 1.3\]. 6

3.  Desired Performance \[Tracker + Muon\] of CMS Muon System \[1.8\]. 7

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1.  Dowel Locations of DCOPS Sensor Brackets (CMS Coordinates) in ISR
    Hall. 39

2.  Comparison of Dowel Locations in ISR Hall for Sensor et3 39

3.  Dowel Orientations for Sensor et3 as derived by COCOA 40

4.  Deviation of COCOA Reconstruction of DCOPS Axial Dowel Pin Positions
    from Expected Survey Location with es10 Survey as Final Reference 48

5.  Deviation of COCOA Reconstruction of DCOPS SLM Dowel Pin Positions
    from Expected Survey Location with Laser 302 and es10 Survey as
    Final Reference 48

6.  Deviation of COCOA Reconstruction of DCOPS SLM Dowel Pin Positions
    from Expected Survey Location with Laser 303 and es10 Survey as
    Final Reference 48

7.  Deviation of COCOA Reconstruction of Axial DCOPS Dowel Pin Positions
    from Expected Survey Location with es9 Survey as Final Reference 55

8.  Deviation of COCOA Reconstruction of SLM DCOPS Dowel Pin Positions
    from Expected Survey Location with Laser 302 and es9 Survey as Final
    Reference 55

9.  Deviation of COCOA Reconstruction of SLM DCOPS Dowel Pin Positions
    from Expected Survey Location with Laser 303 and es9 Survey as Final
    Reference 55

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1.  Contributions to Final Error in Determination of Pixel-to-CSC
    Reference Pin Calibration. Uncertainties due to misalignment and
    pixel array length are estimated as the worst case errors in the
    determination of the final active pixel position. 75

2.  Estimation of Error of DCOPS Positioning Above First Strip Layer
    (local Y axis). This table shows the uncertainties associated with
    the determination of the displacement between the DCOPS mounting
    plate and the first plane of cathode strips. 81

3.  Estimation of Error Transverse to CSC Chamber Centerline. This table
    shows the uncertainties associated with the determination of the
    displacement between the DCOPS alignment pin and the cathode strips
    transverse to the chamber centerline (local chamber X axis). 82

4.  Estimation of Error of DCOPS Orientation About DCOPS CCD Plane
    Normal (local DCOPS Z axis). This table shows the uncertainties
    associated with the determination of the orientation between the
    DCOPS CCDs and the first plane of cathode strips. Most uncertainties
    were less than 1 µrad and have been rounded up. 82

5.  Estimation of Error of DCOPS Orientation of DCOPS CCD Plane (local
    DCOPS X/Y axis). This table shows the uncertainties associated with
    the determination of the orientation between the DCOPS CCDs and the
    first plane of cathode strips. Most uncertainties were less than 1
    µrad and have been rounded up. 83

6.  Estimation of LINK System Uncertainties. This table shows the
    estimated uncertainties associated with components in the Link
    Alignment System included in the EMU Idealized COCOA Simulation. 83

7.  Uncertainty in CSC locations along the SLM lines for the Idealized
    EMU System. The uncertainty estimates for chambers in ME ±1/2 layer
    have been done using two sets of resolutions for the inclinometers
    placed on the ME ±1/2 CSC chamber frames. 87

8.  Uncertainty in CSC Orientations About Axes Parallel to CMS
    Coordinate System and Through CSC Chamber Center Idealized EMU
    System. The uncertainty estimates for chambers in ME ±1/2 layer have
    been done using two sets of resolutions for the inclinometers placed
    on the ME ±1/2 CSC chamber frames. 87

9.  Uncertainty in ME ±1 CSC locations along the SLM lines for the
    Idealized EMU System without ME ±1/2 Inclinometers. The uncertainty
    estimates where prepared in an Idealized EMU ME±1 simulation. 88

10. Uncertainty of ME ±1 CSC Orientations About Axes Parallel to CMS
    Coordinate System and Through CSC Chamber Center for Idealized EMU
    System without ME ±1/2 Inclinometers. The uncertainty estimates
    where prepared in an Idealized EMU ME±1 simulation. 89

11. Sample Correlations between Reconstructed Entries for CSC Chamber
    ME--22_15 (SLM-23). The correlation between entries shown in the
    table is taken directly from the off-diagonal matrix elements of the
    variance-covariance matrix used in the COCOA fit. This sample (it is
    not complete) of entries represents the largest correlations found
    for this chamber and was prepared from an ME 1 and ME 2 simulation.
    Entries are taken to be in the local coordinate system of the
    objects they describe (see Appendix A). 91

12. Sample Correlations between Reconstructed Entries for Transfer
    Plate. The correlation between entries shown in the table is taken
    directly from the off-diagonal matrix elements of the
    variance-covariance matrix used in the COCOA fit. This sample (it is
    not complete) of entries represents the several non-zero
    correlations found between transfer plates in an ME 2, 3, 4
    simulation. Transfer plates labeling has all objects designated as
    'transfer_plateAB', where two plates with the same value of 'B' lay
    on the same Transfer laser line (see Appendix A, Section 5.2.6). 92

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1.  Relative shift in L3 Muon System + Inner Tracker p~t~^-1^
    resolutions from perfect alignment with random CSC misalignment. The
    relative shift in the resolution is defined by Equation 5.1. 138

2.  Percentage of Entries Beyond Three Standard Deviations of the
    Initial Muon System + Inner Tracker (ORCA L3) p~t~^-1^ Residual
    Distributions for Various Degrees of Misalignments. 142

3.  Relative shift in ORCA L2 Standalone Muon System + Vertex Constraint
    p~t~^-1^ resolutions from perfect alignment with random CSC
    misalignment. The relative shift in the resolution is defined by
    Equation 5.1. 148

4.  Percentage of Entries Beyond Three Standard Deviations of the
    Initial Muon System + Inner Tracker (ORCA L2) p~t~^-1^ Residual
    Distributions for Various Degrees of Misalignments. 149

5.  Relative Shift in Standalone Muon System + Vertex Constraint Fit
    (ORCA L2) p~t~^-1^ resolutions from perfect alignment for ME Station
    Motions. The relative shift in the resolution is defined by Equation
    5.1. 159

6.  Averaged Standalone Muon System + Vertex Constraint (ORCA L2) Single
    Muon p~t~ Resolution for Random CSC Misalignment for Low p~t~ Muons.
    The measurement ranges are grouped and averaged in a manner to
    approximate measurements made with ME 1/1 + ME234/2 (1.3 ≤ \|η\| ≤
    1.7) and ME 1/1 + ME234/2 (1.7 ≤ \|η\| ≤ 2.3) for the range in
    momentum likely to be important in determining Trigger Performance.
    163

7.  Averaged Standalone Muon System + Vertex Constraint (ORCA L2) Single
    Muon p~t~ Resolution for ME Station Misalignment for Low p~t~ Muons.
    The measurement ranges are grouped and averaged in a manner to
    approximate measurements made with ME 1/1 + ME234/2 (1.3 ≤ \|η\| ≤
    1.7) and ME 1/1 + ME234/2 (1.7 ≤ \|η\| ≤ 2.3) for the range in
    momentum likely to be important in determining Trigger Performance.
    163

**Appendix Table**

1.  Location of First Active Pixel of CCDs of a Typical DCOPS Sensor in
    the Local DCOPS Coordinate System as Defined by Figure A.4. Values
    followed by an asterisk (\*) denote a dimension which will require
    calibration. 177

2.  DCOPS Primary Dowel References and Sensor Orientations for "Left
    Handed" CSCs. "Right Handed" CSCs differ by rotations of 180 degrees
    and have inverse X values. Dimensions are given with respect to the
    CSC Reference Center in local chamber coordinates. Coordinates have
    been extracted from CMS CSC production drawings (FNAL). ME ±1/2
    chambers have two LINK sensors and only a single DCOPS reference
    sensor and are detailed in Table A.5. 180

3.  Location and Orientation of CSC Chamber Centers Along all SLM Lines
    in the CMS Detector. Dimensions are given with respect to the local
    SLM coordinate system origin. Locations and orientations of chambers
    in the + and - Endcap exhibit mirror symmetry about the CMS XY
    plane. Coordinates have been extracted from CMS layout drawings. 182

4.  COCOA Position and Rotation of SLM Lines For All ME Stations. 183

5.  COCOA Position and Rotation of SLM Lines For ME 1 Stations. ME 1 SLM
    lines do not traverse the entire ME disc, rather they terminate at
    the reference DCOPS sensor placed on the ME 1/2 frame. The SLM lines
    project along lines parallel to the Secondary Link Lines from (0,0,
    6782), but offset 66mm. 186

6.  COCOA Position and Rotation of Secondary Link Lines In ME 1. All
    Primary Link Lines project from (0, 0, 6690). Secondary Link Lines
    run parallel to Primary Lines and are offset by 66.000 mm in the CMS
    XY Plane. 186

7.  DCOPS Primary Dowel References and Sensor Orientations for ME ±1/2
    CSCs. Sensors on the ME ±1/2 chambers have rotations of -185 or 5
    degrees and two possible locations for the placement of the
    reference DCOPS (designated as type 1 or 2), both are dictated by
    the projection of ideal laser lines along the ME±1 SLM lines.
    Dimensions are given with respect to the CSC Reference Center in
    local chamber coordinates. Coordinates have been extracted from CMS
    CSC production drawings (FNAL). ME ±1/2 chambers have two LINK
    sensors and only a single DCOPS reference sensor. 187

