Citation
Measurement of the Charge Ratio of Atmospheric Muons at the Compact Muon Solenoid in Events with Momenta Between 5 GeV/c and 1 TeV/c

Material Information

Title:
Measurement of the Charge Ratio of Atmospheric Muons at the Compact Muon Solenoid in Events with Momenta Between 5 GeV/c and 1 TeV/c
Creator:
Schmitt, Michael
Place of Publication:
[Gainesville, Fla.]
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (145 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Physics
Committee Chair:
Avery, Paul R.
Committee Members:
Matchev, Konstantin T.
Lee, Yoonseok
Furic, Ivan Kresimir
Gregory, Frederick G.
Graduation Date:
8/7/2010

Subjects

Subjects / Keywords:
Barrels ( jstor )
Calorimeters ( jstor )
Cosmic rays ( jstor )
Curvature ( jstor )
Magnetic fields ( jstor )
Momentum ( jstor )
Muons ( jstor )
Physics ( jstor )
Pixels ( jstor )
Silicon ( jstor )
Physics -- Dissertations, Academic -- UF
charge, cms, cosmic, muons, ratio
City of Orlando ( local )
Genre:
Electronic Thesis or Dissertation
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
Physics thesis, Ph.D.

Notes

Abstract:
The ratio of positive to negative charges in the secondary cosmic muon flux is measured at the Compact Muon Solenoid experiment. Muons with momenta between 5 GeV/c and 1 TeV/c are observed in data collected at ground level or 89 m underground; and found to be a constant 1.2766 +/- 0.0032 (stat.) +/- 0.0032 (syst.) for momenta below 100 GeV/c, and rising with higher momenta. The fraction of charged pions and kaons in the secondary cosmic flux resulting in positive muon production has been estimated, with the fraction for pions = 0.553 +/- 0.005 and for kaons = 0.66 +/- 0.06, respectively. The results presented herein are in good agreement with cosmic ray shower models, consistent with previous measurements, and represent the most precise measurement to date for atmospheric muons up to 500 GeV/c. This is also the first physics measurement involving muons at the completed CMS detector. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2010.
Local:
Adviser: Avery, Paul R.
Statement of Responsibility:
by Michael Schmitt.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Embargo Date:
10/8/2010
Resource Identifier:
004979574 ( ALEPH )
709593993 ( OCLC )
Classification:
LD1780 2010 ( lcc )

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by the crystal. As the crystal absorbs energy, it emits light which is then collected by

photodetectors on the back of the crystal. The total amount of light measured in the

photodetectors is then proportional to the energy of the incident particles.









Figure 3-19. Left: photo of a single ECAL crystal with sensors (next to a house key for
scale). Right: photo of ECAL crystals with sensors installed
(Copyright CERN).


Lead tungstate crystals have a short radiation length, Xo = 0.89 cm, so that

even highly energetic showers will be stopped within their length; and a Moliere radius

(indicating the characteristic spread of an electromagnetic shower in the material) of just

2.2 cm, which is helpful to localize the likely entry point of the particles.

The material is a fast scintillator; emitting approximately 85% of its light yield within

the first 20 ns of a particle traversing it. Although the total light yield of the crystals

will decrease as it is exposed to radiation from LHC collisions; the photodetectors

are sensitive enough to allow recalibration, and resolutions are not expected to suffer

because of it.

ECAL Barrel. Within EB, there are 61,200 individual ECAL crystals arranged by 5

x 5 arrays into 144 modules. Four modules make up a unit called a supermodule; there

are a total of 36 supermodules in ECAL each one providing 200 of coverage over one

half of the barrel. A schematic of the EB sub-detector is given in Figure 3-20.

Photographs of a single EB module, a supermodule, and an entire half-barrel

assembly are shown in Figures 3-21 and 3-22.

ECAL End-cap. Instead of modules and supermodules, the two ECAL end-caps

are constructed from four "dee" (half-moon) structures; two per side. Each dee contains









TABLE OF CONTENTS
page

ACKNOWLEDGMENTS ................... ............... 4

LIST O FTABLES ..................... ................. 8

LIST OF FIGURES .................... ................. 9

ABSTRACT .................... ................... .. 13

CHAPTER

1 CO SM IC RAYS . . 14

1.1 History ..................... ................. 14
1.2 Theory ..................... ................. 15
1.3 Scope .................... .................. 21

2 THE LARGE HADRON COLLIDER ......................... 23

2.1 Member Experiments ................... ......... 23
2.2 Accelerator chain ................ ............. 24
2.3 Current Operational Status ... 25

3 THE COMPACT MUON SOLENOID ...................... 27

3.1 Introduction ................... ............. 27
3.1.1 Coordinates and Geography ... 29
3.1.2 Cavern Geometry ..... ... 29
3.2 Solenoid M agnet . .. 31
3.3 Inner Tracking System ............................. 32
3.3.1 Pixel Detector . .. 34
3.3.2 Silicon Strip Detector .......................... 36
3.4 C alorim etry . .. 39
3.4.1 Electromagnetic Calorimeter .. ... 40
3.4.2 Hadronic Calorimeter .......................... 46
3.5 Muon Spectrometers ................... ........... 49
3.5.1 Drift Tube Cham bers .......................... 51
3.5.2 Resistive Plate Chambers ..... ... ... 52
3.5.3 Cathode Strip Chambers ........................ 53

4 CHARGE RATIO ANALYSES ............................ 55

4.1 The MTCC Analysis ................. ......... .. 55
4.2 The CRAFT Analyses ................. .......... 56
4.2.1 Analysis with Stand-Alone Muons . ... 57
4.2.2 Analysis with Global Muons .. .. 57
4.3 Sum m ary .. ... .. .. .. .. .. .. .. 58




















































Figure 3-3.


Barrel profile of CMS in the xy-plane, showing the 0 coordinate. The

changing curvature of the p track indicates the radius-dependent magnetic

field (which reverses direction in the return field outside of the solenoid).


T2E0m





-4 rm



--2.Om


l= :.4


1 51 m "


-0031m
00"M


Figure 3-4. Quarter profile of CMS in the y-z plane, showing the rI coordinate.

simple function of the polar angle: T = In(tan 0/2).


T is a


+
e
3"105 3
I \









B.3 Effective Elevation


The effective elevation, in terms of atmospheric depth, is quite fluid with time. It may

be computed by solving Equation B-1 for h, using the standard atmospheric pressure

(101.325 kPa for the ISA) as its reference pressure. The resulting elevation as a function

of time is presented in Figure B-3.

B.4 Atmospheric Density

The local air density, near ground level, may be measured [108] from:


(Pd Md + Pv M) (
P= RT (B-2)
R-T
... where Pd and Pv are the partial pressures of dry air and water vapor, T is the

temperature in Kelvin, R is the universal gas constant, and Md and My are the molecular

weights of dry air and water vapor, respectively. The partial pressure of water vapor was

computed using the Lowe [109] approximation (which depends only on the measured

dewpoint temperature).2

B.5 NRLMSISE-00 Atmospheric Simulation

NRLMSISE-00 is typically used for atmospheric simulations in rocketry and satellite

applications, but suits the requirements of this study well. The model was used to

simulate the atmospheric densities above CMS as a function of both time and altitude,

using the main drivers of the upper atmosphere solar ultra-violet radiation [110] and

geomagnetic heating [111] as inputs. Low altitude meteoroligical effects are accounted

for indirectly by simulating from the effective, atmospheric altitude (computed previously)

rather than the true elevation.

The air density at ground level, computed from the weather station data using

Equation B-2, and simulated directly in NRLMSISE-00, is illustrated in Figure B-2.



2 The polynomial approximation introduces a negligible error thousandths of a per-
cent presumed much smaller than the measurement accuracy.


130











> Fluxes of Cosmic Roys


"A __ (1 particle per mn'-second)









10 -








Ankle
'?



(1 particle per m myar -yeor)















1 10 10l 10 10i 105 106 l0 e 10' 10' 10 1011 102
E (GeV)

Figure 1 -1. The total flux of the incident primary cosmic ray spectrum [21].


decays of the secondary mesons; of which, pions and kaons are the most important

contributors. According to this parameterization, the flux may be written:




dpd1 10 102 .1 0 1 10 107 10p 10 10 10 1012
115 GeVc 850 GeV/c(eV




cosmic muon spectrum, expressed as the charge ratio of positive to negative muons, as

a function of momentum. Because the primary cosmic rays are nearly entirely positively

charged, the charge ratio of the incident primaries is very high, and positive meson

production is favored; however, as additional pions and kaons are produced, the initial
charge imbalance is spread out over larger and larger multiplicities, resulting in a more
charge imbalance is spread out over larger and larger multiplicities, resulting in a more









Only muons in the barrel region of CMS are considered; therefore, any tracks

containing hits in the Tracker Endcaps or Cathode Strip Chambers are removed. Muons

must have a transverse momentum of at least 10 GeV, and be traveling downward along

the detector-y (approximately pointing down, into the earth); such that the 0 of their

momentum vector is negative at the PCA.1

Splitting. In Section 5.4, the methodology for obtaining a data-driven estimate

for detector resolution is described. As part of this methodology, the track must be fully

splittable within the silicon tracker; in other words, there must be at least one hit in the

silicon both above and below the PCA, in order to construct separate upper and lower

tracks with unshared tracker hits.2 The split requirement is most efficient for tracks

passing close to the geometric center of CMS (and thereby passing through a maximum

amount of tracker material), with efficiency rapidly dropping for distances larger than

about 50 cm, as may be inferred from Figure 5-2. The components of the PCA are the

cosmic muon analogs of the impact parameters traditionally used in collider physics.

Thus, in Figure 5-2 the traditional notation for impact parameters is used; do refers to the

shortest distance between the trajectory of the particle and the z-axis/beam-line, and zo

refers to the displacement of that point from the center of the detector along the z-axis.

5.2.3 Quality Selection

Each of the selection quality requirements are applied individually to the top and

bottom legs of the reconstructed tracks. A minimum of 20 hits in the DT chambers were

required. At least three of the DT hits must be in Superlayer-2, which measures the



1 Although cosmic muon reconstruction is seeded assuming downward momentum,
occasionally non-downward trajectories result, most typically because the muon has
low momentum and is actually turned around by the magnetic field of CMS, or has been
"back-scattered" off of material below. More exotic explanations are also possible, but
exceedingly unlikely [64].
2 Standard split tracks in CMS cosmic muon reconstruction do not require the legs to
have unshared silicon hits, thus this is a more strict selection requirement.









A0 from 0.087 to 0.175 radians, and the sub-detector provides coverage from |r\ = 1.3

to Il = 3.















Figure 3-28. Photograph of the HCAL End-Cap (Copyright CERN).


Outer Hadronic Calorimeter. The outer hadronic calorimeter (HO) is a sampling

calorimeter placed outside of the solenoid which acts as a "tail-catcher" for extremely

high energy jets; that is, for particles which could not be completely absorbed within the

bulk of the inner system. Rather than a half-barrel design like the inner calorimeters,

HO is mounted to the rings of the iron return yoke; it is therefore separated into five

sections (one for each of the five wheels of CMS). It consists of a single scintillator

layer at r = 4.07 m mounted on top of a 19.5 cm iron absorber for the full rI range, and

an additional scintillator layer mounted on the underside of the iron in the very central

region. Because it is meant as a complementary detector to HB, its granularity and Tr

and 0 parameters are matched to those of HB.

Forward Calorimeter. HF provides coverage up to an rT = 5.0, with a granularity

of AT/ x A0 = 0.175 x 0.175. Because of the extreme radiation levels near the beam

line and in the forward region, traditional shower sampling calorimeters are not suitable;

a Cherenkov light counting calorimeter is used instead. In this sub-detector, iron is

used as an absorber material; when charged particles interact with the iron, they will

begin showering (either electromagnetically or hadronically). The resulting shower will









[72] A. H6cker and V. Kartvelishvili, "SVD Approach to Data Unfolding," Nuclear

Instruments and Methods in Physics Research Section A, vol. 372, issue 3, no. 1,

pp. 469-481, Apr. 1996.

[73] G.D'Agostini, "A multidimensional unfolding method based on Bayes theorem,"

Nuclear Instruments and Methods in Physics Research Section A, vol. 362, issue

2-3, pp. 487-498, Aug. 1995.

[74] CMS Collaboration, "Performance of CMS muon reconstruction in cosmic-ray

events", JINST, vol. 5, pp. T03022, 2010.

[75] G. Flucke et al., "CMS silicon tracker alignment strategy with the Millepede II

algorithm", JINST, vol. 3, pp. P09002, 2008.

[76] CMS Collaboration, "Precise mapping of the magnetic field in the CMS barrel yoke

using cosmic rays", JINSTvol. 5, pp. T03021, 2010.

[77] S. Ivy-Ochs, H. Kerschner, A. Reuther, F Preusser, K. Heine, M. Maisch, P. Kubik,

and C. Schluchter, "Chronology of the last glacial cycle in the European Alps,"

Journal of Quaternary Science, vol. 23, issue 6-7, pp. 559-573, Aug. 2008.

[78] Geotechnique Appliquee Deriaz S.A., "Projet LHC Reconnaissances de la

molasse Rapport de synthese," Jul. 1997.

[79] H. Rammer, "Two New Caverns for LHC Experiments: ATLAS and CMS,"

presented at the CERN-ST Workshop, Chamonix, France, 1998.

[80] CMS Collaboration, "Alignment of the CMS muon system with cosmic-ray and

beam-halo muons", JINST, vol. 5, pp. T03020, 2010.

[81] CMS Collaboration, "Alignment of the CMS silicon tracker during commissioning

with cosmic rays", JINST, vol. 5, pp. T03009, 2010.

[82] CMS Collaboration, "Simulation of Cosmic Muons and Comparison with Data from

the Cosmic Challenge using Drift Tube Chambers," CMS-NOTE, 2007.

[83] CMS Collaboration, "Tracking and Vertexing Results from First Collisions", CMS-

PAS, 2010.


140
































c 800 --- ------ --------- --...... Gravitational
.0
S-- Effective Atmospheric
D 700 -


600


500


400



10/16 10/19 10/23 10/26 10/29 11/01 11/05 11/08 11/11


Figure B-3. The effective elevation of ground level above CMS during the time of the
experiment, using data published by the Geneva Airport.


133













CMS 2008 preliminary
1.8
Sraw, stat
unfolded, stat
1.6
unfolded, stat + sys


S1.4

^ ~ ~ 9 i s -


CMS 2008 preliminary
1.8 i 1


1.6


, 1.4


1.2


1


103
p. cosOz (GeV/c)


Figure 7-3.


(Blue open squares) Measured charge ratio. (Black solid circles) Unfolded
charge ratio, statistical error only. (Red lines) Statistical and systematic
errors. Left: In p bins. Right: in pcosOz bins.


Table 7-1. Unfolded charge ratio as a function of p and pcos z with all corrections
applied, along with the statistical and systematic uncertainties.
p range (GeV/c) average (GeV/c) R ustat rsyst
30- 50 39 1.268 0.031 0.015 0.027
50 70 62 1.302 0.018 0.016 0.008
70 100 84 1.274 0.015 0.011 0.009
100 200 135 1.280 0.011 0.011 0.004
200 400 263 1.295 0.026 0.021 0.016
400 00 640 1.349 0.067 0.048 0.047
p cos Oz range (GeV/c) average (GeV/c) R astat asyst
30- 50 39 1.265 0.029 0.014 0.025
50-70 62 1.280 0.017 0.011 0.013
70-100 82 1.281 0.015 0.011 0.009
100-200 131 1.291 0.016 0.013 0.008
200-400 259 1.336 0.042 0.034 0.025
400 00 613 1.440 0.114 0.092 0.067


109


103
p (GeV/c)


t


^^-









collisions): surpassing the Tevatron at Fermi National Laboratory (with proton and anti-

proton beams of 0.98 TeV for a total of 1.96 TeV center-of-mass) to become the world's

highest energy particle accelerator, and the most powerful particle collider ever built.

On March 30th, 2010; the LHC successfully collided protons at 7 TeV center-of-mass,

where it is expected to hold steady for 18 to 24 months. Eventually, the LHC will be

able to produce proton-proton collisions at up to 14 TeV; and is expected to deliver an

instantaneous luminosity of 1034 cm-2-1 at that energy.









are not picked at a local (charge-bias inducing) maxima, the relative effect on the charge

ratio is plotted against the choice of requirement in Figure 6-13.

6.2.3 Mis-Alignment

The precise alignment [74] of all the tracking-detector components is crucial for

accurate reconstruction of high-pT muons, which experience only slight curvatures

within the detector. In particular, because this analysis involves hit information from

both the muon spectrometers and the silicon tracker, the reconstructed charge and

moment of the cosmic tracks are highly sensitive to the relative alignment between

the tracker and muon systems. In order to estimate the effect of such alignments, a

comparison is performed using two alignment scenarios with the Monte Carlo: one in

which the detector has been arranged in an "ideal" alignment, and one in which it has

been randomly misaligned by realistic amounts equal to the uncertainties of the realistic

"startup" alignment of the detector (as they are currently understood).

A study was conducted in both scenarios; with the charge ratio measured sepa-

rately in both sets of detector conditions. The difference in the resulting measurement

is assessed as the charge bias due to misalignment, as in Equation 6-12. The result of

this study is given in Figure 6-7.