8.  COCOA/CMS Position of Transfer Lines and MAB Reference Sensors 188

9.  Transfer Plate Definition. ME4 Transfer Plates are identical to
    those in the ME3 layer. ME-3 and ME-4 Transfer Plates are mirror
    symmetric to ME2 Transfer Plates with the exception of ME-3 Plate 5.
    ME-2 Plates are mirror symmetric to ME3 plates. 190

10. COCOA/CMS Position of Transfer Plate. ME4 Transfer Plates locations
    along the SLM lines are identical to those in the ME3 layer. ME-3
    and ME-4 Transfer Plate locations are mirror symmetric to ME2
    Transfer Plate locations and orientations with the exception of ME-3
    Plate 5. ME-2 Plates are mirror symmetric to ME3 Plates with the
    exception of ME-2 Plate 5. 191

11. Labeling of EMU Objects in COCOA Scripts. 192

# **LIST OF FIGURES** {#list-of-figures .unnumbered}

**Figure** **Page**

1.  Range of possible Higgs masses calculated from experimental
    determinations of top quark mass and W boson mass in the context of
    the Standard Model. The shaded areas on the plot represent the
    measurement and associated errors that have been determined from
    direct top and W measurements at Fermilab CDF and D0 detectors,
    direct W measurements at LEP2000, and indirect measurements of top
    and W masses from LEP, SLC, and Fermilab neutrino
    experiments\[1.6\]. 4

2.  A 3D View of the Principle CMS Detector Subsystems \[1.7\]. 5

3.  Cross Section of one quadrant of the CMS detector detailing
    placement Barrel Muon chambers (labeled MS1-4, in red) and the
    Endcap Muon chambers (labeled MF1-4, in red). \[1.7\] 7

4.  The orientation and spacing of the Endcap Muon CSC chambers. The RF
    iron, upon which the chambers are mounted, is not shown. \[1.8\] 8

5.  Feynman Diagrams for the two dominate production channels --
    gluon-gluon fusion (left) and WW (ZZ) fusion (right). 9

6.  Cross Section of two dominate production channels as a Function of
    the Higgs Mass (m~H~) \[1.9\]. 10

7.  Plot of the expected dominate branching ratios for SM Higgs particle
    as a function of possible Higgs masses (m~H~). The red band
    indicates the most likely mass region for m~H~ based on the
    experimental evidence from LEP2000 and Figure 1 (114.1 - 250
    GeV/c^2^) data \[1.10\]. 11

8.  Estimated discovery potential for SM Higgs particle as a function of
    possible Higgs masses (m~H~) with 5pb^-1^. The red band indicates
    the most likely mass region for m~H~ based on the experimental
    evidence from LEP2000 and Figure 1 (114.1 - 250 GeV/c2) data \[1.7,
    adapted\]. S \> 5 indicates sufficient statistical certainty to
    claim discovery. The plots use the CTEQ2 and the EHLQ structure
    functions and were done in PYTHIA v5.7. 13

9.  Distribution of muons in the CMS Barrel and Endcap Muon Systems from
    H ZZ 4µ events. Each histogram contains 1000 events generated with a
    Monte Carlo simulation and denote the location in the CMS Muon
    System where each muon is likely to be found: the Barrel Region,
    Endcap Region, or outside the active area of the detector. 19

10. Distribution of muons in the CMS Barrel and Endcap Muon Systems
    for (A) W± µ + ν~µ~ and (B) Z0 2µ. Figures (A) and (B) each contain
    8200 events generated with a Monte Carlo simulation and denote the
    location in the CMS Muon System where each muon is likely to be
    found: the Barrel Region, Endcap Region, or outside the active area
    of the detector. 20

11. The Digital CCD Optical Position Sensor (DCOPS) concept. The
    position and orientation of the two Reference DCOPS are known and
    allow for the definition of the unknown laser line. Once the
    direction and orientation of the laser line is known, the position
    and orientation of the unknown DCOPS on the CSC can be determined in
    the directions perpendicular to the laser line. 24

12. The Bi-Directional DCOPS Sensor. The face of the CCDs point toward
    the inside of the box and have red prisms attached. The crosshair
    laser line enters the box from the ±Z axis. 24

13. View of CSC chamber arrangement and location of Straight Line
    Monitor (SLM) laser lines used in tracking chamber positions. This
    view of the Endcap corresponds to a 'head on' view of Figure 1.14.
    DCOPS sensors are shown at each end of the CSC chambers (drawn on
    only one SLM line). 25

14. Diagram of Endcap Alignment System showing Transfer laser lines and
    Straight Line Monitor (SLM) laser lines used in tracking CSC
    positions. 26

15. ME 1 Chamber Arrangement and Placement of SLM and Secondary Link
    Laser Lines. Overlap of MAB Structures is shown, though they do not
    touch ME1. ME 1/1 chambers are not shown. Note SLM lines do not
    cross the disc, but terminate at the edge of the ME1/2 rings.
    \[1.27\] 28

16. Detail of ME 1 SLM and Secondary Link Laser Lines. The drawing shows
    a ME1/3 DCOPS Sensor SLM line (three sensors along the red laser
    line) and the ME1/2 CSCs Secondary Link Line (the green laser line
    intersecting a blue Link sensor). The DCOPS attached to the out edge
    of the ME1/2 Chamber serves as the final reference sensor in the ME
    1/3 SLM line. 29

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1.  A Schematic Representation of the ISR Setup 35

2.  NEU DCOPS Calibration Parameters D1, D2, D3, and D4 36

3.  Typical Distribution of Reconstructed Positions for an SLM sensor in
    July/August for Laser 302 Using es10 as the Final Reference Sensor.
    (Bands are non-physical) 42

4.  Typical Distribution of Reconstructed Positions for an SLM sensor in
    July/August for Laser 303 Using es10 as the Final Reference Sensor.
    (Bands are non-physical). 43

5.  Typical Distribution of Reconstructed Positions for an SLM sensor in
    September for Laser 302 Using es10 as the Final Reference Sensor.
    (Bands are non-physical) 44

6.  Typical Distribution of Reconstructed Positions for an SLM sensor in
    September for Laser 303 Using es10 as the Final Reference Sensor
    (Sensor es4). (Bands are non-physical) 45

7.  Transfer Line Results of COCOA Reconstruction for July/August and
    September Runs Using es10 as the Final Reference Sensor. Error bars
    indicate total uncertainty in sensor location as determined by
    COCOA. 47

8.  SLM Line (Laser 302) Results of COCOA Reconstruction for July/August
    and September Runs Using es10 as the Final Reference Sensor. Error
    bars indicate total uncertainty in sensor location as determined by
    COCOA. 49

9.  SLM Line (Laser 303) Results of COCOA Reconstruction for July/August
    and September Runs Using es10 as the Final Reference Sensor. Error
    bars indicate total uncertainty in sensor location as determined by
    COCOA. 49

10. Typical Distribution of Reconstructed Positions for an SLM sensor in
    July for Laser 302 Using es9 as the Final Reference Sensor. (Bands
    are non-physical) 51

11. Typical Distribution of Reconstructed Positions for an SLM sensor in
    July for Laser 303 Using es9 as the Final Reference Sensor. (Bands
    are non-physical) 51

12. Typical Distribution of Reconstructed Positions for an SLM sensor in
    Sept for Laser 302 Using es9 as the Final Reference Sensor. (Bands
    are non-physical) 53

13. Typical Distribution of Reconstructed Positions for an SLM sensor in
    Sept for Laser 303 Using es9 as the Final Reference Sensor. (Bands
    are non-physical) 53

14. Transfer Line Results of COCOA Reconstruction for July/August and
    September Runs Using es9 as the Final Reference Sensor. Error bars
    indicate total uncertainty in sensor location as determined by
    COCOA. 56

15. SLM Line (Laser 302) Results of COCOA Reconstruction for July/August
    and September Runs Using es9 as the Final Reference Sensor. Error
    bars indicate total COCOA uncertainty. 56

16. SLM Line (Laser 303) Results of COCOA Reconstruction for July/August
    and September Runs. Error bars indicate total uncertainty in sensor
    location as determined by COCOA. 57

17. Summary of Reconstructed SLM and Transfer Sensor Locations for es9
    Reference Reconstruction. Histograms represent the deviation of all
    reconstructed sensor locations from their initial photogrammetry
    survey location. Both Laser 302 and 303 reconstructions are included
    in the data. The averaged for both test periods is 187µm. 58

18. Distribution of raw CCD means in es4 during the July/August Run.
    Three distinct jumps in the pixel distributions can be seen. 60

19. Distribution of COCOA Reconstructed location of es4 in the ISR hall
    during the July/August Run. No jumps in the data are evident. (Bands
    are non-physical) 60

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1.  The Simulated CSC Chamber Geometry and Local Coordinate System in
    the Idealized COCOA Model. The 'Average Active Center' of the CSC
    chambers is taken as the Reference Center for COCOA EMU simulations.
    69

2.  The Simulated EMU Alignment System. This is a COCOA generated VRML
    representation of the simulated geometry used for the idealized
    simulations of the EMU Alignment System. 70

3.  SONY ILX-551 CCD Specification and Direct Measurement (mm). The
    dimensional specifications and tolerances for the ILX-551 (A) quoted
    from Sony and the dimensions of a CCD taken from the small sample of
    studied ILX-551s (B) which exhibit the greatest deviation of the
    pixel array (in red) placement from the optimal location. 73

4.  Placement of Pins, Holes, and Etchings on CSC Chamber \[3.2\]. 77

5.  Reconstructed CSC RPhi Chamber Uncertainty vs. Tolerance on MAB
    Position. The plot shows the average uncertainty in reconstructed
    chamber locations as a function of the uncertainty estimate on the
    determination of the placement of the MABs within CMS. 94

6.  Reconstructed CSC RPhi Chamber Uncertainty vs. Secondary Link Line
    Resolution. The plot shows the average uncertainty in reconstructed
    chamber locations as a function of the uncertainty estimate on the
    placement of the Secondary Link Line. 95

7.  Reconstructed CSC RPhi Chamber Uncertainty vs. DCOPS-CSC Reference
    Center Tolerance. The plot shows the average uncertainty in
    reconstructed chamber locations as a function of the uncertainty
    estimate on the relative placement of the primary DCOPS calibration
    pin with the chamber reference centerpoint. 96

8.  Reconstructed CSC RPhi Chamber Uncertainty vs. DCOPS Pixel
    Resolution. The plot shows the average uncertainty in reconstructed
    chamber locations as a function of DCOPS pixel resolution. One pixel
    is 14 µm wide. ME 1/2 chamber sensors are not DCOPS sensors and have
    not been varied. 97

9.  ME±1 CSC Chamber Resolution vs ME±1/2 Inclinometer Resolution. 98

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1.  Trajectory of a Muon Traversing the CMS Endcap Region \[4.1\]. 101

2.  GEANT Based Determination of Xo In the CMS Muon System (at = 10).
    The two curves indicate the total radiation length (Xo) of material
    in front of the first (lower curve) and last (higher curve) muon
    chambers. The highlighted regions of the plot indicate regions which
    contain Endcap Muon Chambers. The red and green areas denote regions
    which do not contain the additional YN1 and YN2 iron. All incident
    particles falling in the red and yellow regions lie solely in the
    Endcap Muon System (\> 3 chamber hits). \[4.6\] 106

3.  Energy Loss for a Muon Traversing a per unit Volume of Iron. The
    total energy loss is shown in red. \[4.6, adapted\]. 109

4.  Sample Particle Trajectory and Emergence of the Resulting Cathode
    LCT Pattern \[4.5\]**.** Cathode strip patterns can be immediately
    identified to within one-half a strip width for processing into
    Level 1 Trigger algorithms. 111

5.  Spatial Resolution as a Function of Strip Width (2000 Test Beam
    Data, 200 GeV muons). Single CSC plane resolution varies as a
    function of strip width. The 0 and 1 points on the x axis correspond
    to a particle trajectory which crosses exactly between the strips.
    The single plane resolutions are extrapolated to six plane
    resolutions by Monte Carlo. The improvement is dramatic as the six
    cathode plane arrangement includes overlapping strips \[4.4\]. 113

6.  Quarter Plane Magnetic Field Map of the CMS Detector. The pink
    shaded region corresponds to field strength of approximately 4T,
    yellow to 3T, green to 2T, aqua to .9T, and blue \< .75T. 115

7.  CMSIM Simulated Muon System Performance As a Function of . The plot
    on the left details the simulated performance of the Muon System as
    characterized by the Standalone Muon + Vertex Constraint Fit. The
    plot on the right details the simulated performance as characterized
    by the Muon + Tracker Fit. \[4.6\] 119

8.  Reconstructed p~t~ Resolutions as a Function of Random CSC Chamber
    and ME Station Misalignment. 120

9.  The '3σ Exclusion' Estimate as a Function of Random CSC Chamber and
    ME Station Misalignment 121

10. The Muon System Standalone + Vertex Constraint p~t~ Resolution as a
    Function of η. 126

11. The Muon System + Inner Tracker p~t~ Resolution as a Function of η.
    126

12. Muon Standalone + Vertex Constraint (ORCA L2) Efficiency as a
    Function of η. The error bars are estimated from the binomial
    distribution. 127

13. Muon System + Inner Tracker (ORCA L3) Efficiency as a Function of η.
    The error bars are estimated from the binomial distribution 127

14. Effect of Multiple Scattering on the p~t~^-1^ Distributions in the
    Muon System Standalone + Vertex Constraint Fit (ORCA L2). The
    reconstructed distribution with multiple scattering is shown in
    (red). 129

15. Effect of Multiple Scattering on the p~t~^-1^ Distributions in the
    Muon System + Inner Tracker Fit (ORCA L3). The reconstructed
    distribution with multiple scattering is shown in (red). 130

16. 3σ Efficiency Estimation of the ORCA L2 and L3 Residual
    Distributions as a Function of \|η\|. 131

17. Effect of Multiple Scattering on a p~t~ = 100 GeV Muon Reconstructed
    with the Muon System Standalone + Vertex Constraint Fit (ORCA L2) as
    a Function of \|η\|. 132

18. Effect of Multiple Scattering on a p~t~ = 100 GeV Muon Reconstructed
    with the Muon System +Inner Tracker Fit (ORCA L3) as a Function of
    \|η\|. 132

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1.  Muon System + Inner Tracker (ORCA L3) Resolution for the
    Reconstruction of p~t~ = 10 GeV Muons vs. Random CSC Misalignment.
    136

2.  Muon System + Inner Tracker (ORCA L3) Resolution for the
    Reconstruction of p~t~ = 20 GeV Muons vs. Random CSC Misalignment.
    136

3.  Muon System + Inner Tracker (ORCA L3) Resolution for the
    Reconstruction of P~t~ = 50 GeV Muons vs. Random CSC Misalignment.
    137

4.  Muon System + Inner Tracker (ORCA L3) Resolution for the
    Reconstruction of P~t~ = 100 GeV Muons vs. Random CSC Misalignment.
    137

5.  Sample p~t~^-1^ Muon System + Inner Tracker (ORCA L3) Residual
    Distributions Before (in black) and After (in Red) ±1mm Random CSC
    Misalignment at \|η\| = 1.9 for p~t~ = (A) 20 GeV, (B) 50 GeV, (C)
    100 GeV, and (D) 1000 GeV. 139

6.  Muon System + Inner Tracker (ORCA L3) Resolution for the
    Reconstruction of P~t~ = 1000 GeV Muons vs. Random CSC Misalignment.
    140

7.  Standalone Muon System + Vertex Constraint (ORCA L2) Resolution for
    the Reconstruction of P~t~ = 10 GeV Muons vs. Random CSC
    Misalignment 144

8.  Standalone Muon System + Vertex Constraint (ORCA L2) Resolution for
    the Reconstruction of P~t~ = 20 GeV Muons vs. Random CSC
    Misalignment. 144

9.  Standalone Muon System + Vertex Constraint (ORCA L2) Resolution for
    the Reconstruction of P~t~ = 50 GeV Muons. 145

10. Standalone Muon System + Vertex Constraint (ORCA L2) Resolution for
    the Reconstruction of P~t~ = 100 GeV Muons. 145

11. Sample p~t~^-1^ Standalone Muon System + Vertex Constraint (ORCA L2)
    Residual Distributions Before (in black) and After (in Red) ±1mm
    Random CSC Misalignment at \|η\| = 1.9 for p~t~ = (A) 20 GeV, (B) 50
    GeV, (C) 100 GeV, and (D) 1000 GeV. 146

12. Percentage of Entries in the Muon Standalone + Vertex Constraint
    (ORCA L2) p~t~^-1^ Residual Distributions which Exceed Three
    Standard Deviations of the Original (Perfect Alignment) Residual
    Distribution as a Function of Random CSC Misalignment for p~t~=10
    GeV. 150

13. Percentage of Entries in the Muon Standalone + Vertex Constraint
    (ORCA L2) p~t~^-1^ Residual Distributions which Exceed Three
    Standard Deviations of the Original (Perfect Alignment) Residual
    Distribution as a Function of Random CSC Misalignment for p~t~=20
    GeV. 150

14. Percentage of Entries in the Muon Standalone + Vertex Constraint
    (ORCA L2) p~t~^-1^ Residual Distributions which Exceed Three
    Standard Deviations of the Original (Perfect Alignment) Residual
    Distribution as a Function of Random CSC Misalignment for p~t~=50
    GeV. 151

15. Percentage of Entries in the Muon Standalone + Vertex Constraint
    (ORCA L2) p~t~^-1^ Residual Distributions which Exceed Three
    Standard Deviations of the Original (Perfect Alignment) Residual
    Distribution as a Function of Random CSC Misalignment for p~t~=100
    GeV. 151

16. Muon System + Inner Tracker (ORCA L3) Reconstruction Resolution for
    p~t~ = 20 GeV Muons as a Function of ME Station Misalignment. 153

17. Muon System + Inner Tracker (ORCA L3) Reconstruction Resolution for
    p~t~ = 50 GeV Muons as a Function of ME Station Misalignment. 153

18. Muon System + Inner Tracker (ORCA L3) Reconstruction Resolution for
    p~t~ = 100 GeV Muons as a Function of ME Station Misalignment. 154

19. Muon System + Inner Tracker (ORCA L3) Reconstruction Resolution for
    p~t~ = 1000 GeV Muons as a Function of ME Station Misalignment. 154