SRideal Rstartup (6-12)
align = (6-1 2)
Rideal
A global deformation of the detector could be missed during the alignment proce-

dures (a so-called "x2-invariant" or "weak" mode [75]), and potentially affect the charge

ratio. The most problematic deformation would be a mode which caused a constant

offset in q/pPCA, different from zero, affecting the momentum scale for cosmic muons of

opposite charge in opposite directions. A two-parameter fit of the simulated q/pPCA dis-

tribution to the data is performed using muons in the range pCA > 200GeV/c, leaving

the unknown charge ratio and the q/pPCA offset in the simulation to vary freely in the fit.

An offset of 0.043 0.022 c/TeV is found. The measured muon moment are corrected









for this offset and its uncertainty is included as an additional systematic uncertainty

on R, fully correlated between the two underground measurements. The effect on the

ratio is approximately 1% and 4%, respectively, in the two highest momentum bins; and

neglible below.

6.2.4 Magnetic field

The magnetic field at CMS [76], though generally a uniform 4 T within the tracker

volume, is quite complex throughout the solenoid and out into the return yolk and Muon

Spectrometers. The TOSCA field mapper is used in CMS to estimate the magnetic field.

In order to estimate the effect of uncertainty in the field maps, two separate conditions

were studied; one using an older map of the magnetic field, and one which uses the

map as it is currently understood. It is assumed that the relative difference between the

two maps is roughly equal to the difference between the current field mapping and the

true magnetic field conditions.

The charge ratio was measured for a sample of events in data with both field

conditions, and the relative difference in the result was compared. The expression

for the bias in the resulting charge ratio is written in Equation 6-13, and the resulting

uncertainty is indicated in Figure 6-8.


Current Rold
field = urent- (6-13)
Current

6.2.5 Muon Rates

Some muons, particularly for the lowest considered moment, are absorbed in the

earth before they can reach CMS. A priori, this is expected to be a charge blind process;

however there are several factors which can induce a charge bias in this process. For

instance, positive muons lose slightly more energy (about 0.15%) than do negative

muons as they travel through matter [26]; causing a slight charge bias, as indicated in

Figure 6-9.









z-component of the local trajectory; which is necessary in order to obtain a satisfactory

measurement of the track 0. While two TOB hits are implied by the split track require-

ment, additional hits are effective at reducing charge confusion. Sufficient suppression

of charge confusion is observed with five or more hits in the TOB (with diminishing

returns coupled with a rapid loss of efficiency if more than five hits are required). An

extremely loose requirement on the X2 (1500) is applied to track fits, in order to reject

poorly reconstructed tracks. This requirement was found to efficiently remove events

in which the global muon fit would incorrectly flip the charge of the muon.3 Figure 5-7

shows the efficiency of the X2 requirement as a function of pr; it is nearly 99% for all

moment considered in this analysis.

With split tracks, it is necessary to verify that the two track halves are indeed

consistent with the same muon. This necessitates, first of all, that multi-muon events

(with their unavoidable ambiguities) are suppressed, by requiring exactly two split tracks

in the event; one in the top and one in the bottom of the detector. Even after the removal

of obvious multi-muons, it is occasionally the case that two unrelated tracks may be

incorrectly be associated with one another; so additional matching is required. A logical

variable is the difference in the 0 of their trajectories at the PCA; however this is highly

sensitive to the estimates of the particle charge, and would hence bias the estimation

of detector resolution. In fact, the only way to avoid biasing this measurement is to

restrict the matching to trajectory along the z-axis; because the magnetic field in the

barrel region is highly uniform and parallel to z, and thus the detector does not use

this information to estimate the momentum or charge of the incident muon track. In

particular, a selection requirement on the cotangent of the track 0 (angle of trajectory in

the rz-plane) is used.



3 This was originally necessary due to a bug in the reconstruction algorithm, since
corrected.









By the end of the decade, it was known that cosmic-rays were made up of particles

rather than photons; however the "ray" nomenclature stuck [9, 10]. In 1948, examination

of particle tracks from cosmic ray events captured in nuclear emulsion photographs

taken in balloons at high altitude revealed that primary cosmic rays (those incident

upon the atmosphere from space), were composed of protons, alpha particles, and a

small fraction of heavier atomic nuclei (such as iron). By then, it had been established

that the secondary cosmic rays (produced by collisions between the primary cosmic

particles and gases within the earths atmosphere) consisted of pions (which were only

just discovered [11]), muons, electrons, and photons [12].

Although it was widely conjectured as early as the 1960's that cosmic rays were

produced in supernova [13, 14], it was difficult to account for the very highest energies

observed in the cosmic ray spectrum; and the origin of such cosmic ray events remained

a mystery for many years. Roughly four decades later, in 2007, a Japanese team led by

Yasunobu Uchiyama studying a supernova using NASA's Chandra laboratory confirmed

that a process of amplification of the magnetic field in young supernova remnants can

occur, leading to significant cosmic ray energies [15]. Meanwhile, the Pierre Auger

Collaboration released findings which showed that the very highest moment cosmic

rays arrive on earth from directions highly correlated with nearby active galactic nuclei

- where super-massive black holes, with correspondingly enormous magnetic fields,

are believed to exist and are able to accelerate particles to ultra high (PeV-scale)

energies [16, 17], though this link is still tentative [18].

1.2 Theory

Cosmic ray particles may be produced in many potential astrophysical processes.

Solar flares, supernovae, and black holes emit and accelerate these particles out into

the cosmos; where they are likely to continue accelerating under the action of the

turbulent magnetic fields of the interstellar medium [19]. The spectrum is composed of



















- mean value
- half difference


o tt
011

0 1

0.- 4tt 1 "

o0 1 +
ll ; ** ,l I I I l l l,,,
-5 -4 -3 -2 -1 0 1 2 3 4 5
test variable for Exponential tails


a
5

-5 103


102



10



1


- mean value
- half difference


+ +



+t tttt
iff if f qf f

i tl t fl ..


-5 -4 -3 -2 -1 0 1 2 3 4 5
test variable for Exponential tails


- mean value
- half difference


300 f 1

200- 1

100 + i t+ +

-5 -4 -3 -2 -1 0 1 2 3 4 5
test variable for Gausian tails


a


i 103



102


0 ..



1


mean value
half difference



+ +
.* + + I
+ t t+
t i + ti

Ht


-5 -4 -3 -2 -1 0 1 2 3 4 5
test variable for Gausian tails


Figure A-5. Tests of the resolution function behavior when picking events in such a
fashion as to "sculpt" the half-difference distribution by selecting on events
which agree on curvature. Events were picked such that the curvature
between the top and bottom leg agree.


C :
" 600

- 500
(D 500


c 800

" 700
-5(
(D









curvatures measured within the detector, CPCA, to measures of curvature on the earth

surface, C:


CA > C,2 (5-8)
propagation
To complete the determination of the measured curvatures on the earth surface,

an additional resolution effect due to non-uniform energy loss in the earth must be

accounted for. Only mean energy losses are estimated in the extrapolation to the earth

surface; though in reality there is a wide spread of energies (referred to as "straggling")

that may be lost as the particles pass through the earth. In order to estimate the width

of this spread of energy losses, the Monte Carlo simulation was used, as it was already

available. Muons were propagated through the CMS volume in two ways: once using

the standard GEANT simulation, and once using an analytical extrapolator (similar to

the one used to transport muons from CMS up to the surface of the earth). While both

methods agreed on the mean energy loss, GEANT also produces a realistic spread of

energy losses. The relative energy spread within the CMS detector was computed as

the difference between the two computed energy losses, divided by the mean energy

loss from GEANT. Figure 5-13 illustrates the result: the relative smearing is found to vary

from 10% up to more than 20%. Since the actual molasse is fairly homogeneous and

uniformly dense that is, compared with the CMS detector; which has large pockets of

gas, particularly in the drift tubes this is likely an overestimation of the true effect of

straggling. Thus, a spread of 10% is assumed to apply to the mean energy loss through

the earth, which is applied as a correction to the detector resolution.

5.5.2 Construction of Migration Matrix

For each muon, the two measured values for the curvature, C1 and C2, are propa-

gated individually from the detector, as described in Section 5.5.1. Each of the measure-

ments produces an entry for the migration matrix two per muon with the correspond-

ing true curvature estimated from the half-sum of the two measurements. The resulting









APPENDIX B
ATMOSPHERIC DEPTH

B.1 Introduction

The CMS experiment is located at 460 18' 34" north latitude, 6 4' 37" east longi-

tude; where ground-level is roughly 505 m above sea-level. The atmospheric conditions

during CRAFT08 were measured using meteorological data reported by the Geneva

Cointrin International Airport [106], approximately 5 miles away, and simulated to high

altitudes using the NRLMSISE-00 (US Naval Research Laboratory, Mass Spectrometer

and Incoherent Scatter Radar, Extended) model [107].

B.2 Measured Atmospheric Pressure

Published weather data is calibrated according to the station elevation; such that the

reported pressures are actually extrapolations to sea-level, Psi; rather than the actual

Stationn. In order to convert the reported values to meaningful atmospheric densities,
the data must be recalibrated to the appropriate altitude in this case; from sea-level, to

the station elevation (430 m) and finally, to the elevation above Point-5 (505 m). These

conversions are performed by applying the ideal gas relation, Equation B-1.


P = Po e RT (B-1)

Here, h is the altitudinal difference between P and Po, M is the molecular weight

of the gas, g is acceleration due to gravity, T is temperature in Kelvin, and R is the

gas constant. The International Standard Atmosphere (ISA) was used for this study:

g = 9.807, M = 28.964 g/mol, and R = 8.3145 J/K mol.



1 This is so that isobar pressure contour maps are not unduly influenced by topogra-
phy; but complicates any application of the data in this context.


129


















CMS 2008 preliminary



002








-0 02


-0 02 0 002
true q / p (c/GeV)


CMS 2008 preliminary



002 E


002
true q / p (c/GeV)


CMS 2008 preliminary
03



02



0 1



0


-0 02 0 002
q / p (c/GeV)


Figure 5-14. Migration histogram which connects measured curvatures with the

estimations of true curvature on the surface of the earth in q/p bins. (Left)

Fine inning for illustration. (Center) Actual inning. (Right) Off-diagonal

spill-over by column.


CMS 2008 preliminary CMS 2008 preliminary


002
0

o




E -002


-002 0 002 -002 0 002
true q / p cosO (c/GeV) true q / p cosO (c/GeV)


CMS 2008 preliminary
03



02





01

0 - --..- .- - .


-0 02 0 002
q / p cosO (c/GeV)


Figure 5-15. Migration histogram which connects measured curvatures with the

estimations of true curvature on the surface of the earth in q/pcos z bins.

(Left) Fine inning for illustration. (Center) Actual inning. (Right)

Off-diagonal spill-over by column.










80









The high altitude uncertainties on the NRLMSISE-00 model have been solved

elsewhere using low orbital satellite data [112], and has been found to vary from 10-

15% up to around 200 km, rising to a maximum of 30% at altitudes near 600 km. By

comparison with measured values (after correcting for elevation) an error of at most 2%

is observed at ground level.

The resulting, altitude dependent, simulations of atmospheric density are indicated

in Figure B-1. Also indicated in the figure are the total (altitude dependent) variations

in the resulting densities (over the duration of the experiment), and the theoretical

uncertainty. Nearly all of the integrated atmospheric mass is in the first 30 km above

ground level, where the total error and time-dependent variations are quite small.

B.6 Summary

The effective elevation, considering the mass of air above CMS as a function of time

during the 2008 CRAFT exercise is given in Figure B-3. Given that the earth material

is at least 1500 times more dense than air, the 500 m elevation of the surface at CMS

is equivalent to no more than 30 cm of moraine. Including atmospheric effects, the

effective altitude during CRAFT varied from just below 300 m to more than 600 m; or

between 24 cm and 36 cm of moraine equivalent. Given that material uncertainty above

CMS is already 5 m of moraines, no additional uncertainty is expected from the small

variations in the atmosphere.









5.5 Unfolding


Various methods of unfolding the spectrum incident upon CMS in order to arrive at

measures at the surface of the earth were considered for this analysis [71], including
Singular Value Decomposition (SVD) [72], Bayes iteration [73], and several other

methods; though a simple matrix inversion was the method chosen for this analysis.
The momentum-binned counts of measured muons, Nmeasured, may be expressed

as the result of the action of a migration matrix, M, applied to the binned true number
of muons, Ntrue. The true but unknown migration matrix element, MjZ, gives the
probability that a muon with a true curvature Ctrue, which belongs in momentum bin j, will
be measured with a curvature (Ci or C2) located in bin i. An estimate of the migration
matrix, denoted M, is constructed (as detailed in Section 5.5.2) from the measured
curvatures. Given an approximation for the migration matrix, it is possible to obtain an
estimate for the true number of muons, Ntue, given the measured numbers by a process
of matrix inversion:



Nimeasured = MjN rue

M M (5-5)

Mirue = .- Njmeasured


The momentum bins are represented on the surface of the earth. These bins are

chosen empirically, with the main requirement being that the spill-over (transfer of muons
between bins due to off-diagonal elements in the matrix) is minimized:


p = (30, 50, 70,100,200,400, oc) GeV/c (5-6)

One obvious difference between M and M is the normalization, since the true
migration matrix involves the loss of muons as they travel through the earth (Ntrue >










uniform charge distribution. Thus, the exact nature of the charge imbalance in muons

is sensitive to the production and interaction cross-sections of pions and kaons in the

gaseous earth atmosphere, as well as their decay lengths.

Models of cosmic ray showers predict a rise in the charge ratio at higher muon

moment; in part because such muons are likely produced when there are fewer gen-

erations between the parent meson and the incident primary cosmic ray; and also

because kaon production, which produces relatively more positive muons than pions,

becomes much more important at higher energies. There is also some disagreement

amongst the models at moment above several TeV/c; mostly due to the uncertainty as-

sociated with interactions of highly energetic pions and kaons with atmospheric protons

and neutrons. Several of these models, along with recent experimental results [24], are

displayed in Figure 1-4.



S1.6
c A L3+C
0 Utah
(U) MINOS



S 1.5 3 o
S1.5 LVD
S OPERA
z g with s rK model
S_ ..... .K + RQPM model
1.4 .......... K + QGSM model ... *
__ K + VFGS model








1.1 -





102 103 104 105
eC cos 0 (GeV)

Figure 1-4. Results of the cosmic muon charge ratio from various recent experiments,
along with shower model predictions [24].









[104] CMS Collaboration, "Measurement of the charge asymmetry of atmospheric

muons with the CMS detector," CMS-PAS, 2010.

[105] CMS Collaboration, "Measurement of the charge ratio of atmospheric muons with

the CMS detector," arXiv:1005.5332v1 [hep-ex], submitted to Phys. Lett. B, 2010.

[106] Weather Underground, published to the web: "http://www.wunderground.com/

history/airport/LSGG," "History for Geneva, Switzerland (Meteorological Data),"

retrieved on Mar. 10th, 2010.

[107] J. M. Picone, A. E. Hedin, D. P. Drob, and A. C. Aikin, "NRLMSISE-00 empirical

model of the atmosphere: Statistical comparisons and scientific issues," J

Geophys. Res., vol. 107, pp. 1468, Dec. 2002.

[108] W. Brutsaert, "Evaporation Into the Atmosphere," D. Reidel Publishing Company,

pp. 37-38, 2007.

[109] P. R. Lowe, "An Approximating Polynomial for the Computation of Saturation Vapor

Pressure," Journal of Applied Meterology, vol. 16, no. 1, pp. 100-103, Jan. 1977.

[110] NOAA Space Weather Prediction Center, published to the web: "http://

www.swpc.noaa.gov/ftpdir/indices/old_indices/2008_DGD.txt," "Daily

Geomagnetic Data 2008," Jan. 2009.

[111] NOAA National Geophysical Data Center, published to the web: "ftp://ftp.

ngdc.noaa.gov/STP/SOLAR_DATA/SOLAR_RADIO/FLUX/2008.ADJ," "Adjusted Daily

Solar Flux 2008," Jan. 2009.

[112] F A. Marcos, B. R. Bowman and R. E. Sheehan, "Accuracy of earth's themo-

spheric neutral density models," Amer. Inst. of Aero. and Astro., pp. 6167, 2006.


143









Neglecting simulation jitter, dc,sim -which arises from a charge disagreement ow-

ing to a mismatch of simulated hits the true resolution, 6C, is found to be fairly well

modeled by the estimator, dc, for the aggregate total Monte Carlo sample presented in

Figure 5-10. Dividing these distributions up into bins of true transverse momentum, how-

ever, illustrates some discrepancies; as may be seen in Figure 5-12. The distributions

are fit with Gaussian resolution functions and the ratio of widths, ((dc) to a(6C), are

obtained. These ratios, depicted in Figure 5-11, are used as a correction,5 6dc, to the

resolution estimator:



^c) dc
6dc = (c dc (5-3)
(= (6 C) 6dc

The measured curvatures, Ci and C2, are then predicted to lie within the (now

corrected) resolution estimator, dc, of the true curvature. Therefore, the expressions

may be asserted as in Equation 5-4.



true (C + C2)

(5-4)

C1,2 = Ctrue dc

Note that the true curvature of the muon within CMS need not be estimated at all

for the final measurement of charge ratio, since it is reported on the earth surface. In

Section 5.5, the methodology for extrapolating the measured curvatures within CMS up

to the earth surface will be described; and it is from these propagated measurements

that the true curvature, on the surface of the earth, is estimated.