20. Standalone Muon System + Vertex Constraint (ORCA L2) Reconstruction
    of Muon p~t~ at \|η\| = 1.3 and 2.1 for 1mm ME Station Misalignment.
    156

21. Standalone Muon System + Vertex Constraint (ORCA L2) Reconstruction
    Resolution for p~t~=10 GeV Muons as a Function of ME Station
    Misalignment. 157

22. Standalone Muon System + Vertex Constraint (ORCA L2) Reconstruction
    Resolution for p~t~ = 20 GeV Muons as a Function of ME Station
    Misalignment. 157

23. Standalone Muon System + Vertex Constraint (ORCA L2) Reconstruction
    Resolution for p~t~ = 50 GeV Muons as a Function of ME Station
    Misalignment. 158

24. Standalone Muon System + Vertex Constraint (ORCA L2) Reconstruction
    Resolution for p~t~ = 100 GeV Muons as a Function of ME Station
    Misalignment. 158

25. Expected Level 1 Muon Trigger Rates in the Endcap for the Three
    Principle Operating Luminosities at the LHC. Arrows have been added
    to indicate the 3kHz trigger rate budgeted for the Muon Endcap and
    the resulting p~t~ cuts which must be made. The cuts assume perfect
    alignment of the CSC chambers and CSC chamber resolutions determined
    by CMSIM \[5.2\]. 161

26. Inclusive Endcap Muon Trigger Rates For CSC Chambers with Various
    Resolutions as a Function of Threshold p~t~. The red arrows indicate
    the intersection of each curve with the budgeted 3kHz Trigger Rate
    in the Endcap and is labeled with the required p~t~ threshold
    required to meet it. 164

27. Histogram of the Highest p~t~ Muons From 1000 H→ ZZ →2μ^+^μ^-^
    Events with All Four Muons Falling in the Range 1.1 ≤ \|η\| ≤ 2.4
    For 6 Different Higgs Masses Generated With PYTHIA 6.1. 166

28. Efficiency of Inclusive Muon p~t~ Trigger For H→ ZZ →2μ^+^μ^-^
    Events in the Endcap for the 5 p~t~ Thresholds Illustrated in Figure
    5.26. 167

**Appendix Figure**

1.  Typical ME Layout. Drawing of ME2, as viewed from interaction point,
    with proper labeling of CSC chambers. \[A.1\] 172

2.  Cross Section of Six Layer Cathode Strip Chamber. Dimensions in mm
    173

3.  Single Cathode Strip Chamber Labeling Scheme 174

4.  3-D View of a DCOPS Sensor. The local right handed coordinate system
    of the DCOPS is shown in red (Y axis runs vertically). Calibration
    of the sensor is done by referencing of the first active pixel in
    this local system. \[A.3\] 177

5.  Strip Layout and Reference Center Definition (definition of active
    center) 179

6.  Detail of SLM Lines and SLM Reference Points 1-6 for ME 2 \[A.1\]
    183

7.  ME 1 Chamber Arrangement and Placement of SLM and Secondary Link
    Laser Lines. Overlap of MAB Structures is shown, though they do not
    touch ME1. ME 1/1 chambers are not shown. Note SLM lines do not
    cross the disc, but terminate at the edge of the ME1/2 rings.
    \[A.1\] 185

8.  Sample Layout of Transfer Plate. The figure shows the relative
    orientation of the two DCOPS sensors on a ME2 Point 2 transfer plate
    as well as the location of the SLM crosshair laser. The dashed red
    line on the Transfer DCOPS sensor denotes the slot assembly for the
    calibration pin. 189

#   {#section .unnumbered}

# **ABSTRACT** {#abstract .unnumbered}

Lee, Robert H. Ph.D., Purdue University, May, 2002. Simulation and Study
of the CMS Endcap Muon Alignment Scheme. Major Professor: Dr. Laszlo
Gutay.

The successful operation of the CMS Endcap Muon detector will entail
meeting several significant technical challenges. Among these challenges
will be the ability to accurately estimate the performance of the Endcap
Muon detector and to anticipate or correct any potential problems during
the design stage. This thesis presents the simulation and study of the
Endcap Muon Alignment Scheme, a component of the Endcap Muon Detector
designed to determine and track the location of Cathode Strip Chambers.

Information about the performance of the CMS Endcap Alignment System was
gathered through an extensive testing of a prototype system and then
used to create a simulation to predict the behavior of the system as
designed. The results of these simulations indicate that the design of
the EMU Alignment System is viable and can successfully reconstruct
chamber locations along designated alignment lines throughout the CMS
Endcap. A detailed error analysis and subsequent examination of the
principle sources of uncertainty across multiple simulations show that
the tolerances on components and their calibration are well understood
and will ensure the successful reconstruction of CSC chamber positions
within approximately 200μm in CMS RФ and 500μm in CMS Z. In addition,
physics studies of single muon events were performed with the general
CMS Reconstruction Software (ORCA 5_3_1) to understand CSC misalignment
effects on muon track reconstruction and predict how the Alignment
System will impact the final determination of muon p~t~ and trigger
rates in the Endcap Muon System.

# **INTRODUCTION**

Modern high energy physics is driven by the enormous accelerators and
detectors which allow physicists to probe interactions at very large
energies. The Large Hadron Collider (LHC) at CERN is presently under
construction and will ultimately offer a glimpse of physics at an energy
level more than seven times of what is presently accessible. To observe
interactions at the LHC, the Compact Muon Solenoid (CMS) detector is
being constructed. It is hoped that data taken at CMS will contribute
toward further understanding physics within the Standard Model \[1.1\]
and/or discovering new physics beyond it.

The design and construction of CMS is technically complex and
challenging. Each subsystem in the detector will require a substantial
effort to develop hardware and software solutions for the challenges
encountered. This thesis is focused on the development of only a small
portion of this project, the Alignment Scheme of the CMS Endcap Muon
(EMU) Subsystem. More specifically, this thesis examines the components
which comprise the EMU Alignment System and makes an estimation of the
System's performance and impact on CMS physics.

## The Higgs Boson

The Standard Model has enjoyed much success in predicting the
interactions of particles. Electroweak theory \[1.2\] in the Standard
Model has shown that weak and electromagnetic interactions arise from a
common SU(2) x U(1) symmetry, however the Standard Model does not
account for why particles which mediate the weak force have mass while
other force carriers are massless. Experimental evidence shows that
while the photon may be massless, the W and Z^0^ mediators are massive.
Moreover, the Standard Model fails to predict any of the quark or lepton
masses. An important part of completing the Standard Model will be to
explain what hides the symmetry between weak and electromagnetic
interactions and thus how particle masses may be generated.

The simplest prediction as to the origin of the mass within the Standard
Model postulates that particles interact with a field (called the 'Higgs
Field') to acquire mass. The degree to which these particles interact
with this field would determine their mass. An important requirement of
a theory utilizing such a field would be the preservation of the
electroweak SU(2) x U(1) symmetry. Spontaneous symmetry breaking, in
which the lowest energy states of the field have less symmetry than it
Lagrangian, offers a way to give the W and Z^0^ bosons mass while
keeping this symmetry invariant. The manner in which spontaneous
symmetry breaking is employed with the concept of local gauge invariance
in the generation of the Higgs field is called the Higgs Mechanism.

A direct consequence of the Higgs Mechanism and in keeping with the
mediation of other field-particle interactions, a neutral Higgs boson is
postulated. The experimental confirmation of such a particle would
validate the presence of a Higgs field. As a consequence, a large effort
has been made to find this particle with existing particle accelerators.
To date, no experiments have confirmed the existence of the Higgs with a
high degree of statistical certainty. Presumably, if a Standard Model
Higgs particle exists at all, it is simply too heavy to produce enough
of with existing accelerators. Other theories have also been proposed to
extend the present Standard Model. Several of these theories postulate
multiple Higgs particles (the Minimal Super Symmetric Model \[1.3\], for
example) while others predict no Higgs particles at all (Technicolor
\[1.4\]). In any case, what remains important is the Standard Model can
in principle accommodate a Higgs particle which would indicate the
presence of a mechanism to explain the aforementioned problems within
the Standard Model.

LEP 2000 data indicates that the lower boundary of the Higgs mass is
114.1 GeV/c^2^ at a 95% confidence level \[1.5\]. Though LEP 2000
announced several potential Higgs candidates at the end of its final run
near 115 GeV/c^2^, the results were not conclusive. The Aleph and Delphi
experiments at LEP initially reported five Higgs 4-jet candidate events
at a mass of around 114 GeV against an expected background of 0.3
events. By the end of 2001, following a brief extension on LEP operation
and an updated analysis of all available LEP data, the LEP L3 detector
reported a Higgs candidate from a two jet and missing energy (neutrinos)
event, the OPEL detector reported, with very low confidence, two 4 jet
candidates, the Aleph detector maintained confidence in their initial
results, while the Delphi detector lowered the significance on both of
their initial 4 jet candidates with further recalibration of their
detector. The lower bound on the Higgs mass was also revised to 114.1
GeV (at the 95% confidence level). \[1.5\]

Since the Higgs particle is expected to provide the mechanism for the
generation of the quark and vector boson masses, the Higgs mass can be
calculated directly from the top quark and W boson masses. However, the
accuracy to which the Higgs mass can be determined from these parameters
is very sensitive to the certainty with which these masses are known.
Figure 1.1 shows the range of possible Higgs masses allowed if such a
calculation is done with the present experimental measurements (and
uncertainties) of the top and W masses in the context of the Standard
Model.