5 In fact, these corrections can even be predicted analytically (to some extent) based
on the strength of the correlations, as shown in the Appendix, Section A.2.














CMS 2008 preliminary


p (GeV/c)


Figure 6-4.


Charge bias ( a~)/R from selection on three or more z
(Drift Tube Superlayer-2).


p cosOz (GeV/c)


measuring hits


CMS 2008 preliminary


4


S2

S0



o -2
I-

-4


CMS 2008 preliminary


4


2



S-2
o-
I--


p (GeV/c)


Figure 6-5. Charge bias ( 7 a)/R from selection on five or more
hits.


p cosz (GeV/c)



outer tracker barrel


- raw

- unfolded


- raw

unfolded




S.. ... ..... ....... ......... .. ............. .. ......................


- raw
- unfolded




S----- *


I I I I I I I I I I I I I


CMS 2008 preliminary

















- mean value
- half difference


- mean value
- half difference


c,
" 103

-52


-4 -3 -2 -1 0 1 2 3 4 5
test variable for Gausian tails


- mean value
- half difference


), 103


-02


102


-4 -3 -2 -1 0 1 2 3 4 5
test variable for Exponential tails


Figure A-4.


-4 -3 -2 -1 0 1 2 3 4
test variable for Gausian tails


- mean value


-5 -4 -3 -2 -1 0 1 2 3 4 5
test variable for Exponential tails


Comparison of the half-sum and half-difference distributions for different
resolutions between top and bottom. In the top left panel, Gaussian
smearing where the resolution of one leg is three times worse than the
other. In the top right panel, the same distribution in logarithmic scale. In the
bottom left panel, exponential smearing where the lifetime for one leg is
three times larger than the other. In the right panel, the same distribution in
logarithmic scale.


123


S 350
-5c
(0 1-


-D 350

- 3
a) 300


















CMS 2008 preliminary
15000 '


i *




20 30 40 50
minimum NDT


CMS 2008 preliminary


=8=




5 10 15
minimum NTOB
* -


CMS 2008 preliminary
3 1 I .


20 30 40 50
minimum NDT


CMS 2008 preliminary
3 1


5 10


15
minimum NTOB


Figure 6-13. Left: distributions of p+ and p
better shape comparison) vs.
Right: ratio of the normalized


-, with the second normalized to the first (for a
different choices for selection requirements.
distributions.


. 10000

a,

5000




0


60000



40000

a,

a,20000



0









From the parameterization written in Equation 1-2, the charge ratio may be writ-

ten [26] as a function of the fractions f,+ and fK+ of the ensemble of all charged pion

and kaon decays that yield positive muons:



Nt, f.+ 0.054 fK+ 1 f+ 0.054 (1 fK+) (1-3)
N+ -1 1.1-pycos 1 + 1.1-p 'cos6e/ + 1.1-pi.cose 1.1-PG /cos
115 GeV/c 850 GeV/c 115 GeV/c 850 GeV/c

These fractions are not known a priori, and must be obtained by fitting the mea-

sured data. Obtaining these fractions is one of the chief motivations of measuring the

charge ratio in the sub-TeV regime in particular, because additional data is required

in order to determine if these factors will have their own (higher order) momentum

dependence. The charge ratio of pion contributions is predicted [27] to be around

1.27 (f,+ = 0.56); and higher for kaons, due to roughly an order of magnitude smaller

likelihood of interaction before decay1 and because of associated production.

The term "associated production" refers to a particular sort of interaction involving

the production of "strange" particles. Strange particles are produced only in pairs in

strong nuclear interactions, such that a property dubbed "strangeness" is conserved,

but decay only via the weak nuclear force. An example of an associated production

event is illustrated in Figure 1-5, in which a cosmic proton interacts with an atmospheric

proton or neutron, producing a neutral strange hadron (the A) and a positively charged

kaon. The lambda most likely decays back into a proton plus a negative pion; thus,

associated production events such as the one depicted will increase the charge ratio up

in kaons.



1 This is due to: a shorter lifetime (roughly half that of pions, about 12 ns compared
with 26 ns); a smaller probability of interacting with protons (about 25%); and a higher
mass (roughly three times that of pions), which causes kaons to experience less time
dilation than pions for a given amount of kinetic energy, and therefore, a shorter effective
lifetime.












p8m e [10, 20], = 15.7 GeV/c

Gausian Fit
x2/NDF = 13.5/11
Fit Prob: 26.10%
S= -0.03 0.01
S0=.10 0.01
S---... Landau Fit
X2/NDF = 29.3/11
Fit Prob: 0.20%
p1 = -0.07 + 0.01
S. P2 = 0.05 + 0.01

^_________


Co
C)





LU
3

2


1


LO


40
30



20


10
0













40o
Q.
4C35
30
LU~
2C










20
15



410






5
S4C


| 3C


2C
IE
1C


-1 0 1 2 3
(AEsim AEprop)/AEprop


LU
0


2
LU


p8m e [20, 30], = 24.6 GeV/c

Gausian Fit
0 x2/NDF = 19.0/14
Fit Prob: 16.54%
0 = -0.05 + 0.01
S0 = 0.13 0.01
0 ------- Landau Fit
X2/NDF = 34.4/14
!0 Fit Prob: 0.18%
p = -0.10 0.01
0 'P2 = 0.06 + 0.01

0
-1 0 1 2 3
(AEsim AEprop)/AEprop


p8m e [50, 100], = 67.9 GeV/c

5 Gausian Fit
0 x2/NDF= 36.8/22
Fit Prob: 2.50%
5 | = -0.11+0.01
= 0.14 + 0.01
20 ------- Landau Fit

5 x2/NDF= 61.1/22
Fit Prob: 0.00%
0 p = -0.18+ 0.02
P2 = 0.07 + 0.01

0 -----2-
-1 0 1 2 3
(AEsim AEprop)/AEprop


p8m e [100, oo], = 185.3 GeV/c

Gausian Fit
X2/NDF = 20.6/18
Fit Prob: 30.27%
=-0.16 + 0.02
0=0.26 + 0.02
......------- Landau Fit
x2/NDF= 26.7/18
\\ Fit Prob: 8.48%
Sp, = -0.29 + 0.03
P2 = 0.15+ 0.02

--._ +


-1 0 1 2 3
(AEsim AEprop)/AEprop



Figure 5-13. Normalized energy loss distributions for muons propagated through the
CMS detector, from GEANT Monte Carlo simulation. The distributions are
fitted with a Gausian (red dashed) and Landau (blue) and the
corresponding fit qualities and parameters are reported


-1 0 1 2 3
(AEsim AEprop)/AEprop

p8m e [30, 50], = 39.3 GeV/c


Gausian Fit
S2/NDF = 23.8/21
Fit Prob: 30.19%
S= -0.06 + 0.01
S= 0.17+ 0.01
S .... ----- Landau Fit
x2/NDF = 36.2/21
Fit Prob: 2.05%
p| = -0.14 + 0.01
S p = 0.06 +0.01

--- ------------


o 30

25

S20
LU
15

10

5

n


I


I












Table 6-1. Selection relative biases in


p bins
DT


a/R (%)
p range (GeV/c) R stat. 2 + o /o1e
30- 50 1.2682 1.15 2.56 -1.28 2.22 -0.58
50-70 1.3020 1.22 0.45 -0.42 0.17 -2.51
70-100 1.2745 0.87 0.18 -0.13 0.12 -1.04
100-200 1.2798 0.83 0.23 -0.20 0.12 -1.73
200 -400 1.2945 1.60 0.27 0.16 0.22 0.74
400 c0 1.3493 3.53 0.62 -0.40 0.47 -0.85
SL2
a/R (%)
p range (GeV/c) R stat. Vr2 + 7- 1 /7,
30-50 1.2682 1.15 1.12 -0.01 1.12 -0.01
50-70 1.3020 1.22 0.14 -0.11 0.09 -1.34
70- 100 1.2745 0.87 0.18 -0.17 0.07 -2.44
100-200 1.2798 0.83 0.16 -0.14 0.07 -1.95
200-400 1.2945 1.60 0.16 0.05 0.15 0.36
400 c0 1.3493 3.53 0.44 0.29 0.33 0.87
TOB
a/R (%)
p range (GeV/c) R stat. Vr2 + -7 /-
30-50 1.2682 1.15 1.75 0.89 1.51 0.59
50-70 1.3020 1.22 0.13 0.11 0.07 1.55
70 -100 1.2745 0.87 0.06 0.04 0.04 0.99
100-200 1.2798 0.83 0.12 -0.12 0.04 -2.88
200-400 1.2945 1.60 0.17 -0.15 0.08 -1.89
400 c 1.3493 3.53 0.59 -0.55 0.21 -2.61
X
_a/_R (%)
p range (GeV/c) R stat. J2 + 0-j /E-
30 -50 1.2682 1.15 0.88 0.30 0.83 0.36
50-70 1.3020 1.22 0.13 -0.11 0.07 -1.71
70 -100 1.2745 0.87 0.07 -0.05 0.06 -0.84
100-200 1.2798 0.83 0.11 0.08 0.07 1.03
200-400 1.2945 1.60 0.58 -0.55 0.19 -2.91
400 c 1.3493 3.53 0.91 -0.75 0.52 -1.45


















Table 5-3.


Response matrix which transforms event counts in bins of true p cos Oz (x-axis) to event counts in bins of
measured pcos z (y axis). Matrix elements that remain smaller than 10-20 are not represented here.


-30 0.9743 0.0138 < 10-4 0.0010
-50 0.0254 0.9101 0.0692 < 10-4 0.0002 0.0020 0.0028 0.0001 < 10-4 < 10-4 0.0001
-70 0.0001 0.0761 0.9036 0.0395 0.0010 < 10-4 < 10-4
-100 0.0272 0.9517 0.0409 0.0030 0.0014 0.0002 < 10-4 -
-200 0.0087 0.9466 0.0813 0.0021 0.0001 < 10-4 < 10-4 < 10-4
-400 < 10-4 0.0120 0.9018 0.0028 0.0001 < 10-4 -
400 0.0002 0.0030 0.8927 0.0154 < 10-4 < 10-4
200 < 10-4 0.0020 0.0922 0.9420 0.0086 -
100 < 10-4 0.0002 0.0010 0.0034 0.0415 0.9509 0.0266 < 10-4 < 10-4
70 < 10-4 < 10-4 0.0010 0.0002 0.0402 0.9063 0.0771 < 10-4
50 <10-4 <10-4 <10-4 <10-4 0.0030 0.0028 0.0001 <10-4 0.0670 0.9086 0.0263
30 0.0001 <10-4 <10-4 0.0142 0.9735
-I30 -50 -70 -100 -200 -400 400 200 100 70 50 30









3.4.2 Hadronic Calorimeter

The hadronic calorimeter (HCAL) [48] consists of a a conventional sampling-

type calorimeter throughout the barrel (HB) and forward end-cap (HE) regions, and

a quartz fiber sub-detector unit in the very forward region (HF). It is designed to be

as hermetic as possible that is, having the largest possible coverage. Having a

hermetic calorimeter allows for the indirect observation of undetectable particles such as

neutrinos (by balancing the total amount of transverse energy measured in the products

of a collision).

The calorimeter uses thick steel and brass absorbers interleaved with plastic scin-

tillator tiles. Particles passing through the absorption layers may interact with the heavy

nuclei of the dense materials and will shower; the resulting spray of particles passing

through the scintillator layers cause them to emit ultra-violet light. This light produced

in the scintillators is converted to visible light by 1 mm diameter wavelength-shifting

fibers and carried to hybrid photodiodes to provide read-out. A "hybrid" photodiode is a

photocathode held at high voltage (-8 kV) a short distance (3.3 mm) away from a silicon

photodiode; the high voltage accelerates photoelectrons produced by the scintillator light

and results in a total signal gain of approximately 2000.

Brass3 was chosen as the main absorber material for HCAL because it provides

sufficient density (8.53 g/cm3, yielding an interaction length of 16.42 cm) while having

excellent machinability.

HCAL Barrel. HB consists of brass absorber (either 5.05 cm or 5.65 cm thick),

and front and back plates of steel, 4.0 cm and 7.5 cm thick respectively, which provide

additional rigidity and strength. Fourteen of the scintillator layers are 3.7 mm thick,

however the inner and outer layers are 9 mm (16 layers total). It is constructed from



3 Specifically, 70%Cu, 30%Zn C26000/cartridge brass much of it melted down from
artillery shells contributed by the Russian Navy.









[53] A. Ball and A. Sharma, "CMS collaboration takes on a cosmic challenge," CERN

Courier, Mar. 2nd, 2007.

[54] D. Lazic for the CMS Collaboration, "The CMS Magnet Test and Cosmic Chal-

lenge (MTCC) Operational Experience and Lessons Learnt," Nucl. Phys. B -

Proceedings Supplements, vol. 172, pp. 3-7, Oct. 2007.

[55] CMS Collaboration, "Commissioning of the CMS experiment and the cosmic run

at four tesla", JINSTvol. 5, pp. T03001, 2010.

[56] CMS Collaboration, "CMS Trigger Technical Design Report", CERN-LHCC-2000-

38, 2000.

[57] A. Calderon, U. Gasparini, A. Gresele, A. Fanfani, S. Marcellini, etal., "Measure-

ment of Charge Ratio in Cosmic Rays using Standalone Muon Reconstruction in

CRAFT Data," CMS-NOTE AN-2010/013, 2010.

[58] I. K. Furic, T. N. Kypreos, J. Piedra, and P. Avery, D. Bourilkov, M. Chen,

R. Cousins, C. Jiang, C. Liu, N. Neumeister, Y. Pakhotin, J. Pivarski, A. Safanov,

M. Schmitt, J. Tucker, et al., "Measurement of the Charge Ratio in Cosmic Rays

using Global Muon Reconstruction in CRAFT Data," CMS-NOTE AN-2009/102,

2009.

[59] I. K. Furic, T. N. Kypreos, J. Piedra, and P. Avery, D. Bourilkov, M. Chen,

R. Cousins, C. Jiang, C. Liu, N. Neumeister, Y. Pakhotin, J. Pivarski, A. Safanov,

M. Schmitt, J. Tucker, et al., "Upgraded Measurement of the Charge Ratio of

Cosmic Rays using Global Muon Reconstruction in CRAFT Data," CMS-NOTE

AN-2009/190, 2009.

[60] J. Piedra, "Measurement of the cosmic muon charge asymmetry," presented at

the Europhysics Conference on High Energy Physics, Krakow, Poland, 2009.

[61] CMS Collaboration, "CMS Physics Technical Design Report (Volume 1)," CERN-

LHCC-2006-02, 2006.


138









provide an invaluable source of information regarding the overall muon triggering

performance of CMS.

3.5.3 Cathode Strip Chambers

The CSC's are multi-wire proportional chambers consisting of seven cathode

layers, milled to have a constant AO along the length of the trapezoidal chamber,

interleaved with six gold-plated tungsten anode wire layers. The chambers are filled with

Ar/C02/CF4 gas in a 40-50-10 mixture. There are a total of 468 chambers distributed

between the two end-caps, with an additional 72 chambers planned for a future upgrade.

Each station provides either 100 or 200 of coverage in 0 and the entire system covers

0.9 < Irl < 1.2. Spatial resolutions of 100-200 pm are possible in the CSC's. As in

the DT chambers, charged particles traversing the CSC's will ionize the gas and free

electrons, which avalanche in the presence of a high electric field towards the anode

wires. The charges collected on the anode wires induce a reflected image charge on

the strips, which can be integrated in order to find the centroid (most likely position of

the particle position) for an accurate measure of the 0 position of the particle; while

the differential signal obtained from the anode wires yield a fast response for timing

purposes as well as a measure of the muon Tl.

Commissioning with Cosmics. Although the CSC detectors are not suitable for

use in this measurement (incident cosmic muons are primarily vertical, and therefore

parallel to their active detection surfaces leading to unpredictable behavior and poor

efficiencies), they have been partially commissioned on cosmic muons before. In 2004,

several CSC chambers were used in a cosmic muon test at the University of Florida.

A test stand was constructed, and CMS-like triggering logic was simulated.4 With the



4 The author contributed to both efforts; machining the necessary steel extender arms
for the stand, helping to install and cable the scintillator panels used to provide the trig-
gering signal, and also designing and assembling the NIM crate used to provide trigger-
ing logic.













dc vs. DT SL2 hits

S1
0~ _
0.8
0.8
t t A


0d
A co( d0


).6

).5
o3


4 6 8 10 1

Number of DT SL2 hits


Charge Confusion vs. DT SL2 hits

o


0.01 -


0.008


0.006


0.004


0.002


4 6 8 10 12

Number of DT SL2 hits


Figure 5-6.


Left: curvature resolution metric dc vs. number of DT hits in SL2. Right:
charge confusion vs. number of DT hits in SL2. SL2 is the superlayer
responsible for providing measurements of the z-position. A selection cut of
three or more such hits is applied.


CMS Preliminary max GlobalX2 Distribution for a Muon Pair

103
LL\


max X2 for a pair


CMS Preliminary X2 cut efficiency vs. T

a0, 1
o


, 0.995-


0.99



0.985



0.98


10 102 103
PT [GeV/c]


Figure 5-7. Global fit X2 requirement. Left: X2 of the pair. A selection
1500 or less is applied. Right: selection efficiency vs pr.


requirement of


-+ +T


0P w)
A P( qupq I-)









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[10] S. H. Neddermeyer and C. D. Anderson, "Note on the nature of cosmic-ray

particles," Phys. Rev., vol 51, pp. 884-886, Mar. 1937.

[11] C. F Powell, et al., "Processes Involving Charged Mesons," Nature vol. 159, pp.

694-697., 1947.

[12] J. A. Van Allen, "The Nature and Intensity of the Cosmic Radiation," Physics

and Medicine of the Upper Atmosphere, The University of New Mexico Press,

Albuquerque, pp. 239-266, 1952.

[13] B. Rossi, "Cosmic Rays," McGraw-Hill, New York, 1964.































.
macwA cm


I dc,slm
U dc










V.

: : ,-,
lv-s^**^ ..


-8.01 -0.005 0 0.005 0.01
C resolution (c/GeV)


CMS MC



-. dc
103



rec sim
102 r


1 .. .
10 r .

** .


:i. 1


-0.005 0


0.005 0.01
C resolution (c/GeV)


Figure 5-10. Comparison of the resolution proxy dc (black points) with the simulation
jitter dc,sim (solid blue histogram) and the true resolution bC (hashed red
histogram). Left: linear scale. Right: logarithmic scale.





CMS simulation


- fit o

- rms


psm (GeV/c)
T


Figure 5-11. dc/SC ratios of widths from the Gaussian fits of the core distributions, and
ratios of rms, in bins of true transverse momentum at the PCA.


CMS MC

















Table 6-3. Total systematic uncertainty


a/R (%)
p range (GeV/c) R stat. syst. selection alignment B field trigger rates rock resolution
30-50 1.268 1.15 2.13 1.59 T0.10 0.20 T0.47 1.30 :0.26 :0.04
50 70 1.302 1.22 0.63 0.45 0.01 :0.01 :0.25 0.10 :0.35 :0.07
70-100 1.274 0.87 0.74 0.14 0.10 0.01 :0.10 0.10 0.70 :0.03
100-200 1.280 0.83 0.33 0.25 T0.08 T0.16 T0.01 0.10 :0.04 :0.08
200-400 1.295 1.60 1.25 0.59 T0.22 0.44 0.14 0.10 0.84 0.48
400 00 1.349 3.53 3.48 1.01 T0.99 T2.55 0.59 0.10 1.21 1.33
a/R (%)
pcos z range (GeV/c) R stat. syst. selection alignment B field trigger rates rock resolution
30-50 1.265 1.11 1.96 1.25 T0.00 0.10 0.46 1.39 :0.36 :0.05
50-70 1.280 0.85 1.00 0.85 0.10 T0.07 0.09 0.03 0.51 0:.07
70-100 1.281 0.89 0.73 0.48 T0.43 T0.13 0.12 0.03 :0.27 :0.10
100-200 1.291 1.04 0.60 0.19 0.18 0.18 0.02 0.03 0.49 0.13
200-400 1.336 2.52 1.90 1.16 0.93 T0.67 0.09 0.03 0.47 0.86
400 00 1.440 6.39 4.68 1.76 0.58 T2.39 T0.44 0.03 0.44 3.52









an analytical formula. Assuming that the widths of the top and bottom measurements of

curvature are the same (UT = 0B = -) then:



1
a = 2;' -1 = 02 =
2'


C+ = a C1 + a C2



C- = a C1 a C2

(A-1)

a+ = a22 + a22 + 2a2 COV1,2



a- = a22 + a22 2a2 COV1,2


2_ / COV1,2
S+ V 0-2 + COV1,2

0-_ -p1,2
o- 1 +P1,2


The amount of correction required may be predicted by the strength of the covari-

ance between the two measurements. In Table A.2, the predicted ratios are compared

with those previously observed. In general, the predicted value is found to lie some-

what between the value from the Gaussian fit and the RMS; and furthermore, that the

prediction agrees with the value obtained from the RMS to better than 10%.


120






























Figure 3-14. A photograph of the tracker outer barrel ready for insertion into CMS
(Copyright CERN [43]).

side), as shown in Figure 3-15, which are distributed into seven distinct rings (defined by

a range of radii).










Figure 3-15. Left: illustration of two TEC disks (in series); each is equipped with eight
"petals" per side. Right: photograph of a test bench assembly with three
rings of petals (Copyright CERN).


3.4 Calorimetry

Beyond the silicon tracker, though still within the solenoid, are separate electromag-

netic and hadronic calorimeter sub-detectors. Because these systems are completely









Although the asymmetric access shafts were removed as a source of bias by

application of the parabolic selections on both sides of the detector, other (unaccounted

for) features of the cavern or detector may induce a charge bias. In order to check, two

samples of Monte Carlo, each divided up according to muon charge, are examined. The

first sample is a representation of the ideal muon flux at the earth surface (without any

influence due to the local geometry of CMS or the shafts and caverns of Point-5). The

second sample is representative of the portion of the spectrum expected to reach the

tracker volume; and is thus subject to all of the aforementioned complications. The ratio

of the two fluxes, representative of the relative acceptance of CMS, is:


Accepted (6-14)
Nearth
... where Naccepted and Nearth are the counts (for either positive or negative muons)

from the sub-sample reaching the silicon tracker of CMS, and the sub-sample represent-

ing the total spectrum at the surface of the earth, respectively. The charge bias is then

expressed as in Equation 6-15.



&rates = -1 (6-15)
rl-

The result of this exercise is represented in Figure 6-10. The statistical uncertainty,

due to the practical limitation of finite Monte Carlo statistics (very few muons at the

surface of the earth actually reach the detector), is found to be significantly larger than

the bias estimated to come from this source.

6.2.6 Molasse Model

An accounting of the geology of the detector site in order to understand the

material overburden is one of the first considerations which must be made in order

to convert any measurements of cosmic muons incident upon the detector into mea-

surements at the surface of the earth. While no comprehensive geological survey was

performed after the excavation of the shafts and caverns for CMS; extensive surveying















CMS Preliminary A9 Trigger Match for Upper Leg p


S104
LLI


CMS Preliminary A9 Trigger Match for Upper Leg i


104
W
z


AO at 5 m


CMS Preliminary A9 Trigger Match for Lower Leg i

S 104
w


-3 -2 -1 0 2 3
AO at 5 m


AO at 5 m


CMS Preliminary A9 Trigger Match for Lower Leg p


S 104 i
w f
z


AO at 5 m


Figure 5-1.


DT trigger matching AO distributions between the stand-alone muon track
propagated to 5 m, and all simultaneous muon triggers. The dashed line at
0.2 marks the position of the cut. Top Left: Upper leg distribution for p
events. Top Right: Upper leg distribution for p+ events. Bottom Left: Lower
leg distribution for p- events. Bottom Right: lower leg distribution for p+
events.









the material densities used in the material map (known within 5%), yields a negligible

uncertainty on the charge ratio except for in the lowest momentum bin. Additional biases

due to selection are expected, however predicted to be small (below 1%). The hardware

trigger has a slight asymmetry with regards to its efficiency on positive and negative

muons, again less than 1%, and which is correlated between the two underground

analyses. The effect of such trigger bias has been estimated using information from

each half of the detector, using a so-called tag-and-probe technique to test for the

presence of a trigger in one side given a trigger in the opposite side of the detector. In

the 2006 MTCC (surface) analysis, systematic uncertainties arise mainly from the finite

precision of the detector alignment parameters [82], from the correction of the charge

mis-assignment probability, and from the slightly larger uncertainty, ~5%, in the scale of

the magnetic field in the steel return yoke.

In the global muon analysis, the effect of charge mis-assignment is small (due to

the accurate momentum resolution within the silicon tracker), and ranges from less than

0.01% at 10 GeV/c to about 1% at 500 GeV/c. These mis-assignments are automatically

corrected for in the unfolding procedure, using a data-driven estimation of the detector

resolution. In the underground stand-alone muon analysis, charge mis-assignment

is estimated and corrected for using the Monte Carlo simulation, with an additional

uncertainty due to the difference of momentum resolution between the Monte Carlo

and the data. Possible effects from potential residual mis-alignment that could lead to

momentum migrations and incorrect charge assignments were evaluated by studying

various realistic mis-alignment scenarios in data and simulation. Only the two highest

momentum bins are potentially affected by such a mis-alignment, yielding a bias in the

charge ratio around 1% in the two highest momentum bins for the global-muon analysis.

For the standalone-muon analysis, the effect in the charge ratio is less than 1% up to

400GeV/c, and 4% in the highest momentum bin. The alignment uncertainties assumed

in these analyses are well confirmed by the latest results from LHC collisions [83].









[25] T. K. Gaisser, "Cosmic Rays and Particle Physics," Cambridge University Press,

1990.

[26] P. A. Schreiner, J. Reichenbacher, and M. C. Goodman, "Interpretation of the

Underground Muon Charge Ratio", Astropart. Phys., vol. 32, issue 1, pp. 61, 2009.

[27] G. Fiorentini, V. Naumov, and F Villante, "Atmospheric neutrino flux supported by

recent muon experiments", Phys. Lett. B, vol. 510, pp. 173, 2001.

[28] O. BrOning, P. Collier, P. Lebrun, S. Myers, R. Ostojic, J. Poole, P. Proudlock, et a.,

"LHC Design Report", CERN-2004-003-V-2, 2004.

[29] J. Evans and P. Bryant, "LHC Machine", JINST, vol. 3, pp. S08001, 2008.

[30] CERN, published to the web: "http://lhc-proj-qawg.web.cern.ch/

1hc-proj-qawg/LHCQAP/Instructions/images/maplhc .gif," "Map of CERN

sites and LHC access points," retrieved on Feb. 4th, 2010.

[31] CMS Collaboration, "CMS Technical Design Report", CERN-LHCC-94-38, 1994.

[32] CMS Collaboration, "The CMS Experiment at the CERN LHC", JINSTvol. 3, pp.

S08004, 2008.

[33] ATLAS Collaboration, "ATLAS detector and physics performance. Technical design

report. Vol. 2," ATLAS-TDR-15, 1999.

[34] TOTEM Collaboration, "TOTEM: Technical design report. Total cross section,

elastic scattering and diffraction dissociation at the Large Hadron Collider at

CERN," CERN-LHCC-2004-002, Jan. 2004.

[35] LHCf Collaboration, "Technical Design Report of the LHCf experiment," CERN-

LHCC-2006-004, Feb. 2006.

[36] Alice Collaboration, "The alice experiment at the CERN LHC," Nucl. Phys. B -

Proc. Suppl., vol. 117, supp. 1, pp. 62-64, Apr. 2003.

[37] LHCb Collaboration, "LHCb: Technical Proposal," CERN-LHCC-98-004, 1998.

[38] M. Chirnside, "The 66,000 Ton Myth," The Irish Titanic Historical Society's White

Star Journal," vol. 15, no. 3, pp. 20-21, 2007.


136









CHAPTER 4
CHARGE RATIO ANALYSES

The cosmic muon charge ratio is a measure of the relative number of positive and

negative muons present within the cosmic muon spectrum. Because few machines

exist that can provide precision measurements of the moment of individual charged

muons in the GeV to TeV energy range,1 the measure of this quantity remains an area

of some interest in the ranges of energies to which CMS, with its large size and powerful

magnetic field, has the capability to access. Three separate analyses were performed

to measure the charge ratio at CMS though just one is described in detail in this

dissertation (the one introduced in Section 4.2.2). In this chapter, all three analyses are

briefly introduced.

4.1 The MTCC Analysis

The first analysis [50, 51] was performed on data collected from the "Magnet Test

and Cosmic Challenge" (MTCC) exercise [52-54], conducted as part of commissioning

on the pre-assembled detector at the end of 2006, while it still sat on the surface of the

earth. Around 15 M events were recorded during MTCC in runs with a stable magnetic

field of at least 3.67 T

During pre-assembly, only a small fraction of the detector was instrumented;

as such, only the bottom sectors of two out of the five wheels of DT chambers were

available for track reconstruction, as illustrated in Figure 4-1 (bottom). Even with

the limited detector area, the probability of charge misassignment is small for low-

momentum muons. At higher moment, resolution effects increase the chance of

random charge misassignment; resulting in an artificially low value for the charge



1 The two commonly studied regimes are for muons with a low enough energy to be
curved in small or weak magnetic fields; and extremely energetic muons, which can be
measured using calorimetry.









field2 of CMS will cause measurable curvature of tracks up to particle moment of

several TeV.

The LN2 cooled superconducting solenoid magnet is located between the hadronic

calorimeter and the muon detectors it is 12.9 m long, and has a diameter of 5.9 m.

The windings of the magnet have a total inductance of 14 H and carry approximately

18,160 A of current. Approximately 2.3 Gigajoules of energy are stored in the magnetic

field while it is running [44].

3.3 Inner Tracking System

The silicon tracker systems [45] provide high precision measurements of particle

momentum and position close to the interaction point for collision events. The diameter

of the tracker, including both subdetectors (pixels and strips), is approximately 2.5 m;

and includes 76 million detector channels. In total, it is the largest silicon particle

detector ever built; with approximately 205 m2 of active detection area. The layout of the

tracker systems is illustrated in Figure 3-7.

----D IWUlEiSE
I- -3MEC


fI I I I I I i I I l l
I I I I -- --- -----

ilM






a lowo o

Figure 3-7. Quarter profile schematic of the CMS inner tracker.



2 The field strength was designed for and is nominally referred to as 4 T, however has
been reduced to 3.8 T in order to extend the lifetime of the magnet.









CHAPTER 1
COSMIC RAYS

1.1 History

Indirect evidence for the presence of extrasolar radiation on earth was first discov-

ered by Theodor Wulf; the Jesuit priest-turned-physicist of the early 20th century who, in

1910, climbed the Eiffel tower with his newly invented radiation-detecting electrometerr"

and found a surprising abundance of radioactivity at the top [1]; more even than at its

base. The result was certainly unexpected at the time, since ionizing radiation was

believed to be caused entirely by radioactive elements in the ground, or by heavy gases

such as Radon (discovered a decade earlier [2]) in the air; and it was therefore assumed

radiation should decrease with altitude.

Wulf's result was confirmed and expanded upon by Vector Hess; who, in 1912,

conducted a similar experiment at various altitudes using balloons; and found that,

above 1 km, a clear inverse relationship existed between altitude and the intensity of

ionizing radiation. Hess eliminated the sun as the source of this radiation (by performing

his experiment during a solar eclipse), and deduced that 'a radiation of very great

penetrating power (likely) enters our atmosphere from above' [3, 4]. Meanwhile, the

first evidence for showering of this mysterious radiation was uncovered by Domenico

Pacini, who observed that ionization intensity seemed to be correlated across spans of

distance [5].

Despite mounting evidence that the radiation phenomenon was extrasolar in nature,

doubts remained, and in fact the term "cosmic-ray" did not come into usage until 1931,

when Robert Millikan first posited that high energy gamma-ray photon radiation may be

incident upon the earth from deep space [6]. In 1935, Arthur Compton used correlations

between cosmic ray intensity on earth and galactic rotation to provide compelling

evidence that at least some of the observed cosmic rays originated beyond our own

galaxy [7].









At Points 5 and 1, respectively, are the Compact Muon Solenoid (CMS)[31, 32] and
ATLAS (A Toroidal LHC Apparatus) experiments [33] which are large, general purpose

detectors, with collaborations numbering in the thousands. TOTEM [34] (Total Cross

Section, Elastic Scattering and Diffraction Dissociation) is a small, forward1 physics

experiment; which sits nestled partially within, and sharing the collisions produced for,

CMS. The smallest of the experiments, LHCf [35] (Large Hadron Collider forward), is

designed to study beam remnants2 and straddles the ATLAS experiment, with detectors

placed 140 m in either direction away from Point 1. ALICE [36] (A Large Ion Collider

Experiment) is a dedicated heavy-ion experiment3 located at Point 2. The LHCb [37]

(Large Hadron Collider beauty) is a specialized b-physics detector located at Point 8.

2.2 Accelerator chain

Before the LHC can begin accelerating beams of protons to high energies, a

complex sequence of must occur in order to deliver the beams to the collider ring.

The beam begins as hydrogen gas; from which a duoplasmatron source ionizes and

extracts protons. These protons are then accelerated in bunches to 50 MeV by Linac2,

a linear accelerator, and fed into one of the four (overlapping) 50 m diameter Proton

Synchrotron Booster (PS-Booster) rings, which accelerates the beams to 1.4 GeV. The

boosters deliver the beams into the 200 m Proton Synchrotron (PS), which combines

the proton bunches and accelerates the beams to 26 GeV. At this point, the bunches are

structured such that they are separated by 25 ns in time (or about 8.3 m in distance),

and injected into the Super Proton Synchrotron (SPS), the large 6.9 km accelerator ring



1 Such as soft elastic scattering and diffractive processes.
2 Which can be used, for example, to model the interactions of cosmic rays in the at-
mosphere.
3 The LHC is actually a dual purpose machine, able to be configured for ion colliding
as well as for protons.









MEASUREMENT OF THE CHARGE RATIO OF ATMOSPHERIC MUONS AT THE
COMPACT MUON SOLENOID IN EVENTS WITH MOMENT BETWEEN 5 GEV/C AND
1 TEV/C

















By

MICHAEL HOUSTON SCHMITT

















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2010

















- mean value
- half difference


U,
5 103


102


10


- mean value
- half difference


test variable for Gausian tails


Figure A-3.


test variable for Gausian tails


Comparison of the half-sum and half-difference distributions for a
combination of Gaussian and exponential smearing. In the left panel, in
linear scale; in the right panel, logarithmic scale.