The experimental evidence presented in Figure 1.1 indicates the most
likely mass of the Higgs will be (at a 1 confidence level) less than 500
GeV/c^2^. The upper bound for the Higgs mass consistent with the
agreement of all the experimental data in Figure 1.1 is 250 GeV/c^2^.

![](media/image2.png)

Figure 1.1: Range of possible Higgs masses calculated from experimental
determinations of top quark mass and W boson mass in the context of the
Standard Model. The shaded areas on the plot represent the measurement
and associated errors that have been determined from direct top and W
measurements at Fermilab CDF and D0 detectors, direct W measurements at
LEP2000, and indirect measurements of top and W masses from LEP, SLC,
and Fermilab neutrino experiments\[1.6\].

## LHC and role of the CMS Detector

The CERN Large Hadron Collider (LHC) is being constructed to probe
previously unobtainable energy regions and will be used in the search
for the Higgs Boson. In addition to expanding the available range of
energies to continue this search, the LHC is being designed to provide a
high number of events to study. The LHC will principally operate at two
luminosities (10^33^ cm^-2^sec^-1^ and 10^34^ cm^-2^sec^-1^) and is
expected to collide protons with at a 14TeV center of mass energy.

The Compact Muon Solenoid (CMS) detector is a general purpose detector
to be constructed at one of the LHC interaction points and will be used
in the search for the Higgs boson, study of t- and b-quark decays, and
the search for physics beyond the Standard Model. The fundamental design
of this detector was premised on the implementation of a very good muon
system motivated in part by the H ZZ 2^-^ 2^+^ Higgs Boson decay
channel. To facilitate the identification of particle type and charge of
muons and other charged particles, the detector features a
superconducting solenoid capable of fields exceeding 4 Tesla. Aside from
the muon system, all components of the detector are placed inside the
solenoid. This arrangement is expected to be particularly advantageous
in the search for H decays. The endcaps of the detector consist of
alternating layers of muon chambers and iron discs to return the large B
field generated by the solenoid.

The principle components of the CMS detector include the Inner Tracker,
Electromagnetic Calorimeter (ECAL), Hadronic Calorimeter (HCAL), and
Muon System. Figure 1.2 shows the spatial arrangement of these
components.

![](media/image3.png){width="4.559722222222222in"
height="3.283333333333333in"}

Figure 1.2: A 3D View of the Principle CMS Detector Subsystems \[1.7\].

### Inner Tracking and Calorimetry in CMS 

The Inner Tracker is being designed to measure the p~t~ of charged
tracks in the region \|\| \< 2.6 ( regions of CMS are shown in Figure
6). The Inner Tracker will employ solid state and microstrip gas
detectors for efficient b-tagging and lepton charge determination up to
p~t~ = 2 TeV. The Electromagnetic Calorimeter lies immediately outside
the Inner Tracker, also covering \|\| \< 2.6, and utilizes lead
tungstate crystals to measure EM energy. The ECAL is optimized to search
for H decays at high luminosity (10^-34^ cm^-2^sec^-1^) and will be able
to make direct measurements of the photons direction in the \|\| \< 1
region. The Hadronic Calorimeter is constructed around the ECAL and will
make complementary energy measurements of particles. To perform these
tasks, this calorimeter must have good hermeticity, energy resolution,
and segmentation as well as sufficient depth for the containment of
hadron showers. The Hadronic Calorimeter consists of 18 identical wedges
and is segmented in a manner that closely matches the arrangement of the
barrel muon chambers and ECAL segmentation. The characteristic
parameters describing the ECAL and HCAL are summarized in Table 1.1 and
Table 1.2.

**Table 1.1: Key parameters of the CMS Electromagnetic Calorimeter.
Resolution is given as a function of incident photon energy while**
![](media/image1.wmf){width="0.18055555555555555in" height="0.19375in"}
**denotes the terms add in quadrature \[adapted from 1.3\].**

  ----------------------------------- ---------------------------------------------------------------
  Resolution \[MeV\] (high            $$5\text{\%}\sqrt{E} \oplus \text{.}5\% E \oplus \text{150}$$
  Luminosity)                         

  Resolution \[MeV\] (low Luminosity) $$2\text{\%}\sqrt{E} \oplus \text{.}5\% E \oplus \text{150}$$

  Segmentation in x                   .0145 x .0145

  Depth in ~R~ (radiation lengths)    25

  Depth in ~I~ (interaction lengths)  1.1
  ----------------------------------- ---------------------------------------------------------------

Table 1.2: Key parameters of the CMS Hadronic Calorimeter. Resolution is
given as a function of incident single particle energy while
![](media/image1.wmf){width="0.18055555555555555in" height="0.19375in"}
denotes the terms add in quadrature \[adapted from 1.3\].

  ----------------------------------- ------------------------------------------------------
  Resolution \[MeV\]                  $$\text{70}\text{\%}\sqrt{E} \oplus 9\text{.}5\% E$$

  Segmentation in x                   .087 x .087

  Depth in ~I~ (interaction lengths)  25
  ----------------------------------- ------------------------------------------------------

### Muon System

As previously discussed, the CMS detector is equipped with a Muon System
that will provide excellent muon identification, momentum measurement,
and triggering. Muon identification will be achieved with large area
muon chambers placed behind a large absorber. At least 16 interaction
lengths (~I~) of material is present across \|\| \< 2.4. The muon system
is subdivided into two distinct subsystems: the Barrel Muon and Endcap
Muon.

![](media/image4.png){width="5.375in" height="2.9375in"}

Figure 1.3: Cross Section of one quadrant of the CMS detector detailing
placement Barrel Muon chambers (labeled MS1-4, in red) and the Endcap
Muon chambers (labeled MF1-4, in red). \[1.7\]

The expected resolution of the CMS Muon system is summarized below, in
Table 1.3. Resolutions in the Barrel and Endcap regions are comparable
to each other.

Table 1.3: Desired Performance \[Tracker + Muon\] of CMS Muon System
\[1.8\].

  ---------------------------- ------------------------------------------
  p~t~                         Expected Resolution

                               

  10 GeV                       .5 -- 1 GeV

  100 GeV                      1.5 -- 5 GeV

  1 TeV                        50 -- 200 GeV
  ---------------------------- ------------------------------------------

#### Barrel Muon 

The barrel muon system is comprised of two stations on the inside and
outside of the iron return yoke (MS 1 and 4, Figure 6) and two stations
located in slots within the iron (MS 2 and 3, Figure 6). The stations
are segmented into five equal pieces parallel to the beam pipe and
comprised of 60 drift chambers on the interior of the detector and 70
drift chambers on the outer layer. Each drift chamber is comprised of
twelve planes of drift tubes organized into four-plane 'Super Layers'.
The planes comprising each Super Layer have parallel wires allowing each
chamber to have two Super Layers to measure particle tracks in the plane
and a third to monitor tracks along the Z plane. Moreover, each chamber
plane in the Super Layers are staggered by half a drift cell length
making it possible to determine the coordinate and orientation of
impinging tracks without external timing by correlating the drift times
in each plane. The maximum drift time for any drift cell in the chambers
is 400ns, allowing the chambers to be used in first level triggering.

#### Endcap Muon 

The Endcap Muon System is comprised of 4 discs of Cathode Strip Chambers
(CSC) separated by the Return Field (RF) Iron discs (Figure 7, below).
The RF iron acts as the principle mechanical support for the CSCs,
absorber for incident particle showers, and a return for the large
magnetic flux leaving the central solenoid. The CSCs on each disc are
placed into two rings with 18 or 36 chambers in each ring. Chambers in
the system form slight overlaps so that there is near 100% coverage for
any incident muon track.

![](media/image5.jpeg){width="2.647222222222222in"
height="2.716666666666667in"}

Figure 1.4: The orientation and spacing of the Endcap Muon CSC chambers.
The RF iron, upon which the chambers are mounted, is not shown. \[1.8\]

The CSC chambers employed in the Endcap are multiwire proportional drift
chambers with 50 m intrinsic resolution and fast readout. Similar to the
Barrel drift chambers, the CSCs are comprised of 6 planes, with each
plane recording a two dimensional position of incident particles.

### Expected Behavior of SM Higgs at the LHC 

Production of the Higgs at the LHC is expected to be dominated by
gluon-gluon fusion and WW (ZZ) fusion (Figure 1.5, below).

![](media/image6.wmf)

Figure 1.5: Feynman Diagrams for the two dominate production channels --
gluon-gluon fusion (left) and WW (ZZ) fusion (right).

The production cross sections as a function of Higgs mass are shown in
below in Figure 1.6. As the figure indicates, the production cross
sections increase rapidly with the decrease in Higgs mass. Although
other processes are expected to contribute to Higgs production in the
LHC, the cross sections of these processes are significantly lower than
WW (ZZ) fusion.

![](media/image7.wmf)

Figure 1.6: Cross Section of two dominate production channels as a
Function of the Higgs Mass (m~H~) \[1.9\].

Since the Higgs particle coupling is proportional to mass, branching
ratios are expected to be dominated by dominated by heavier particles.
For a Higgs mass less than 90 GeV, the H b bbar branching ratio is
extremely large, as the b quark is the heaviest possible particle
accessible for a Higgs decay. As Figure 1.7 indicates, decays in to
quarks or leptons less massive than the b quark will be very small
(decay into gluons involves a quark loop).

For Higgs masses which lie between 90 and 600 GeV/c^2^, decays into
vector bosons become increasingly dominate. The H decay emerges at
approximately 90 GeV and, although extremely small, is potentially very
important since the b bbar signal, as well as other quark and gluon
decay signals, must be reconstructed from final decay products or
intermediary particles and will involve large backgrounds (see Section
1.2.4.). Also of particular interest is the mass range 150 GeV/c^2^ \<
m~H~ \< 200 GeV/c^2^ where the threshold of ZZ (though one Z must be
below mass shell) and WW (where the WW may be on mass shell) production
is met. This mass range corresponds to the dip in the ZZ branching ratio
and slight elevation in the WW branching ratio on Figure 1.7. For a m~H~
≈ 2 m~z~, the so called 'Golden Decay Channel' for H ZZ 4 leptons
exists. The H ZZ 4 leptons ( or e ) decay, though infrequent (Z or e
branching ratio is only 3%), will likely prove to be a critical channel
to monitor as the signal-to-background ratio is very favorable (See
Section 1.2.4). The emergence of a ttbar decay channel becomes available
for Higgs masses approaching 2m~t~.

![](media/image8.jpeg){width="4.791666666666667in"
height="3.5833333333333335in"}

Figure 1.7: Plot of the expected dominate branching ratios for SM Higgs
particle as a function of possible Higgs masses (m~H~). The red band
indicates the most likely mass region for m~H~ based on the experimental
evidence from LEP2000 and Figure 1 (114.1 - 250 GeV/c^2^) data \[1.10\].

As previously discussed, there are several indications that the mass of
the Higgs will be light. However, for a heavier Higgs (\>800 GeV/c^2^),
domination of H ZZ and H WW decays are still expected with a persistence
of a somewhat smaller branching ratio for H t tbar. The theoretical
upper limit on the mass of the Higgs is expected to be on the order of 1
TeV, beyond which the Standard Model no longer provides an adequate
explanation of observed phenomena (this is explained further in the
following section).

### Discovery Potential for Standard Model Higgs at CMS 

The 'discovery' of a Higgs particle will occur after a sufficient number
of Higgs decay channels are reconstructed over the remaining background
(a Statistical Significance \> 5, see Figure 1.8). The branching ratios
of the various Higgs decays (Figure 1.7, red band) give some indication
of likely discovery channels at CMS, but large backgrounds preclude the
study of several of these channels. A short summary of the viability of
each potential discovery channel is given in Section 1.2.4.1-5.

Simulation studies of the expected physics at the CMS detector
\[1.3,1.4,1.7\] have indicated that the H ZZ 4 leptons and H W+W- 2
leptons 2 neutrinos channels offer potential Higgs discovery at the 5
level with 10^5^ pb^-1^ of data (initial 3 year operation at L~LHC~ ≈
10^33\ cm-2^s^-1^ will give 10^4^pb^-1^/year). As Figure 1.8 indicates,
the H ZZ 4 lepton and H W+W- 2 lepton 2 neutrino channels offer
discovery potential across the full range of possible Higgs masses
consistent with all available experimental data (see Figure 1.1).

Of the potential discovery channels, only the decays H ZZ 4 leptons and
H γγ are likely to be determined by direct mass reconstruction. The H
W+W- 2 lepton 2 neutrino channel must rely on the determination of
missing E~t~ in the calorimeter rather than direct reconstruction of
masses.

![](media/image9.jpeg){width="3.7930555555555556in"
height="4.548611111111111in"}

Figure 1.8: Estimated discovery potential for SM Higgs particle as a
function of possible Higgs masses (m~H~) with 5pb^-1^. The red band
indicates the most likely mass region for m~H~ based on the experimental
evidence from LEP2000 and Figure 1 (114.1 - 250 GeV/c2) data \[1.7,
adapted\]. S \> 5 indicates sufficient statistical certainty to claim
discovery. The plots use the CTEQ2 and the EHLQ structure functions and
were done in PYTHIA v5.7.

#### H b bbar (Z, W± b bbar)

The H b bbar decay can in principle be determined by direct mass
reconstruction; however very large background and the difficulty of
reconstructing jet 4-vectors at the LHC has thus far precluded any Higgs
discovery signatures in simulated analyses of this channel \[1.12\]. The
same is true for the decay of any particle into q qbar immediately after
the initial pp collision and is expected to preclude the study of other
channels utilizing Z b bbar and W± b bbar decays. This effectively
limits the study of H W+W- and H ZZ to the H W+W- 2 lepton 2 neutrino
and H ZZ 4 lepton channels as Z and W decays generally go to hadrons
(branching ratio of 70%).

#### H γγ

The H γγ decay channel was once thought to provide the best chance for
Higgs discovery in CMS. Despite the difficulties of discriminating
potential signals in this channel in a pp collider (hadronization, large
π^o^ production, etc.), a substantial financial and technical effort was
made on the part of the CMS collaboration to optimize the performance of
the Electromagnetic Calorimeter (ECAL) for H γγ decays across a Higgs
mass range of 90 GeV to 150 GeV \[1.7\].

Prior to the measurement of the top quark mass in mid-1994, many
physicists expected a 'light' top quark of \< 160 GeV \[1.13\] (compared
to the Particle Data Group Dec. 2001 accepted value of 174.3 ± 5.1 GeV).
Consequently, many theoretical predictions of the SM Higgs upper mass
bound during the initial ECAL design stage (1992-1994) tended to be
quite low -- with claims of stringent mass limits of m~H~ \< 100 GeV to
less stringent predictions of \< 200 GeV \[1.14\]. LEP searches had by
this time set the lower Higgs mass bound at only \> 63.5 GeV (at 95%
CL).

Theoretical arguments providing an upper bounds on the Higgs mass
typically characterize the Higgs model as an effective field theory
which only remains valid up to some energy Λ (where Λ \> m~H~). In
general, larger values of Λ imply smaller values of m~H~; a Λ 10^18^ GeV
(the Planck scale, at which new physics must enter) imply a value of
m~H~ \< 200 GeV \[1.15\].

Arguments placing further restrictions on this boundary, as well as
arguments favoring a light Higgs (\< 140 GeV), often cite the desire for
a Higgs field vacuum expectation value that is fixed by the known
strength of weak interactions, but a Λ value that is set well below the
Planck scale. For example, with a m~H~115 GeV (the LEP limit), a value
of Λ 100 TeV is implied \[1.16\]. This argument is made since the vacuum
expectation value of the Higgs field depends upon Λ and hinges upon the
demand that the stability of the vacuum may only be maintained if the
coupling of the quartic self coupling term (the ^2^ term in the
potential) does not become negative while running from the weak scale up
to the scale Λ. If an additional condition is on the Higgs particle is
made, that the self coupling term is small, the theory can be shown to
restrict m~H~ \< 140 GeV -- precisely the range for which the CMS ECAL
is optimized. The restriction is 'justified' by the desire to find a
Higgs particle compatible with the previous two restrictions (low Λ,
vacuum stability) and consistent within the framework of perturbation
theory \[1.17\]. However, this last restriction also requires some fine
tuning of parameters within the Standard Model that critics (and there
are many \[1.18\]\[1.19\]\[1.20\]\[1.21\]) point out is unnatural and
has no analog elsewhere in the Standard Model theory. Moreover, several
recent articles have also suggested that these restrictions do not
necessarily confine m~H~ to \< 130 GeV \[1.22\]\[1.23\] and that a large
value of Λ ( Planck Scale) accommodates values of m~H~ which can only be
found within a narrow range of 130 and 200 GeV \[1.23\].

Regardless of the theoretical arguments favoring the light Higgs for
which the CMS ECAL is optimized, it is expected that the FNAL Tevatron
will push the lower mass boundary of m~H~ to 125 GeV \[1.24\] by 2006,
the year operation of the LHC is anticipated to commence. As Figure 1.8
indicates, S(H γγ) ≈ S(H ZZ 4 lepton) for a 125 GeV Higgs mass. This
suggests that if the SM Higgs particle exists and has a mass \> 125 GeV,
discovery is much more likely to occur outside the H γγ channel.

#### H W^+^W^-^ 2 lepton 2 neutrino Events in CMS 

A Standard Model Higgs particle with a mass \> 125 GeV has a branching
ratio favoring W+W- (Figure 1.7). The large WW branching ratio will make
the monitoring of W± decays crucial to Higgs discovery. As Figure 1.8
indicates, the H W^+^W^-^ channel in which both W bosons decay into a
lepton and neutrino offers the greatest discovery potential for a Higgs
mass of 155-180 GeV. Studies of channels utilizing decays of either W
into a non lepton-neutrino pair are restricted by large backgrounds.

#### H ZZ 4 lepton Events in CMS

####  {#section-1 .unnumbered}

The H ZZ channel in which both Z bosons decay into four leptons covers
the largest Higgs mass range for the most promising CMS discovery
channels. ZZ 4 lepton decay would also provide the cleanest and most
unambiguous signal for Higgs discovery.

Studies of H ZZ channels utilizing non-leptonic decays of either Z are
restricted by large backgrounds (See Section 1.2.4.1).