Table A-1. The corrections to the resolution, a(dc)/l(deltaC) and corresponding RMS
ratios compared with the analytical prediction.
pCA range (GeV/c) 7 (dc) /o (SC) rms(dc) /rms (C) p1,2[%] predicted ratio
10 20 0.97 0.97 2.75 0.973
20 -30 0.91 0.93 8.35 0.920
30 -50 0.82 0.89 14.9 0.861
50 -100 0.72 0.82 24.3 0.780
100-300 0.64 0.83 27.1 0.757
300 00 0.59 0.88 19.2 0.823


122


- 700
-5
a) 600









Nuclear Science Symposium and Medical Imaging Conference, Orlando, Florida,

2009.

[97] M. Dinardo for the CMS Tracker Collaboration, "Cosmic Ray Study of the CMS

Pixel Tracker," presented at the IEEE Nuclear Science Symposium and Medical

Imaging Conference, Orlando, Florida, 2009.

[98] R. Rougny for the CMS Tracker Collaboration, "Commissioning the CMS pixel

detector with Cosmic Rays," presented at the 11th ICATPP Conference on

Astoparticle, Particle, Space Physics, Detectors and Medical Physics Applications,

Villa Olmo, Italy, 2009.

[99] M. Malberti for the CMS ECAL Collaboration, "Commissioning of the CMS ECAL

calibration with muons from cosmic rays and beam dumps," presented at the IEEE

Nuclear Science Symposium and Medical Imaging Conference, Orlando, Florida,

2009.

[100] V. Hagopian for the CMS HCAL Collaboration, "The Performance of the CMS

Hadron Calorimeter with Cosmic Muons," presented at the 11th ICATPP Con-

ference on Astoparticle, Particle, Space Physics, Detectors and Medical Physics

Applications, Villa Olmo, Italy, Oct. 2009.

[101] T. Maki for the CMS Collaboration, "Commissioning the CMS trigger with cosmic

rays," presented at the Europhysics Conference on High Energy Physics, Krakow,

Poland, 2009.

[102] S. Bansal, J. B. Singh, K. Muzamdar, I. Mikulec, "Data driven methods for

estimation of L1 trigger efficiency using CRAFT08 Cosmic Muon data," CMS Note,

IN-2009/024, 2009.

[103] D. Piccolo for the CMS Muon Collaboration, "Resistive Plate Chambers perfor-

mance with Cosmic Rays in the CMS experiment," presented at the 11th Pisa

Meeting on Advanced Detectors: Frontier Detectors for Frontier Physics, Pisa,

Italy, 2009.


142









Sym m etric acceptance ...............................

Resolution proxy vs. true resolution in Monte Carlo .. .............

Ratio of resolution estimator to actual resolution in Monte Carlo ........

Resolution in Monte Carlo, binned in Momentum .. ..............

Realistic spread of energy losses for propagations through the detector com-
pared w ith analytical result . .


5-9

5-10

5-11

5-12

5-13


5-14

5-15

6-1


6-2

6-3

6-4

6-5

6-6

6-7

6-8

6-9

6-10

6-11

6-12

6-13

6-14

6-15

7-1

7-2

7-3

8-1


bias from hardware trigger .

bias from DT hits selection .

bias from z-hits selection .

bias from TOB hits selection .

bias from X2 track .

bias from alignment uncertainty .

bias from magnetic field uncertainty .

bias from asymmetric energy loss between po

bias from muon rate uncertainty .


Pulls means. (Right)
. .


sitive and negative muons


bias from molasse uncertainty . .


Relative fraction of positive and negative muons vs. impact parameter .

Relative fraction of positive and negative muons vs. various hit requirements

Relative fraction of positive and negative muons vs. path traveled through earth

Pulls of charge ratio due to unfolding procedure . .

Individual systematic uncertainties for global muon analysis .

Statistical and systematic uncertainties for global muon analysis .

Charge ratio measurement from global muons . .

Muon charge ratio from 2006 MTCC analysis . .


Migration in q/p bins .....................

Migration in q/pcosOz bins .................

Charge ratio pulls distributions for 500 experiments. (Left)
Pulls widths. (Top) In p bins. (Bottom) In p cos z bins. .


80

80


94

95

95

96

96

97

97

98

98

99

99

100

101

102

103

108

108

109

114


Charge

Charge

Charge

Charge

Charge

Charge

Charge

Charge

Charge

Charge









The inter-strip distance (strip pitch) of TIB varies from 80-120pm. Despite having

sensors roughly 100 times as large as the pixels, due to its increased distance from the

interaction region, TIB is able to maintain no more than about 3% occupancy per bunch

crossing (at LHC design luminosity) and boasts a positional resolution only slightly

worse than the pixels, at 23-34 pm in r and 23 pm in z.





















Figure 3-13. A photograph of a mock-up of a layer of the tracker inner barrel
(Copyright CERN [43]).

Tracker Outer Barrel. The six layers of TOB sit between a radius of 55 cm and

120 cm, with their furthest extent to z = 110 cm. As with the inner barrel, the first two

layers of TOB provide a stereo measurement. The cell size of an individual detector

element is 25 cm by 180 pm; however despite it's large size, at this distance from the

interaction point, sensor occupancy is sub-percent. Positional resolution in the outer

barrel is approximately 35-52 pm in r-O and 52 pm in z.

Tracker End-Cap. TEC consists of nine disks, arranged along the z axis between

120 cm and 280 cm. Each cell in the end-cap is up to 20 cm in length with a strip pitch

of up to 200 pm. Each TEC disk has sixteen petals of sensor elements (eight on each



























Figure 3-16. A photograph of one of the two tracker end-caps (TEC), installed in a
rotating cradle (Copyright CERN).

contained within the solenoid, they must be extremely resistent to magnetic fields a

non-trivial requirement, particularly for electronics.

Unlike the tracker system which is designed to be light-weight, the calorimeters are

as dense as possible in order to absorb the maximum amount of energy; this, of course,

also implies that they must have a great deal of radiation hardness. Although there are

far fewer channels in the calorimeters than in the inner tracker, calorimeter technology

must have a very quick response in order to keep up with the LHC collision rate.

3.4.1 Electromagnetic Calorimeter

The electromagnetic calorimeter (ECAL) [47] consists of two technologies: crystal

scintillators in the barrel region and both crystals and a complementary silicon strip

preshower system in the end-cap. In total, the sub-detector contains nearly 90 tons of

scintillating lead tungstate (PbWO4) crystal (approximately 80,000 individual crystals).

ECAL provides excellent energy resolution for electrons and photons of o/E =

3%//E E 0.3% (typical), and granularities of around 2 cm. Each crystal used in














- mean value
- half difference


-5
( 10


10


fit

1 4


LUU .

\
100- t4 ff

0 4I
-5 -4 -3 -2 -1 0 1 2 3 4 5
test variable for Gausian tails


- mean value
- half difference


,3


-Q 800

-5 700

600

500

400

300


Figure A-1.


Comparison of the half-sum and half-difference distributions for Gaussian
smearing with the same resolution for top and bottom. In the left panel, in
linear scale; in the right panel, logarithmic scale.


- mean value
- half difference


1t1{ltlf if


a
(0
"5 103



102



10



1


-5 -4 -3 -2 -1 0 1 2 3 4 5
test variable for Exponential tails


- mean value
- half difference


-5 -4 -3 -2 -1 0 1 2 3 4 5
test variable for Exponential tails


Figure A-2.


Comparison of the half-sum and half-difference distributions for exponential
smearing with the same resolution for top and bottom. In the left panel, in
linear scale; in the right panel, logarithmic scale.


+

0 ft

0 i





-5 -4 -3 -2 -1 0 1 2 3 4 5
test variable for Gausian tails


C :
t 600:

500









The geometry of the Silicon Tracker is, by far, the most stringent selection criteria for

this analysis. With respect to all of the 270 M or so cosmic muon events collected during

CRAFT, the fraction of muons which propagate into the tracker is less than a percent;

and only about 25% of those are splittable. All other selection requirements, if taken

together, are more than 40% efficient on the remaining sample.

5.3 Monte Carlo Simulation

The CMS Collaboration has adapted a cosmic muon generator called CMSCGEN

(The Compact Muon Solenoid Cosmic Generator [65]) from software developed for the

L3+C experiment; which generates single random cosmic ray muons (above an energy

threshold of 10 GeV) at the surface of the earth based on distributions of muon energy

and angles of incidence based on the CORSIKA [66] air shower program.

A map describing the various materials between the Earth's surface and the CMS

detector is used to obtain the expected energy loss of simulated muons as a function

of their energy, impact point, and incidence direction at the surface [67-69]. Only

mean energy loss through the earth is considered for the extrapolated particles, and

no multiple scattering has been modeled; since the spread of angles is considered a

minor effect on the incident spectrum of cosmic muons. The residual magnetic field

surrounding CMS (though it may reach hundreds of gauss) is considered a small effect

on the arrival location of muons incident upon the detector, and is not included. The

CMS detector response is simulated using the GEANT4 program [70], which takes into

account the effects of energy loss, multiple scattering, and showering in the detector.

5.4 Curvature Measurement

Curvature, denoted C = q/p, is the main observable used in this analysis to

measure charge ratio. Within CMS, however, curvature occurs only in the transverse

plane; therefore, it is more appropriate to work with the transverse component of the









... where the N are the count of positive and negative muons, R = N+/N_, and the

o- terms are the total uncertainties on the counts. If the systematic uncertainties on R

are presumed to be equally distributed between N+ and N_:


tsyst,+ syst,- Jsyst,R (6
S (6-3)
N N -vr. R
... then, the total uncertainty on the separate counts of positive and negative muons

(per momentum bin) may be written:



2 2 2
-tot,N = 7stat,N + syst,N
2
= N+ N2. systR (6-4)
2. R2

The true count of positive or negative muons in the ith momentum bin is computed

by multiplying the raw counts from the various j momentum bins by the normalized and

inverted migration matrix. The uncertainties on the unfolded ratios are then computed as

in Equation 6-5.



-iunfolded ( -1 )2 (6-5)


The relative systematic uncertainties on R are reported both raw and after ac-

counting for the unfolding procedure in either case using the split form defined in

Equation 6-2. For the raw uncertainty, the o- terms are computed from Equation 6-4;

while for the unfolded one, they are computed from Equation 6-5.









CHAPTER 8
COMBINED RESULT OF CHARGE RATIO MEASUREMENT

8.1 Systematic Uncertainties

Systematic uncertainties arise from reconstruction and instrumental effects that

can affect differently the detection efficiency and momentum measurement of p+

and p-. They are evaluated as a function of the muon momentum estimated on the

earth surface. The systematic uncertainties of the global muon CRAFT analysis were

described in Chapter 6. The stand-alone muon analysis based on the same data-

set had shared, or similarly estimated, errors; with a few differences, eg., to produce

an additional correction for charge mis-assignment. The MTCC uncertainties were

largely based on the limited detector resolution, given the fact that it was only partially

instrumented, and did not require many sophisticated error assessments since the data

was collected on the earth surface.

Within each analysis, several of the systematic uncertainties are assumed to be

correlated between momentum bins including the trigger efficiency,1 charge mis-

assignment, and asymmetries in the detector acceptance. In the global and stand-alone

muon analyses, systematic uncertainties from material densities, event selection,

alignment, and magnetic field, are treated as uncorrelated between momentum bins;

however correlated between the two analyses.

For the 2008 CRAFT (underground) analyses, the magnetic field is known with

high precision in the region inside the superconducting solenoid, however with less

precision in the steel return yoke [76]. Systematic effects on the charge ratio due to the

uncertainty on the magnetic field are less than 1%. A possible bias in the positive and

negative muon rates, due to asymmetries in detector acceptance and uncertainties in



1 The trigger efficiency "turn-on" occurs around a few GeV/c just enough to pene-
trate a few layers of the steel yoke and much below the 10 GeV/c threshold used in the
analyses.


110










combined resolution for muons, including both the muon spectrometers and the inner

tracker, is indicated in Figure 3-31.



0.0 _


10 -- -----------
-----*,--- 10 -1 4 "
101........,. ,.... .... --- 1 ..........




10-2- 10-2

Full system e Full system
mMuon system only 0 Muon system only

103-3 1 l l 1 1 1 1 111 110'3 1 11
10 102 103 10 102 103
p[GeV/c] p[GeV/c]

Figure 3-31. Muon momentum resolution, including both the inner tracker and the muon
spectrometers. Left: the barrel region. Right: the end-cap regions [61]. This
result is for design usage of the CMS detector (that is, muons produced in
collisions). The situation isn't as simple for cosmic muons, where the
resolution has complex dependencies on the location and angles of particle
incidence.


3.5.1 Drift Tube Chambers

The drift tube chambers are constructed from aluminum cathode tube (1.3 cmx4.2 cm)

with a central gold-plated, 50 pm stainless steel anode wire, and filled with Ar/C02 gas

in a 85-15 mixture. There are either two or three "super-layers" (SL) in a DT chamber;

two provide r 0 measurements and a third one, present only for the inner three sta-

tions, provides a measure of particle z. A single SL is made up of four layers (consisting

of a wire and a tube). In total, there are therefore either 8 or 12 detection layers in a

single DT chamber. Because the DT adopted an essentially frameless design, rigidity

and structure is provided by an aluminum honeycomb layer in the center of the chamber.

There are a total of 250 DT chambers installed at CMS, divided up into the 5 wheels and

12 2 sectors.









was done both prior to the construction of the ring in the early 1980's for the construction

of LHC's predecessor (LEP), and in the mid 1990's for the two main excavations needed

for the LHC (that is, the CMS and ATLAS caverns at Point 5 and Point 1, respectively).

The molasse above CMS is known to be composed of more than 70 m of moraines

and rock left behind during glacial advances and retreats during the Alpine Riss and

Wurm eras [77]. The moraine itself is a complex array of strata with thin layers (nomi-

nally 50 cm) of silt, sand, gravel; along with layers of sandstone up to 5 m thick. Within

the moraine, there are also two aquifer levels each estimated to vary from 10 m to

22 m thick over the region [78, 79].

In order to estimate the molasse model systematic, two additional propagations of

the muons were performed; one through an extra amount of material overburden (equal

to the molasse uncertainty), and one through correspondingly less material. Divided by

material type, there are roughly 50 m of moraines and 22 m of sandstone, with a relative

uncertainty on the density of each component of ~5%. This uncertainty corresponds

to a total of 3 m of rock (or, equivalently, about 5 m moraines). The resulting charge

bias is expressed in Equation 6-16, with the corresponding uncertainty indicated in

Figure 6-11.


r R+3m rock R-3m rock (1
Rock = (6-1 6)
R

6.2.7 Resolution Estimates

In Section 5.4, it was shown that the two legs of the split muon track were found

to have a persistent correlation within the realistic Monte Carlo sample, due to some

aspect of the underlying track reconstruction. Such a correlation would cause the

prescribed detector resolution estimator, dc, to underestimate the actual resolution

by a predictable amount; however the correlation itself cannot be derived from the

data. A correction, given in Equation 5-3, was constructed by comparing the resolution

estimator with the true resolution. In order to account for the fact that the correction itself









LIST OF TABLES
Table page

5-1 Selection efficiencies for global muon analysis ..... 71

5-2 Response matrix in p bins ..... ..... 81

5-3 Response matrix in pcos z bins .......................... 82

6-1 Selection relative biases in p bins ..... .. .... .. 104

6-2 Selection relative biases in pcos z bins .... 105

6-3 Total systematic uncertainty ............................. 106

7-1 Unfolded charge ratio as a function of p and p cos 0z for the global muon anal-
ysis ........... ...... ................... .... 109

8-1 Charge ratio and uncertainties in bins of p for all three analyses ... 115

8-2 Charge ratio measurement vs. p and pcos . ... 116

A-1 Predicted corrections to the data-driven resolution, 7(dc)/l(6C), based on
amount of correlation .................. ............. 122









Measuredd, and the approximation of the migration matrix is built entirely from the mea-

sured tracks. The uncertainty in the result due to this effect is estimated in Section 6.2.5.

5.5.1 Propagation to the Earth's Surface

In order to obtain an approximation for the migration matrix, it is necessary to

transfer the measured curvatures within CMS to a measure at the surface of the earth.
The transverse curvatures measured at the PCA, CPCA and CCA, are first converted to

regular curvatures, CPCA and CPCA, as in Equation 5-7. The numeric subscript indicates

that the two terms are nominally independent measures one from the reconstructed

track segment in the top half of the detector and one from the track segment in the

bottom half of the detector.



CPCA 1
PT,1 /1 + cot2 01
(5-7)

CPCA 2 1
PT,2 1 + cot2 02

The measured curvatures obtained at the PCA are individually propagated to the

earth surface. The propagation occurs in two steps. First, a standard helical propagator

is used to transfer the tracks out of the CMS volume (to a radius of 8 m), using GEANT

to simulate the detector material, and accounting for the magnetic field. Once the track

is propagated out of CMS, an analytic extrapolation takes the track through the shaft and

cavern geometry, up to the surface of the earth. This extrapolation is linear (a straight

line to the surface); which is a reasonable approximation, since the fringing magnetic

field outside of CMS is fairly weak (at most a few hundred Gauss), and other effects

(such as multiple scattering) produce only negligible errors on the angles of trajectory,

which may be accounted for in the systematic uncertainty. Propagation transforms the













Event 2916729 Run 68021, Oct 2008 Event 2935068


on



S I. .. i



I' / /


/


standalone-mu
track













Run 4406, Oct 21


Sglobal-muon
track
(top half)






global-muon
track
(bottom half)


006


-1 _
-I1
1* -#
P JIMENNE

1 ri


Figure 4-1.


standalone-muon
track (In bottom sector)


Types of tracks used in each of the three analyses. Upper left: the
stand-alone muon analysis utilizes hits from both halves of the muon system.
Upper right: the global muon analysis requires hits in both the silicon tracker
and the muon system. Bottom: the MTCC had only a single sector of two
wheels in the bottom of the detector to use for tracking.