## Endcap Muon Position Monitoring System (EMPMS) 

The manner in which the mounting of the CSC chambers on the YE Iron
discs will be preformed should ensure local location accuracy for every
chamber of at least 2mm using dowel pin holes machined into the discs.
The dowel pin holes have been measured by photogrammetry during a trial
assembly of each disc and determined to an accuracy of approximately
200-1000m depending on the location of the hole. Although the chamber
locations can be defined in this manner in the field free case and prior
to installation, the location of the chambers will certainly change as
the individual discs are installed into the final detector assembly and,
more significantly, under the extremely high magnetic forces ( \> 10000
tones) generated by the solenoid.

The estimated positioning accuracy with which the individual YE Iron
disc assemblies can be placed into the closed detector is estimated to
be ±3mm prior to the activation of the solenoid. The deformation of the
RF iron by magnetic forces once the solenoid is activated is expected to
induce variations in the position and orientation of the CSCs by ≥ 5mm.
Due to the non symmetric distribution of the iron support structures
which hold the discs in place, these distortions will almost certainly
be non-uniform. CSC chambers in the Endcap are located on three or four
point kinematics mounts that will move with local YE iron distortions
and end up in different positions and/or orientations. The determination
of CSC positions across the CMS RΦ coordinate is the most critical
parameter to establish and track, as they will directly impact the
determination of muon p~t~.

The shifting of CSC chamber locations after installation and activation
of the magnetic field is not unique to the Endcap Muon System. The
Barrel Muon System will also require a mechanical alignment system.
Additionally, both the Barrel and Endcap Alignment Systems must be
referenced to the Central Tracker and Global CMS Coordinate System by a
third mechanical alignment scheme, the Link Alignment System. The Link
alignment system establishes a set of twelve laser lines that are
accessible to both the Tracker and Muon alignment systems. These laser
lines ("Primary Link lines") follow the phi segmentation of the Muon
system and define twelve half planes in the CMS phi coordinate (six in
each endcap, every 60 degrees). Two primary points on each MAB are used
to reference a corresponding phi half plane. Due to the separation of
the ME 1/2 and ME1/3 CSC rings along the CMS Z coordinate, the ME1/2 CSC
chambers will require an additional Link laser line (a "Secondary Link
line", running parallel to the Primary line) provided by the addition of
a small rhomboid prism in the Primary Link laser line.

### The Need for an Endcap Muon Position Monitoring System

Since the final installation of the discs will place the CSC chambers on
the interior of the detector, it will be impossible to make any accurate
photogrametric survey of the chamber locations after final installation.
However, the initial operation of the CMS detector will still require
high definition of CSC chamber positions relative to the Central Tracker
enable trigger on and define the tracks of incident particles. For this
reason, it will be necessary to redefine and track the location and
orientation of the CSCs with a mechanical position monitoring
("alignment") system that is able to determine the location of CSCs with
the solenoid magnetic field at its maximum.

#### Level 1 Trigger Requirements in the CMS Endcap 

The number of muons from H ZZ 4 lepton events which can be expected to
fall within the Muon Endcap System is largely dependent upon the mass of
the Higgs particle. In general, higher pt muons can be expected to enter
the Barrel region over the Endcap region. Thus it can be expected that
muons from H ZZ 4 lepton events which arise from a high mass Higgs
particle are likely to go toward the Endcap. A topology of H ZZ 4 muons
events are shown in Figure 1.9. The histograms indicate that the number
of muons from these events that can potentially be measured by CMS
gradually increases as the Higgs mass approaches 500 GeV. This is do in
part to the fact that the additional p~t~ imparted to the final state
muons by virtue of arising (ultimately) from heavier Higgs particle
pushes the particles toward lower regions in \|η\|. The net effect is to
make the number of muons found in the Endcap System approximately equal
to the number of muons found in the Barrel System.

The histograms in Figure 1.9 where generated with CMSIM 120 (PYTHIA
v6.157b) Monte Carlo simulation of H ZZ 4 µ by gluon-gluon fusion and WW
(ZZ) Production at √s = 14TeV across all possible phi and eta ranges
with initial and final state radiation included. Muons with p~t~ falling
below the minimal CMS L1 Trigger Levels were rejected (20 GeV for single
muons, 4 GeV for two muons). The binning of events was determined by the
muon(s) \|η\| location as it encounter the first layer of muon chambers
(see Figure 1.3 for η division of the detector).

![](media/image10.jpeg){width="5.715277777777778in"
height="7.121527777777778in"}

Figure 1.9: Distribution of muons in the CMS Barrel and Endcap Muon
Systems from H ZZ 4µ events. Each histogram contains 1000 events
generated with a Monte Carlo simulation and denote the location in the
CMS Muon System where each muon is likely to be found: the Barrel
Region, Endcap Region, or outside the active area of the detector.

In addition to H ZZ 4 lepton events in CMS, Z and W physics events will
also of interest. Muon decays of these bosons (Z0 2µ, W± µ + ν~µ~) will
require Level 1 triggering. For Z0 decays, only 1 muon is needed to
trigger on the decay. A topology of Z0 and W± decay events likely to be
found in the CMS detector generated via Monte Carlo simulation is shown
below in Figure 1.10.

![](media/image11.jpeg){width="3.479861111111111in"
height="4.585416666666666in"}

Figure 1.10: Distribution of muons in the CMS Barrel and Endcap Muon
Systems for (A) W± µ + ν~µ~ and (B) Z0 2µ. Figures (A) and (B) each
contain 8200 events generated with a Monte Carlo simulation and denote
the location in the CMS Muon System where each muon is likely to be
found: the Barrel Region, Endcap Region, or outside the active area of
the detector.

The histograms in Figure 1.10 where generated with CMSIM 120 (PYTHIA
v6.157b) Monte Carlo simulation of W± µ + ν~µ~ and Z0 2µ direct
production at √s = 14TeV across all possible phi and eta ranges with
initial and final state radiation included. Muons with p~t~ falling
below the minimal CMS L1 Trigger Levels were rejected (20 GeV for single
muons, 4 GeV for two muons). The binning of events was determined by the
muon(s) eta location as it encounter the first layer of muon chambers
(see Figure 1.3 for η division of detector). As the histograms indicate,
far more Z0 and W± decays to muons will involve the Endcap region of the
CMS detector. For the W± µ + ν~µ~ decays, it is evident that finding
these events will require Level 1 triggering in the Endcap since there
is only one muon to trigger on and roughly twice as many muons are
likely to be found in the Endcap Muon System than in the Barrel Muon
System. To trigger on Z0 decays, only one muon in the decay will be
needed to initiate the trigger. The Figure 1.10B shows that the majority
of Z0 2µ events lay exclusively in the Endcap Muon System region and
will require a Level 1 Endcap trigger to trigger on those events.

Trigger simulation studies indicate that the CMS Endcap trigger will
"require phi precision \~ 1 mm (\~0.1 CSC strip)" and, as typical Local
Charge Track resolution (single chamber, average strip width) is
0.14\*CSC strip width (≈1.3mm), the "CSC Track-Finder absolutely must
include alignment corrections" \[1.25\]. If the positions of the CSC
chambers are not defined within 1.3mm in Phi, a significant bias in the
trigger will occur and impede the selection of H ZZ 4 lepton, Z^0^ 2µ,
and W± µ + ν~µ~ events.

#### Endcap Track Reconstruction Requirements

####  {#section-2 .unnumbered}

The standalone resolution of the CSC chambers is 150 µm \[1.26\],
whereas multiple scattering effects for a 100 GeV muon (for which the
muon system is optimized) are on the order of 200µm. Since multiple
scattering precludes the definitive positioning of the particle
immediately prior to its measurement, the relative positioning between
any two chambers does not need to exceed 283µm (=√2 \* 200µm). However,
the determination of particle trajectories and momenta can be further
constrained by attempting to match track segments in the CSC chambers to
the CMS Tracking system. For optimal performance when matching muon
tracks between the muon system and the rest of the CMS detector, the
position of all CSC chambers should be (individually) determined
relative to the Tracker coordinate system. In this case, multiple
scattering restricts the necessary positioning knowledge of CSC chambers
approximately 200µm (a detailed estimate is made in Chapter 4). However,
the resolution of the Inner Tracking System for the final determination
of muon p~t~ is expected to dominate that of the Muon System,
potentially minimizing the impact of CSC chamber misalignment for all
but the highest p~t~ muons. These effects are addressed in detail in
Chapter 5.

#### Design Requirements for the Endcap Alignment System

The design requirements of the Endcap Muon System indicate that the
Endcap Alignment System must:

I.  Establish the Initial Positions and Orientations of all Chambers and
    System Components

II. Track Chamber Positions (R,, and Z)

III. Provide Phi Reference Planes in each Endcap Disc

IV. Transfer Tracker System Coordinate Information from Barrel Muon and
    LINK Alignment Systems

The accuracy with which chamber locations must be established and
tracked is driven by the physics goals of the CMS experiment and
operational requirements of the CMS trigger. The knowledge of chamber
locations required for successful trigger operation is \~1-2mm relative
to the tracker, however the accuracy required to make the requisite
momentum measurements on 100 GeV muons (for which the Muon System is
optimized) imposes much more stringent requirements in the CMS R plane.
As discussed previously (Section IIA), the multiple scattering of muons
through the large amount of tracker material and iron present in the CMS
detector imposes a limit of approximately 200 m on the determination of
any given muon track with the Standalone Muon System. Since the
projected accuracy of the CSC chambers in all layers except ME 1/1 is
150-200 m, the most stringent requirement which might be imposed on the
determination of chamber locations of CSCs in CMS R is approximately 200
m. These requirements are examined in detail in Chapter 5.