10"p GeVc
p GeV/c


Figure 4-2. The effect of mis-assignment on the charge ratio. A mis-assignment rate of
1%, 2%, 3%, and 5% at muon moment of 200 GeV/c is shown, increasing
linearly with momentum. The detector performance in Monte Carlo is used
to estimate the actual form and magnitude of charge mis-assignment.


I--.


CM^,













GLB CMS 2006-2008
STA
S MTCC
1.5 -*- combined



1.3


10 102


103
p (GeV/c)


103
p cose, (GeV/c)


Figure 8-4. Combined result of charge ratio from all analyses. Left: the three CMS
results, and their combination, as a function of the muon momentum. Data
points are placed at the bin average, with the points from the stand-alone
and global muon analyses offset horizontally by 10% for clarity. Right: The
final CMS result, as a function of the vertical component of the muon
momentum, together with some previous measurements and a fit of the
pion-kaon model to the CMS data.





Table 8-2. The muon charge ratio R from the combination of all three CMS analyses, as
a function of p and pcos 0z, in GeV/c, together with the combined statistical
and systematic relative uncertainty, in %

p range (p) R uncertainty p cos z range (p cos z) R uncertainty
5- 10 7.0 1.250 2.45 2.5- 10 5.3 1.274 0.99
10- 20 13.7 1.277 0.85 10- 20 13.6 1.251 1.26
20- 30 24.2 1.276 1.34 20- 30 24.1 1.262 1.88
30- 50 37.8 1.279 1.10 30- 50 37.7 1.292 1.27
50- 70 58.5 1.275 0.54 50- 70 58.4 1.267 0.71
70 -100 82.5 1.275 0.68 70 -100 82.4 1.289 0.70
100-200 134.0 1.292 0.52 100-200 133.1 1.292 0.72
200 400 265.8 1.308 1.29 200 400 264.0 1.330 1.99
> 400 698.0 1.321 3.98 > 400 654.0 1.378 6.04


116









[84] L. Lyons, D. Gibaut, and P. Clifford, "How to Combine Correlated Estimates of a

Single Physical Quantity", Nuc. Inst. Meth. A, vol. 270, pp. 110, 1988.

[85] A. Valassi, "Combining correlated measurements of several different physical

quantities", Nuc. Inst. Meth. A, vol. 500, pp. 391, 2003.

[86] G. K. Ashley, J. W. Keuffel, and M. O. Larson, "Charge ratio of ultra-high-energy

cosmic-ray muons," Phys. Rev. D, vol. 12, no. 1, pp. 20, 1975.

[87] L3 Collaboration, "Measurement of the atmospheric muon spectrum from 20 to

3000 GeV", Phys. Lett. Bvol. 598, pp. 15, 2004.

[88] J. M. Baxendale, C. J. Hume, and M. G. Thompson, "Precise measurement of the

sea level muon charge ratio," J. Phys. G: Nucl. Phys. vol. 1, pp. 781, 1975.

[89] B. C. Rastin, "An accurate measurement of the sea-level muon spectrum within

the range 4 to 3000 GeV/c," J. Phys. G: Nucl. Phys. vol. 10, pp. 1629, 1984.

[90] CAPRICE Collaboration, "Measurements of Ground-Level Muons at Two Geo-

magnetic Locations," Phys. Rev. Lett., vol. 83, pp. 4241-4244, Jul. 1999.

[91] ALEPH Collaboration, "Cosmic Ray Results from the CosmoALEPH Experiment,"

Nucl. Phys. B Proc. Supply vol. 175-176, pp. 286-293, Nov. 2007.

[92] BESS Collaboration, "Cosmic ray data and their interpretation: about BESS

experiment," Nucl. Phys. B Proc. Suppl., vol. 149, pp. 175-176, 2008.

[93] MINOS Collaboration, "Measurement of the atmospheric muon charge ratio at

TeV energies with MINOS," Phys. Rev. D, vol. 76, pp. 052003, 2007.

[94] A. C. Tazon for the CMS Collaboration, "Muon reconstruction performance using

cosmic rays in CMS," presented at Symmetries and Spin Workshop (Prague

Advanced Study Institute), Prague, Czech Republic, 2009.

[95] CMS Collaboration, "Commissioning the CMS Silicon Strip Tracker prior to

Operations with Cosmic Ray Muons," CMS Note, NOTE-2009/021, 2009.

[96] G. Kaussen for the CMS Tracker Collaboration, "The CMS Strip Tracker Calibra-

tion, Methods and Experience with Cosmic Ray Data," presented at the IEEE









of the earth is constructed from a Poisson distribution, using the migration matrix esti-

mated from data to determine the relative numbers. The curvature of each toy muon is

randomly assigned according to the q/p distribution in data, and smeared according to

the energy loss resolution. Two measurements of the resulting curvature are randomly

extracted from the actual migration matrix (to simulate the split track measurements)

and are used to construct a new migration matrix for the experiment. Finally, the toy

sample is unfolded using the new migration matrix to generate a measured curvature

distribution, which is then compared with the input curvatures. The toy experiment was

repeated 500 times; the resulting pulls distributions are summarized in Figure 6-15.

The resulting bias is negligible, as the mean values for all bins are almost zero and the

widths are very close to one.

6.4 Summary

The statistical uncertainty is approximately 1% for all bins except the highest mo-

menta; where it has a maximum of over 3% and 6% for the total momentum and vertical

momentum formulations, respectively. The systematic uncertainty is under 1% in most

bins, except for the lowest momentum bin (due to increased uncertainty in the detector

acceptance) and the highest two momentum bins (due to the increased sensitivity to

magnetic field and alignment effects). The maximum systematic uncertainty in any bin

is under 5%. It is found that selection is an important source of systematic uncertatiny

for all momentum bins. The systematic uncertainty due to selection requirements are

given in Tables 6-1 and 6-2, for the total and vertical moment, respectively. The final

systematic uncertainties, including all effects, are summarized in Table 6-3.
















r1-25


Barrel Mini End-cap End-cap

Figure 3-11. Cutaway view showing one half of the silicon strip subdetector.


Figure 3-12. Examples of tracker strip modules from the outer barrel and end-caps
(Copyright CERN [43]).


q=12
I --------~-laxr









CHAPTER 9
CONCLUSIONS

Cosmic muons have provided the Compact Muon Solenoid with a wealth of useful

data, which has been previously used for commissioning the detector [94-103], but

has now been utilized to produce the first measurement of physics involving muons at

the completed CMS detector. The ratio of positive to negative cosmic muon fluxes has

been measured, and from this measurement; a new, precision estimate on the relative

fractions of muon producing pion and kaon decays has been obtained [104, 105]. The

final result for the measurement of the cosmic muon charge ratio from CMS being

combined from three separate analyses is found to be in agreement with previous

measurements, but with a higher precision up to a muon moment of 500 GeV/c.

This dissertation detailed one of three analyses performed as part of the charge

ratio measurement. The analysis was conducted on 2008 (underground) data, including

information from both silicon tracking and muon spectrometers. In this analysis, data-

driven techniques were used to estimate the detector resolution; the validity of which

has been confirmed using numerous Monte Carlo tests, both idealized and realistic.

Energy loss in the earth was estimated using an analytical extrapolator (with additional

effects due to straggling energy losses accounted for) in order to convert measured

particle curvatures within CMS to measurements at the surface of the earth, and a

matrix unfolding technique was used to convert the measured particle counts into an

estimate of the true particle counts.


117








... and, likewise, p({) zp(). These tests give an accurate estimate of the trigger
efficiency if the spectrum of muons selected by the tag is well representative of the
entire considered spectrum for which the trigger efficiency is desired.1 The probability of
both kinds of triggers accepting the event, p(T and {), may also be estimated in a similar
fashion, with the count of triggers on both sides of CMS firing compared with the count
of events in which either trigger fired:



and n(T and {) p(T and 4)
p(T and $) -
n(T or 4) p(T or 4)
.. p( and 4) p(T and ) p(T or 4) (6-9)

Combining the results from Equations 6-8 and 6-9; Equation 6-7 may be rewritten
in terms of the appropriate estimators:



p(T or =) = p(T) + p(4) p(T and 4)

S(1) + p(4) p(1 and 4). p(T or 4)
P(T)) + 0
1 + p(t and ) (6

From these estimations on the trigger probability, the respective trigger efficiencies
for positive and negative muons are computed. The resulting charge bias, previously
defined in Equation 6-6, is illustrated in Figure 6-2.



1 Such is the case for muons in this analysis, since the split muon requirement guar-
antees that the considered tracks traverse the entire detector; and, further, because
they are constrained to the center of the machine, and therefore have similar ranges of
incident angles as they cross through the Muon Spectrometer.








CHAPTER 6
SYSTEMATIC UNCERTAINTIES IN THE GLOBAL MUON ANALYSIS
In this Chapter, the systematic uncertainties for the analysis described in Chapter 5
are evaluated. The uncertainties are computed separately for each momentum bin (both
p and p cos(O)) at the surface of the earth, both raw and after unfolding, and are divided
up into contributions from the hardware trigger, quality selection, misalignment, magnetic
field, muon rates, molasse model, and detector resolution. Each of them is designed
according to Equation 6-1:


2 yst 2 + 2 (6-1)

... where is the estimated charge bias induced from each source (equal to zero
for the case of no biasing error), and a7 is the statistical uncertainty on the estimation
of that bias. Note that (in this analysis) finite Monte Carlo statistics sometimes prevents
a precision estimation of the systematic error. In such cases, the obtained charge
bias, _, is itself actually consistent with zero (and therefore the term itself is likely an
overestimation of the actual error). As a result, the final systematic error, on a case by
case basis, is sometimes assumed to be given by syst2 = 2.
6.1 Error Propagation and Unfolding
In order to incorporate the various systematic uncertainties into the unfolding
procedure for error propagation, they must first be divided between the individual
positive and negative muon counts for each momentum bin:


R= d2 + (6-2)
R ( )2y+( -









systems [49] of CMS are used to provide triggering capabilities, as well as tracking, to

supplement the inner silicon detectors. The muon systems are divided up into a series

of five wheels in the barrel region and two end-caps, as may be seen in Figure 3-30.

800
1
00 eta RPC 01.04 1.2
7,1O
MB3 /










40 0 4 600 1 00



Figure 3-30. Quarter view showing the muon system.







The muon sub-detector consists of three separate technologies: Resistive Plates
(RP), Drift Tube (DT), and Cathode Strips ( ). Drift tubes provide an inexpensive








solution which works well with low occupancies and in uniform magnetic fields; so they

are used in the barrel region. The cathode strip chambers function well even in rapidly

changing magnetic fields and with higher particle fluxes; hence they are installed in the

end-caps. Resistive plate chambers are a simpler technology used in both the forward

(RPCf) and barrel (RPCb) regions, and provides a complementary system for timing and

triggering purposes. The chambers are installed in four separate stations, or layers of

chambers; one station on each of the five wheels of CMS in the barrel region and four

stations deep in the end-caps. Each of the stations is mounted to the iron yokes. The
0 200 400 5 600 9 10o0 1 i4
Z
Figure 3-30. Quarter view showing the muon system.


The muon sub-detector consists of three separate technologies: Resistive Plates

(RPC), Drift Tube (DT), and Cathode Strips (CSC). Drift tubes provide an inexpensive

solution which works well with low occupancies and in uniform magnetic fields; so they

are used in the barrel region. The cathode strip chambers function well even in rapidly

changing magnetic fields and with higher particle fluxes; hence they are installed in the

end-caps. Resistive plate chambers are a simpler technology used in both the forward

(RPCf) and barrel (RPCb) regions, and provides a complementary system for timing and

triggering purposes. The chambers are installed in four separate stations, or layers of

chambers; one station on each of the five wheels of CMS in the barrel region and four

stations deep in the end-caps. Each of the stations is mounted to the iron yokes. The









6.2 Sources of Systematic Uncertainty


6.2.1 Trigger
Relative differences in the efficiency of the hardware trigger system for muons
of one charge vs. the other can cause an overall charge bias. This bias, trig, may be
expressed:


trig = + 1 (6-6)

The Tl terms in Equation 6-6 refer to the trigger efficiency for any barrel trigger to
fire in response to a muon event of the given charge. In order to estimate the charge
bias, the sample of recorded events is first divided into a set of positive and a set of
negative muons. Within either sample, the probability of a trigger may be expressed:


T = p(1 or 1) = p(1) + p({) p(1 and {) (6-7)

... where the arrows refer to whether a trigger originated in one of the sub-detectors
of the top or bottom of CMS, and the subscript denoting whether the efficiency is for
positive or negative muons has been dropped for brevity. The efficiencies are estimated
using tag-and-probe tests, which are performed by tagging a trigger on one side of CMS
and probing for the existence of a trigger on the opposite side (using the reconstructed
track to determine whether any matches exist). For example, the estimator p(T) of the
true upper trigger probability, p(T), is constructed from the ratio of the number of probes
to the number of tags:



S_ n(t and {) p(T and {) p(T) p(~)
n({) p(G) p(M)


.*. p() p() (6-8)

































CMS 2008 preliminary
n no" ______


u.ul


0.01



0



-0.01



-0.02


CMS 2008 preliminary
n-i ______


U. I


c 0.08
0
'-5

| 0.06-

E
I 0.04 -
E
0
o
E
0.02


103
pPCA (GeV/c)
T


* data
- MC







--0







102 103
pPCA (GeV/c)
T


Figure A-8. Data (black solid circles) and Monte Carlo (red open circles). Left: mean
value of Gaussian fits (momentum scale). Right: width of fits (momentum
resolution).

























127


* data

- MC












Table 6-2. Selection relative biases in pcosOz bins


a-/ R (%)
p cos z range (GeV/c) R stat. 2 + /
30 50 1.2653 1.11 0.78 0.42 0.66 0.65
50- 70 1.2795 0.85 0.85 -0.84 0.11 -7.59
70 -100 1.2815 0.89 0.49 0.47 0.13 3.78
100-200 1.2913 1.04 0.16 0.02 0.15 0.14
200-400 1.3359 2.52 0.84 0.76 0.35 2.18
400 c0 1.4395 6.39 1.22 -0.88 0.85 -1.03
SL2
a,/ R (%)
pcos 0z range (GeV/c) R stat. 2 + 7 o-/
30-50 1.2653 1.11 0.35 -0.05 0.35 -0.14
50-70 1.2795 0.85 0.13 -0.12 0.06 -2.05
70- 100 1.2815 0.89 0.21 -0.20 0.07 -2.67
100-200 1.2913 1.04 0.11 -0.04 0.10 -0.37
200-400 1.3359 2.52 0.26 0.10 0.24 0.42
400 c0 1.4395 6.39 0.83 0.60 0.57 1.04
TOB
,a/R (%)
p cos z range (GeV/c) R stat. 27 + 7 /o
30-50 1.2653 1.11 1.30 -1.17 0.56 -2.08
50-70 1.2795 0.85 0.11 -0.10 0.04 -2.31
70 -100 1.2815 0.89 0.05 0.04 0.04 0.96
100-200 1.2913 1.04 0.10 0.08 0.05 1.82
200-400 1.3359 2.52 0.11 -0.01 0.11 -0.07
400 oc 1.4395 6.39 0.24 0.07 0.23 0.32
X2
a,/ R (%)
p cos z range (GeV/c) R stat. 27 + ,/o
30-50 1.2653 1.11 0.31 -0.14 0.28 -0.51
50- 70 1.2795 0.85 0.09 -0.08 0.05 -1.72
70- 100 1.2815 0.89 0.09 0.05 0.07 0.78
100-200 1.2913 1.04 0.22 -0.19 0.12 -1.55
200 -400 1.3359 2.52 0.94 -0.87 0.36 -2.40
400- c0 1.4395 6.39 1.87 -1.53 1.09 -1.40


105









CHAPTER 5
THE GLOBAL MUON ANALYSIS

This chapter provides a description of the analysis performed using global muon

tracks collected during CRAFT. The final results of all three analyses are ultimately

combined to form the official CMS measurement of the cosmic muon charge ratio.

5.1 Analysis Overview

The analysis is performed by first applying selection requirements on the muons

observed within the detector to ensure good track objects. The collection of objects -

split at the point of closest approach (PCA) to the z-axis are individually propagated

to the surface of the earth in order to estimate the energy losses through the earth and

detector material. An unfolding procedure is used, which consists of approximating the

migration matrix which acts to convert a true count of muons at the earth surface to a

measured count within CMS and inverting it, in order to derive a final count of positive

and negative muons in each bin after accounting for all resolution effects. Unfolding is

handled separately for two cases: muon counts binned by their momentum (p) and the

vertical component of their momentum (pcos Oz), always as estimated at the surface of

the earth.