### Design of the Endcap Alignment System

What follows is a semi-technical description of the EMU Alignment
Scheme. A more detailed discussion of system components and tolerances
can be found in Appendix A and Chapter 3.

The approach taken to meet the design criteria has been to develop two
dimensional transparent sensors for monitoring chambers along a laser
line and to employ simple proximity sensors and calibrated rods for
monitoring the spacing between discs and chambers.

The Digital CCD Optical Position Sensor (DCOPS) is composed of 4 single
array CCDs arranged in a window frame and a control circuit fitted with
an on board ADC and DSP chip. When the beam of a cross hair laser falls
incident on the DCOPS, each CCD is then used to reconstruct the
distribution of charge on its pixel array which corresponds to the
distribution of photons in the corresponding leg of the laser. In this
manner, the centroid of each leg of the crosshair laser can be
determined relative to some point on the CCD window frame. If a
crosshair laser falls incident on a string of DCOPS sensors, knowing the
absolute spatial location of any two sensors (called reference sensors)
in the line will allow for the determination of the incident laser line.
Once the laser has been defined, the transverse locations of any
remaining sensors placed in the laser line can be determined. Figure
1.11 shows how two known sensors can be used to determine the location
of an unknown third. Since each DCOPS sensor utilizes four CCDs in a
single measurement, there is a built in degree of redundancy as well as
an intrinsic ability to resolve the angular orientations of unknown
sensors.

![](media/image12.jpeg){width="4.950694444444444in"
height="1.4916666666666667in"}

Figure 1.11: The Digital CCD Optical Position Sensor (DCOPS) concept.
The position and orientation of the two Reference DCOPS are known and
allow for the definition of the unknown laser line. Once the direction
and orientation of the laser line is known, the position and orientation
of the unknown DCOPS on the CSC can be determined in the directions
perpendicular to the laser line.

A significant improvement to the DCOPS design was accomplished by
attaching prisms to the face of the CCDs and then tilting the CCDs
toward the center of the window. With this design, an additional degree
of redundancy is incorporated into the system since the DCOPS sensors
will now accommodate two independent measurements made from opposing
crosshair lasers. A production model of this 'bi-directional' DCOPS
sensor is shown in Figure 1.12.

![](media/image13.jpeg){width="2.810416666666667in"
height="3.1020833333333333in"}

Figure 1.12: The Bi-Directional DCOPS Sensor. The face of the CCDs point
toward the inside of the box and have red prisms attached. The crosshair
laser line enters the box from the ±Z axis.

#### Straight Line Monitoring and CSC Tracking in ME ±234

To track the location and orientation of CSC chambers in a given layer,
DCOPS sensors will be attached to each end of the CSC chambers to form
Straight Line Monitoring (SLM) lines which transverse the diameter of
each Endcap disc. The location of DCOPS sensors placed on the CSC
chambers, and therefore the location of the CSC chambers, can be
determined by knowing the exact location of two additional reference
sensors, located off the CSC chambers at the endpoints of the SLM line.
Figure 1.13 shows how three SLM lines will be used to define the
location of CSC chambers on the ME ±2, ±3, and ±4 Endcap discs
(reference sensors are not drawn in).

![](media/image14.wmf)

Figure 1.13: View of CSC chamber arrangement and location of Straight
Line Monitor (SLM) laser lines used in tracking chamber positions. This
view of the Endcap corresponds to a 'head on' view of Figure 1.14. DCOPS
sensors are shown at each end of the CSC chambers (drawn on only one SLM
line).

The location of the DCOPS SLM reference sensors must be inferred from a
separate laser line running parallel to the beam pipe (Z-axis) of the
CMS detector -- the Axial Transfer Line, shown in Figure 1.14. The
Transfer Laser Line is defined by two DCOPS sensors mounted on separate
rigid mechanical structures called MABs (Module for the Alignment of the
Barrel Muon) which are located on the outer parameter of the inner
detector at the intersection of the Endcap Muon and Barrel Muon Systems.

![](media/image15.wmf){width="5.995138888888889in"
height="4.590972222222222in"}

Figure 1.14: Diagram of Endcap Alignment System showing Transfer laser
lines and Straight Line Monitor (SLM) laser lines used in tracking CSC
positions.

Since the location of the MAB units are referenced to the Tracker
coordinate system by the LINK system, the location of the DCOPS sensors
mounted on the MABs are known. By using these DCOPS sensors as
references on the Transfer Line, the location of other DCOPS sensors
located along the Transfer laser line can be determined. The location of
the reference DCOPS sensors in the SLM line are determined by a rigidly
connecting them to the DCOPS sensors located on the Transfer line with a
special Transfer Plate (Figure 1.14, Figure A.8). Once the positions of
the connecting Transfer line sensors are determined, the reference
sensors on the SLM line become known and the remaining sensors in the
SLM line can be determined. Since the DCOPS sensors only measure
directions perpendicular to the laser lines, a host of proximity sensors
and inclinometers are employed to determine the spacing between the
DCOPS sensors and their angular orientations.

#### Straight Line Monitoring and CSC Tracking in ME ±1

As Figure 1.3 indicates, the additional iron on YE ±1 means that the
arrangement of SLM lines used on ME ±2, ±3, and ±4 will not work in ME
±1 since there is a large separation between adjacent ME ±1 rings in Z.
More importantly, the additional iron located behind the ME ±1/1 rings
obstructs any line of sight measurements (as in ME ±2, ±3, and ±4)
across the ME ±1 Endcap.

By using two LINK sensors and the Secondary Link Line generated by the
LINK Alignment Group when evaluating the location and orientation of the
MAB units, it is possible to define the location of ME 1/2 chambers
(along the Secondary Link Line). An illustration of the ME±1 disc and
CSC chambers is shown in Figure 1.15. Once the location of the ME ±1/2
chambers are known, the addition of a DCOPS sensor on the outer end of
each ME ±1/2 chamber offers an inner reference point for a shortened
crosshair SLM Line to define the location of DCOPS sensors mounted on
the ME ±1/3. The outer endpoints of these shortened SLM lines are
defined by the inclusion of Transfer Plates on the outer edge of the ME
±1 iron in a manner identical to the ME ±2, ±3, and ±4 SLM lines.

The displacement between the ME ±1/3 and ±1/2 chambers along the CMS Z
axis is handled with an extension of the mounting bracket which secures
the ME ±1/3 DCOPS sensors to the CSC chambers. Figure 1.16 illustrates
the arrangement of the ME ±1/3 and ±1/2 chambers and the sensors along
the SLM and Secondary Link lines. The outer reference sensor for the ME
±1/3 SLM lines are supplied with a transfer plate in exactly the same
manner as in ME ±2, ±3, and ±4 SLM lines.

![](media/image16.jpeg){width="5.48125in" height="5.54375in"}

Figure 1.15: ME 1 Chamber Arrangement and Placement of SLM and Secondary
Link Laser Lines. Overlap of MAB Structures is shown, though they do not
touch ME1. ME 1/1 chambers are not shown. Note SLM lines do not cross
the disc, but terminate at the edge of the ME1/2 rings. \[1.27\]

![](media/image17.jpeg){width="4.81875in" height="3.6875in"}

Figure 1.16: Detail of ME 1 SLM and Secondary Link Laser Lines. The
drawing shows a ME1/3 DCOPS Sensor SLM line (three sensors along the red
laser line) and the ME1/2 CSCs Secondary Link Line (the green laser line
intersecting a blue Link sensor). The DCOPS attached to the out edge of
the ME1/2 Chamber serves as the final reference sensor in the ME 1/3 SLM
line.

The scope of the EMU alignment system does not include the ME ±1/1 ring
of CSC chambers (the innermost ring) and can rely on the alignment of
the ME1/2 ring with the aid of a secondary laser line generated near the
CMS Z axis from the LINK Alignment System. Since the Secondary Link
Laser Line is cylindrical, the measurements of the ME ±1/2 chambers have
a degree of freedom about the laser line which is not present in the
other SLM lines. The initial design of the EMU Alignment scheme
anticipated that a complementing set of measurements between the LINK
sensors and the DCOPS sensor installed on the on outer the edge of these
chambers would provide a sufficient constraint on rotations about the
Secondary Link Line since the two laser lines are offset. It has been
determined by a simulation of the system (see Chapter 3) that the
inclusion of an inclinometer, similar to those on the transfer plates,
will be required.

#### Locations of Off-SLM CSC Chambers 

The EMU alignment scheme allows only for the direct determination of
chambers along the SLM laser lines. CSC chambers located off of these
SLM lines will have to be determined by some other means -- likely by an
extrapolation of the YE iron shape (as determined by the SLM lines) and
a model (or measurements) of the magnetic field in the Endcap. It may
also be possible to determine the location of off-SLM chambers by
particle track reconstruction across the overlapping regions of
chambers. In this case, chambers lying along the SLM lines (i.e.
chambers with known positions and orientations) serve as reference
chambers from which the location of neighboring chambers are found
first. Remaining chambers could then be successively determined by using
neighboring chamber locations (once found) as reference points for
overlapping tracks. Neither of these methods (nor any other method) has
been thoroughly investigated.