5.2 Selection Requirements

5.2.1 Event Selection

Approximately 270 million cosmic muon events were collected over the duration

of CRAFT. This analysis is based on a subset of that data; in particular, events were

skimmed for "tracker pointing" muon tracks: tracks reconstructed in the outer muon

chamber which propagate into a 260 cm long, 90 cm diameter cylinder at the heart of

CMS. This propagation cylinder sits well within the volume of the silicon tracker. Events

were required to have been collected during runs with a stable 3.8 T magnetic field.

Trigger. An "open" trigger path was used at hardware level, which promotes

any valid muon trigger candidates (because the trigger estimates momentum using









The smallest mass possible is preferable in this system, since added material

increases the likelihood of particle showering (which confuses the system's ability to

resolve individual tracks, and otherwise complicates possible interpretations of the

event) and also absorbs energy that would have otherwise been measured in the

calorimeters.

Certain heavy particles that are produced in collisions, such as Charm and Beauty

mesons, have relatively long lifetimes; and particles produced in the decay of such

particles may originate from a position that is displaced from the primary interaction

point. The tracker should be able to make measurements precise enough to allow us

to deduce the point of origin of an observed particle; so as to be able to distinguish the

decay products of such long-lived particles from promptly decaying particles. This is of

particular importance when considering isolated leptons. Isolated leptons are produced

sparingly according to the known laws of physics, however are a feature of some

theoretical models of new physics. Therefore, in addition to being able to determine

whether the lepton originates at the interaction point, the tracker should also be sensitive

enough to distinguish a single, isolated particle from two or more particles with highly

correlated trajectories.

Finally, and most importantly, the tracker must be designed to operate properly with

the requirements of LHC conditions. It needs to work properly within an intense mag-

netic field, and it absolutely must be radiation hard, since it is in such close proximity

to the LHC collision point. When operating at design specifications, LHC collisions will

produce approximately 1000 energetic particles traversing the tracker volume every

25 ns, coming from more than 20 proton-proton interactions in each beam bunch cross-

ing. In total, an average of 40 billion individual highly energetic particles will traverse the

tracker volume every second. In addition to sensor toughness, the LHC environment

also places tough constraints on the minimum readout speed and sensor occupancy of









6.2.2 Selection

The selection requirements applied in this analysis were chosen to be as charge

blind to the measurement of charge ratio as possible; however any selection may

potentially have a different efficiency for positive and negative muons. To estimate the

amount of systematic bias introduced by the muon selection, a so-called N 1 test is

applied for each of the considered requirements. That is, all of the requirements except

for the one under study are applied, and the ratio of efficiencies (?r) of the final selection

on the remaining sample is used as an estimate for the charge bias:


sel = -+ 1 (6-11)
_
The four selection requirements were: the minimum number of DT hits, the mini-

mum number of z-measuring hits in the DT (hits in Superlayer-2), the minimum number

of hits in the Silicon Tracker outer barrel, and the maximum global-fit track X2. The sam-

ple was divided up into positive and negative muons, and the relative efficiencies of the

Nth requirements were compared. The resulting estimate of the charge bias for each of

these requirements are illustrated in Figures 6-3 through 6-6.

An implicit form of selection arises from the split-track requirement. Recall that, in

Figure 5-2, it was shown that requiring split-tracks has the indirect effect of selecting on

small impact parameters; and in particular, the total distance between the PCA and the

center of the detector. Figure 6-12 gives the relative effect on charge against the three

principle impact parameters. Since the split-track efficiencies are sensitive only to the

magnitude of the impact parameter (independent of which side of the detector the track

is on), no charge bias is expected to result from this selection.

Overall, selection is found to be a major source of systematic uncertainty in the

analysis (the results for each selection requirement are given in Tables 6-1 and 6-2).

The two major contributors to this source of uncertainty are the requirements on the

number of hits in the DT and TOB. In order to show that these selection requirements




































Figure 3-8. Schematic drawing of the Pixel sub-detector.


.:... '"~, ,


I t r ~ L .. "'" ,: -
ri, -.'.- .'.. ,- ,,-^
-i :1,.-* ,>^
r, ^-


Figure 3-9. Left: diagram of a pixel module. Right: a photograph of a constructed
module (Copyright CERN).















Charge Confusion vs. Tob hits


2 4 6 8 10


C,
1 5

-.8


3.6 0.6


3.4 0.4


3.2 0.2


Number of TOB hits


0.08-



0.06



0.04



D.02


2 4 6 8 10 -1'


Number of TOB hits


Figure 5-4. Left: curvature resolution metric dc vs. minimum number of TOB hits. Right:
charge confusion vs. minimum number of TOB hits. A selection cut of at
least 5 TOB hits is applied.


dc vs. DT hits

>> I-----



0.8


0.6


0.4


0.2


I .i ,


0
Ao(dc)


20 30 40 50

Number of DT hits


C,
1 5
C-)

).8


Charge Confusion vs. DT hits


o l
.5
0)


AP(q, q w)


Number of DT hits


Figure 5-5. Left: curvature resolution metric dc vs. number of DT hits. Right: charge
confusion vs. number of DT hits. A selection cut of 20 or more DT hits is
applied.


Ao(d, )


"- K


dc vs. Tob hits


i
tt~
ti~
t
m









ACKNOWLEDGMENTS

There are many people whom I would like to thank, and without whom I likely would

not have reached this happy milestone. I thank my advisor and committee chair, Paul

Avery, and former co-advisor Richard Cavanaugh (now at the University of Illinois at

Chicago); John Mocko and Darin Acosta, for giving me my first opportunities to do

physics as an undergraduate. Also, Ivan Furic; whom I thank for an inspired solution -

lighting a path for the last several months of my graduate career (as Rudyard Kipling

once wrote, "If you can meet with triumph and disaster \\ and treat those two imposters

just the same... "). I thank Bobby Scurlock; my political antithesis, who has provided a

constant source of both entertainment and frustration (in addition to the rare piece of

good advice), and who had I not sprained my ankle I would have beaten once on the

hardcourt.

For their leadership and contributions to the charge ratio measurement I thank

Ivan Furic; his student, Nicholas Kypreos; and post-doctoral assistant, Jonatan Piedra.

In addition, various others have provided significant support for my work: Dimitri

Bourilkov, Bockjoo Kim, Yu Fu, Yujun Wu, and the experts at the High Performance

Computing center in particular, Craig Prescott (who, in addition, taught me practically

everything I know about shell programming when we used to work together doing data

production back in the dark ages of Grid computing).

I would like to thank my family for their love and encouragement: my mother, Sue;

my two brothers, David and Steve; Beverly and Richard Yerby, and their daughter -

my wonderful wife, Heather without whom I would (at this very moment) likely be

disheveled, unshaven, and hunting in the pantry for asian-style noodles to warm for

dinner.










Brass


incident hadrons


Figure 3-26.


When highly energetic hadrons scatter off of nuclei in matter, the collision
produces a spray of particles including more hadrons such as neutral
pions (dashed lines); charged pions or kaons (solid lines), which may
collide with more nuclei, creating a cascade effect. As it develops, the
resulting shower will produce light within the scintillator tiles proportional to
the number of particles in the cascade, which is in turn proportional to the
energy of the original hadron.


36 wedges forming two half-barrels; each wedge is bolted together, leaving a gap of at

most 2 mm between adjacent wedges. The scintillators are read out in 16 rI regions.

The granularity of HCAL is square in the barrel region in rT and (, with A/ x A =

0.087 x 0.087. It provides coverage up to Irl = 1.3.














Figure 3-27. Left: a series of HB wedges awaiting assembly. Right: merged together to
form the HB sub-detector (Copyright CERN).


HCAL Endcap. The HE sub-detector contains 7.9 cm thick brass absorber and

9 mm scintillator tiles. The layers are affixed to a 10 cm thick support plate, which is

mounted to the iron return yoke. Granularity in HE varies from An = 0.087 to 0.35 and









histograms, binned in p and p cos Oz at the surface of the earth, are presented in Fig-

ures 5-14 and 5-15, respectively. The column-wise normalization of these histograms

(called the "response matrices") form an approximation, M, of the true migration matrix,

which takes the true count of muons and converts it to measured counts. The response

matrices are presented in Tables 5-2 and 5-3.

Table 5-1. The total number of muons in the barrel region of CMS surviving, along with
both the cumulative and relative selection efficiencies.
requirement N e (%) rel. e (%)
good runs 2372101
matched trigger 2343585 98.80 98.80
two tracker tracks 579183 24.42 24.71
NDT > 20 463342 19.53 80.00
NDT z-hits> 3 442713 18.66 95.55
NTOB > 5 428458 18.06 96.78
A cot 0 < 0.2 428204 18.05 99.94
max X2 < 1500 415173 17.50 96.96
pT > 10 GeV/c 308390 13.00 74.28
symmetrical acceptance 245218 10.34 79.52









[39] J. Bryner, published to the web: "http://www.livescience.com/technology/

091103-cruise-ship-floats .html", "How the World's Largest Cruise Ship

Floats," LiveScience.com, Nov. 2009.

[40] A. Robb, "Optical geometry of motion, a new view of the theory of relativity,"

Cambridge University Press: Heffner and Sons, 1911.

[41] CERN, "ATLAS cavern ready for its detector," CERN Courier, Jul. 1st, 2003.

[42] CERN, "CMS cavern ready for its detector," CERN Courier, Mar. 1st, 2005.

[43] CMS Collaboration, published to the web: "http://cms.web.cern.ch/cms/Media,"

retrieved on Feb. 7th, 2010.

[44] CMS Collaboration, "CMS Magnet Technical Design Report", CERN-LHCC-97-10,

1997.

[45] CMS Collaboration, "CMS Tracker Technical Design Report", CERN-LHCC-98-6,

1998; Addendum CERN-LHCC-2000-16, 2000.

[46] M. Teckenbrock, "Making Good Things Fit in Small Packages," CD Tracks

Newsletter, Nov. 2008.

[47] CMS Collaboration, "CMS ECAL Technical Design Report", CERN-LHCC-97-33,

1997.

[48] CMS Collaboration, "CMS HCAL Technical Design Report", CERN-LHCC-97-31,

1997.

[49] CMS Collaboration, "CMS Muon Technical Design Report", CERN-LHCC-97-32,

1997.

[50] M. Aldaya and P. Garcia-Abia, "Measurement of the charge ratio of cosmic muons

using CMS data" CMS-NOTE 2008/016.

[51] M. Aldaya, P. Garcia-Abia, M. Mulders, "Updated measurement of the charge ratio

of cosmic muons using MTCC data," CMS-NOTE AN-2010/011, 2010.

[52] CMS Collaboration, "The CMS Magnet Test and Cosmic Challenge", CMS-NOTE

2007/005, 2007.


137




















Figure 3-22. Left: photo of a single EB module on a test bench. Right: several modules
combined to form a supermodule mounted onto a rotating cradle
(Copyright CERN).

138 5x5 supercrystals, for a total of 3450 crystals per dee and 14,950 for all of EE. The

layout of EE is indicated in Figure 3-23. A dee, with several EE supercrystals installed, is

shown in Figure 3-24.


Figure 3-23. Design of ECAL End-cap (EE)


Pre-Shower Detector. In order to improve distinguishability between neutral pions

from photons, a pre-shower detector is installed in front of the endcap crystals. The pre-

shower detector contains two layers of lead converters and silicon strip detectors. Since

7o mesons decay to di-y, 7's may be distinguished from prompt photons by broader

charge distributions on the strips.























Figure 3-32. Left: photo of Drift Tube (DT) chambers awaiting shipment to CERN. Right:
as installed in the barrel region (Copyright CERN).

When charged particles (typically muons, since most other particles will be trapped

within the calorimeters) pass through the gas, they will knock electrons free from the

gas. A high voltage between the wire and the tube will cause an electron avalanche;

as the electron will free additional electrons on its path towards the anode wire. The

resulting charge build-up on the wire can be read-out to provide a signal for the cham-

ber. Typical spatial resolution for the DT system is 250 pm (as low as 100 pm in r 0),

with a timing resolution of 5 ns which is well measurable because the drift velocity for

electrons in Ar/CO2 is known precisely (5.4 cm/ps at 1.8 kV; for a maximum drift time of

380 ns).

3.5.2 Resistive Plate Chambers

The RPC chamber are a "double-gap" resistive plate technology which provides

ultra-fast (1 ns, much less than the 25 ns collision frequency) timing information. Anode

strips (running parallel to the beam) separate the two gaps and provide a common

readout. There are a total of 480 RPC chambers; divided up into six layers in the barrel

region (which are distributed amongst the four muon stations) and three layers in the

end-cap region. The RPC chambers, though less accurate than the DT chambers,









is not data-driven, an additional systematic uncertainty equal to half of the correction is

assumed.

A possible explanation for the observed correlations is related to the alignment,

since relative offsets within the detector may result in shifting the two (nearby) mea-

surements similarly. While the Monte Carlo approximates mis-alignments by randomly

shifting groups of detector elements around according to the estimated positional un-

certainties, the data is aligned differently (using individual tracks). Note that despite

this obvious difference a similar correlative effect is likely to appear, since some of the

same tracks used to measure the charge ratio are also used to perform the alignments

of the silicon tracker and muon systems [80, 81], and furthermore, from which the Monte

Carlo alignment uncertainty has been approximated.

6.3 Other Sources of Error

6.3.1 Atmospheric Conditions

The local elevation where CMS is installed is approximately 500 m above sea-level.

In order to explore the effects of atmospheric conditions on measurements involving

cosmic muons; public weather, solar, and geomagnetic data from the run period was

used to estimate and simulate the atmospheric density, from ground level to high

altitudes. No extreme atmospheric conditions were observed during the course of the

experiment, and the relative variation of atmospheric density with respect to the mean

sea-level, as well as the offset between mean sea-level and the actual elevation of the

earth surface near CMS, are extremely small and have been neglected. Details of this

study are presented in Appendix B.

6.3.2 Unfolding Procedure

In order to check whether the unfolding procedure itself induces a charge bias in

the final result, an estimator is constructed using an ensemble of toy Monte Carlo exper-

iments. For each experiment, a number of positive and negative muons at the surface









ratio.2 To demonstrate this effect, the parameterized charge ratio (Equation 1-3) has

been plotted along with various assumptions on the rate of charge mis-assignment

at 200 GeV/c in Figure 4-2, assuming a simple, linearly increasing probability for mis-

assignment.

Up to 200 GeV/c, the rate of charge mis-assignment is low enough to be safely

estimated and corrected for using Monte Carlo simulations. Only muons reconstructed

within a symmetrical fiducial volume were accepted for analysis. Approximately 330 k

out of the original 15 M cosmic muon events remain after all selection requirements have

been applied.

4.2 The CRAFT Analyses

Two analyses were conducted on data from "Cosmic Run at Four Tesla" (CRAFT)

exercise [55], collected between October 17th and November 11th, 2008. During

CRAFT, the entire machine was instrumented and installed underground. One of the

analyses used only muon system hits for tracking, while the other analysis used both

muon system and tracker hits. The kinds of tracks used in both analyses are illustrated

in Figure 4-1.

Cosmic muon events were collected on an open3 muon trigger [56] path, with

triggers originating in either of the barrel sub-detectors (DT or the barrel RPC). Approxi-

mately 270 M cosmic muon events were recorded on these triggers. For both analyses,

a symmetric selection is applied with respect to the yz-plane; removing muons from con-

sideration if they have a trajectory through the two asymmetric auxiliary access shafts at



2 Since the charge ratio is greater than one, there are more positively charged muons
that can be mis-reconstructed with a negative charge than there are negatively charged
muons that can be mis-reconstructed as having a positive charge.

3 That is, no momentum requirement.












CMS 2008 preliminary


4000 -


3000


2000


1000



0 50 100 150
p pCMS (GeV/c)


CMS 2008 preliminary
I Innnl


1000


80 100 120 140 160
Earth path length (m)
e pl O


CMS 2008 preliminary


CMS 2008 preliminary


100 150
p pMS (GeV/c)


CMS 2008 preliminary
3 1 ,


0
80 100 120 140 160
Earth path length (m)


CMS 2008 preliminary


1
COS 8z


1
COS 8,


Figure 6-14. Left: distributions of p+ and p, with the second normalized to the first (for a
better shape comparison) vs. variables relevant to the path the muons take
through the earth to reach CMS. Right: ratio of the normalized distributions.




102


o
0


0 -









n


I \JJ\









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

MEASUREMENT OF THE CHARGE RATIO OF ATMOSPHERIC MUONS AT THE
COMPACT MUON SOLENOID IN EVENTS WITH MOMENT BETWEEN 5 GEV/C AND
1 TEV/C

By
Michael Houston Schmitt

August 2010

Chair: Paul Avery
Major: Physics

The ratio of positive to negative charges in the secondary cosmic muon flux is

measured at the Compact Muon Solenoid experiment. Muons with moment between

5 GeV/c and 1 TeV/c are observed in data collected at ground level or 89 m under-

ground; and found to be a constant 1.2766 0.0032(stat.) 0.0032(syst.) for moment

below 100 GeV/c, and rising with higher moment. The fraction of charged pions and

kaons in the secondary cosmic flux resulting in positive muon production has been esti-

mated, with f,+ = 0.553 0.005 and fK+ = 0.66 0.06, respectively. The results presented

herein are in good agreement with cosmic ray shower models, consistent with previous

measurements, and represent the most precise measurement to date for atmospheric

muons up to 500 GeV/c. This is also the first physics measurement involving muons at

the completed CMS detector.









CMS is 23 cm long; crystals in the barrel region have a cross-sectional footprint of
2.05 cmx2.05 cm, while those in the endcap range in size from about 1.8 cmx2.0 cm to
2.7 cmx2.9 cm. The layout of the detector is indicated in Figure 3-17.









Preshower (ES)
= 2.6
-_-- -- .0 Endcap
-- ECAL(EE)

Figure 3-17. Quarter view of ECAL layout.


Figure 3-18. With sufficient energy and in the presence of a high-Z medium (such as
lead tungstate), ionizing particles (such as electrons) will readily radiate
photons; while photons will decay to e+/e- pairs. Drawing not to scale.


Detector technology. When photons or charged particles pass through high-Z
materials, an electromagnetic shower may develop from Coloumb interactions, inducing

the radiation of photons and e-e- pairs (which in turn also shower). This process
repeats until the energy of each produced particle falls below the threshold for new

pair-production; at which point, the remaining soft electrons and photons are absorbed











r r *r' W W


Figure 3-24. Four ECAL End-cap (EE) supercrystals mounted on a "dee." Each dee has
138 such supercrystals (Copyright CERN).


Figure 3-25. Photograph of an ECAL preshower module on a test bench
(Copyright CERN).


















(unfolded true) pulls mean


1.05


1


0.95


0.9


0.85


pEarth (GeV/c)


(unfolded true) pulls mean


pEarth (GeV/c)


(unfolded true) pulls width


1.1


1.05


1


0.95


0.9


102
pEarth COsO, (GeV/c)


102
pEarth COsO, (GeV/c)


Figure 6-15. Charge ratio pulls distributions for 500 experiments. (Left) Pulls means.
(Right) Pulls widths. (Top) In p bins. (Bottom) In pcos0z bins.


103


(unfolded true) pulls width









focus of this dissertation.3 The methodology of this analysis is presented in Chapter 5;

and estimations on the error are provided in Chapter 6. A detailing of the result from

the main analysis is provided in Chapter 7, while the combined results of all three are

presented in Chapter 8.







































3 As shall be detailed in the next chapter this one being based on the underground
data and using both the silicon tracker data and the muon spectrometer data, as op-
posed to solely muon spectrometer data.









radiate photons as they pass through the quartz fibers (since quartz has a high index of

refraction, charged particles will emit Cherenkov light as they pass through the fibers if

they are traveling faster than the local speed of light) which are arranged parallel to the

z-axis. The threshold for Cherenkov emission in quartz is only 190 keV for electrons.

Because electromagnetic showers develop much more quickly than hadronic

showers, it is possible to distinguish incident electromagnetic particles from hadronic

particles by having fibers of different lengths in HF Two fiber lengths were chosen for HF,

called "long" and "short", which are 1.65 m and 1.43 m in length, respectively; with the

shorter fiber being displaced away from the interaction region. The ratio of measured

energy in the two lengths of fibers (long to short) gives a good indication of whether the

shower is hadronic or electromagnetic; as an electromagnetic shower will leave much

more energy in the long fiber than in the short fiber.


















Figure 3-29. Photograph of wedges of the Forward Calorimeter (HF) awaiting installation
(Copyright CERN [43]).

3.5 Muon Spectrometers

Good muon resolution is a key design goal of the CMS detector; as muons are a

feature of many theoretical models which will be studied at CMS (such as Supersym-

metry, Universal Extra Dimensions, etc.). For this analysis, the muon spectrometer






























To the American soldier who stands opposed to tyranny, who protects the weak, who
carries the beacon of that greatest bastion of liberty the world has ever known; of a
shining city on a hill: one nation, unique in history, founded under God, and governed at
the consent of the people; that she may never be banished from the earth, nor suffer of
the rule of kings














data data


6000


4000


40 60 80
toplegldo| (cm)


-100 -50 0 50 100
all accepted top leg zo (cm)
all II accepted


000 -


000 -


3000D


0 50 100 150
all accepted top leg z + d (cm)


Figure 5-2.


PCA parameter distributions before (black line) and after (red histogram) the
removal of muons without a splittable tracker track. Left: |dol. Center: zo.

Right: total displacement of PCA from geometric center of CMS, z + do.
The PCA from the top and bottom tracks are nearly identical; therefore, only
the measurement from the top leg is displayed.


dc vs. A cot(O)


.0.9

t0.8
0.7

0.6
0.5

0.4

0.3
0.2
0.1


o (d, )


Charge Confusion vs. A cot(e)


0.3 0.35 0.

A cot(e)


0.1 0.15 0.2 0.25 0.C

A cot(e)


Figure 5-3. Left: curvature resolution metric dc vs. Acot(O) between track legs. Right:
charge confusion vs. Acot(O) between track legs. A selection requirement of
Acot(e) < 0.2 is applied.


4000


0 20
all M accepted









A.1.2 Selection on Independent Measures


A temptation in this analysis is to only accept events in which the top and bottom

leg agree about the charge of the muon. To simulate how this affects the result, the

distributions of the half-sum and half-difference are compared if events are accepted

according to whether the two measurements agree on the sign of the measurement.

The outcome is shown in Figure A-5, the two distributions disagree. In the weaker case,

selection may be applied such that the difference between the measures is cut off at

certain value, by selecting on events with curvatures which differ by no more than a set

amount. The result is displayed in Figure A-6. Again, it is clear that the half-difference is

a poor estimator of the true resolution.

From these tests, it is clear that the relative or absolute agreements between the

measurements must not be used as a selection variable if the half-difference is to

be used to estimate resolution effects. Such selection results in "sculpting" the half-

difference, which does little more than hide the actual detector resolution.

A.2 Comparison with the Realistic Monte Carlo

The resolution estimator in Monte Carlo is compared with the data in Figure A-7,

showing that the actual detector performance was relatively worse than the simulation

predicts. The results are summarized in Figure A-8.

In Section 5.4, it was suggested that the half-difference between the two mea-

surements was underestimating the true resolution; and in Figure 5-12, the amount of

the necessary correction to convert the half-difference into a more accurate resolution

estimator was defined. Figure A-9 gives the actual correlation between the top and bot-

tom measures of curvature in the Monte Carlo, and shows that the two measurements

are correlated with each other. The correlation is found to be nearly negligible for low

momentum tracks, but increases significantly with momentum. Assuming Gaussian error

distributions, the under-estimation factors (printed out in Table A.2) can be predicted via


119












direction


\ K+
P
Figure 1-5. Example of an associated production event resulting from primary cosmic
ray interactions in the atmosphere, which tends to favor positive kaon
production.


1.3 Scope

This work is based on a measurement of the cosmic muon charge ratio, repre-

sentative of the relative densities of positive and negative muon fluxes, at the Compact

Muon Solenoid (CMS); a particle detector built for the Large Hadron Collider (LHC). The

LHC, though not used for this measurement, is nonetheless important for this effort2

from the stand-point of the constraints it puts on detector design and operation. A brief

introduction to the LHC is provided in Chapter 2; while the CMS detector is described in

Chapter 3.

A total of three analyses have been conducted as part of the cosmic muon charge

ratio measurement: one, on data collected while the machine was pre-assembled on the

earth surface, and two on data collected after the machine was installed underground.

The final result of the charge ratio measurement is a product of all three analyses,

and so each are briefly introduced in Chapter 4; however just one of them is the main



2 As well as a matter of current interest; as it is now, at the time of this writing, opera-
tional; and successfully producing controlled collisions at heretofore unseen energies.









CHAPTER 7
RESULT OF GLOBAL MUON ANALYSIS

The main focus of this dissertation is the measure of charge ratio in cosmic muons

using global muon tracks. The results of this analysis, obtained using the methodology

of Chapter 5 and with the calculation of systematic uncertainty as in Chapter 6, are

presented here. The systematic uncertainties, broken down according to their source,

are presented in Figure 7-1. The total error from all sources, statistical and systematic,

are provided in Figure 7-2. The statistical and systematic uncertainties are found to

be of roughly equal importance; combining for a total uncertainty of 2% in the lowest

momentum bin, 5% in the highest bin, with a minimum of about 1% in between. The

unfolded ratios of positive to negative muons is summarized in Table 7-1, and illustrated

in Figure 7-3. It is observed that the charge ratio is approximately 1.27 (as predicted) at

low moment; and increasing at high moment up to about 1.4 above 600 GeV/c.

Because the final measurement of charge ratio is based on the combined results of

all three analyses (the earth surface analysis, this analysis, plus the other underground

analysis); the precise fits such as the result for the fraction of pions and kaons produc-

ing muons from this one analysis are not shown here. Instead, they may be found as a

fit for all CMS data in the next chapter.


107




Full Text

PAGE 1

MEASUREMENT OFTHECHARGERATIOOFATMOSPHERICMUONSATTHE COMPACTMUONSOLENOIDINEVENTSWITHMOMENTABETWEEN5GEV/CAND 1TEV/C By MICHAELHOUSTONSCHMITT ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2010

PAGE 2

c r 2010 MichaelHoustonSchmitt 2

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T otheAmericansoldierwhostandsopposedtotyranny,whoprotectstheweak,who carriesthebeaconofthatgreatestbastionoflibertytheworldhaseverknown;ofa shiningcityonahill:onenation,uniqueinhistory,foundedunderGod,andgovernedat theconsentofthepeople;thatshemayneverbebanishedfromtheearth,norsufferof theruleofkings 3

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A CKNOWLEDGMENTS TherearemanypeoplewhomIwouldliketothank,andwithoutwhomIlikelywould nothavereachedthishappymilestone.Ithankmyadvisorandcommitteechair,Paul Avery,andformerco-advisorRichardCavanaugh(nowattheUniversityofIllinoisat Chicago);JohnMockoandDarinAcosta,forgivingmemyrstopportunitiestodo physicsasanundergraduate.Also,IvanFuric;whomIthankforaninspiredsolution lightingapathforthelastseveralmonthsofmygraduatecareer(asRudyardKipling oncewrote,Ifyoucanmeetwithtriumphanddisaster nn andtreatthosetwoimposters justthesame...).IthankBobbyScurlock;mypoliticalantithesis,whohasprovideda constantsourceofbothentertainmentandfrustration(inadditiontotherarepieceof goodadvice),andwhohadInotsprainedmyankleIwouldhavebeatenonceonthe hardcourt. FortheirleadershipandcontributionstothechargeratiomeasurementIthank IvanFuric;hisstudent,NicholasKypreos;andpost-doctoralassistant,JonatanPiedra. Inaddition,variousothershaveprovidedsignicantsupportformywork:Dimitri Bourilkov,BockjooKim,YuFu,YujunWu,andtheexpertsattheHighPerformance Computingcenterinparticular,CraigPrescott(who,inaddition,taughtmepractically everythingIknowaboutshellprogrammingwhenweusedtoworktogetherdoingdata productionbackinthedarkagesofGridcomputing). Iwouldliketothankmyfamilyfortheirloveandencouragement:mymother,Sue; mytwobrothers,DavidandSteve;BeverlyandRichardYerby,andtheirdaughter mywonderfulwife,HeatherwithoutwhomIwould(atthisverymoment)likelybe disheveled,unshaven,andhuntinginthepantryforasian-stylenoodlestowarmfor dinner. 4

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T ABLEOFCONTENTS page A CKNOWLEDGMENTS ..................................4 LISTOFTABLES ......................................8 LISTOFFIGURES .....................................9 ABSTRACT .........................................13 CHAPTER 1COSMICRAYS ....................................14 1.1History ......................................14 1.2Theory ......................................15 1.3Scope ......................................21 2THELARGEHADRONCOLLIDER .........................23 2.1MemberExperiments .............................23 2.2Acceleratorchain ................................24 2.3CurrentOperationalStatus ..........................25 3THECOMPACTMUONSOLENOID ........................27 3.1Introduction ...................................27 3.1.1CoordinatesandGeography ......................29 3.1.2CavernGeometry ............................29 3.2SolenoidMagnet ................................31 3.3InnerTrackingSystem .............................32 3.3.1PixelDetector ..............................34 3.3.2SiliconStripDetector ..........................36 3.4Calorimetry ...................................39 3.4.1ElectromagneticCalorimeter .....................40 3.4.2HadronicCalorimeter ..........................46 3.5MuonSpectrometers ..............................49 3.5.1DriftTubeChambers ..........................51 3.5.2ResistivePlateChambers .......................52 3.5.3CathodeStripChambers ........................53 4CHARGERATIOANALYSES ............................55 4.1TheMTCCAnalysis ..............................55 4.2TheCRAFTAnalyses .............................56 4.2.1AnalysiswithStand-AloneMuons ...................57 4.2.2AnalysiswithGlobalMuons ......................57 4.3Summary ....................................58 5

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5 THEGLOBALMUONANALYSIS ..........................60 5.1AnalysisOverview ...............................60 5.2SelectionRequirements ............................60 5.2.1EventSelection .............................60 5.2.2PhysicsObjectSelection ........................61 5.2.3QualitySelection ............................62 5.2.4SymmetricalAcceptanceSelection ..................64 5.2.5SelectionEfciencySummary .....................64 5.3MonteCarloSimulation ............................65 5.4CurvatureMeasurement ............................65 5.5Unfolding ....................................68 5.5.1PropagationtotheEarth'sSurface ..................69 5.5.2ConstructionofMigrationMatrix ....................70 6SYSTEMATICUNCERTAINTIESINTHEGLOBALMUONANALYSIS .....83 6.1ErrorPropagationandUnfolding .......................83 6.2SourcesofSystematicUncertainty ......................85 6.2.1Trigger ..................................85 6.2.2Selection ................................87 6.2.3Mis-Alignment ..............................88 6.2.4Magneticeld ..............................89 6.2.5MuonRates ...............................89 6.2.6MolasseModel .............................90 6.2.7ResolutionEstimates ..........................91 6.3OtherSourcesofError .............................92 6.3.1AtmosphericConditions ........................92 6.3.2UnfoldingProcedure ..........................92 6.4Summary ....................................93 7RESULTOFGLOBALMUONANALYSIS .....................107 8COMBINEDRESULTOFCHARGERATIOMEASUREMENT ..........110 8.1SystematicUncertainties ...........................110 8.2MeasurementoftheCosmicMuonChargeRatio ..............112 8.2.1MeasuredChargeRatioBelow100GeV/c ..............112 8.2.2ChargeRatioBetween5GeV/cand1TeV/c .............113 9CONCLUSIONS ...................................117 APPENDIX ATESTSOFTHEDATA-DRIVENRESOLUTION ..................118 A.1RandomNumberTests ............................118 A.1.1UncorrelatedMeasurements ......................118 6

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A.1.2 SelectiononIndependentMeasures .................119 A.2ComparisonwiththeRealisticMonteCarlo .................119 BATMOSPHERICDEPTH ...............................129 B.1Introduction ...................................129 B.2MeasuredAtmosphericPressure .......................129 B.3EffectiveElevation ...............................130 B.4AtmosphericDensity ..............................130 B.5NRLMSISE-00AtmosphericSimulation ...................130 B.6Summary ....................................131 BIOGRAPHICALSKETCH ................................144 7

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LIST OFTABLES T able page 5-1 Selectionefcienciesforglobalmuonanalysis ..................71 5-2Responsematrixin p bins ..............................81 5-3Responsematrixin p cos z bins ..........................82 6-1Selectionrelativebiasesin p bins ..........................104 6-2Selectionrelativebiasesin p cos z bins ......................105 6-3Totalsystematicuncertainty .............................106 7-1Unfoldedchargeratioasafunctionof p and p cos z fortheglobalmuonanalysis ..........................................109 8-1Chargeratioanduncertaintiesinbinsof p forallthreeanalyses .........115 8-2Chargeratiomeasurementvs. p and p cos z ...................116 A-1Predictedcorrectionstothedata-drivenresolution, (d C )= ( C ),basedon amountofcorrelation ................................122 8

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LIST OFFIGURES Figure page 1-1 Totalprimarycosmicprotonux ..........................17 1-2Totalprimarycosmicrayux,scaledbyspectralindexfactor ..........18 1-3Totalsecondarycosmicmuonux .........................18 1-4Recentchargeratioresults .............................19 1-5Exampleofassociatedproduction .........................21 2-1MapofLHCandCERNsites ............................23 2-2LocationsofmemberexperimentsalongtheLHCring. ..............25 3-1TheCMSDetector ..................................27 3-2SmallsectionofCMSinthe xy -planeshowingparticleow ...........28 3-3ProleofCMSinthe xy -plane ...........................30 3-4QuarterproleofCMSin y -z plane ........................30 3-5LayoutofshaftsandcavernsatPoint5 ......................31 3-6Photographofthecavernandmainaccessshaft .................31 3-7QuarterproleschematicoftheCMSinnertracker. ................32 3-8SchematicdrawingofthePixelsub-detector. ...................35 3-9DiagramandPhotoofaCMSPixeltrackermodule ................35 3-10DetailofaCMSpixeltrackerendcapdisk .....................36 3-11Cutawayviewshowingonehalfofthesiliconstripsubdetector. .........37 3-12Photooftrackerstripmodules(TOBandTECshown) ..............37 3-13Photooftrackerinnerbarrel(TIB) .........................38 3-14Photooftrackerouterbarrel(TOB) .........................39 3-15Designoftrackerendcap(TEC) ...........................39 3-16Photooftrackerendcap(TEC) ...........................40 3-17QuarterviewofECALlayout. ............................41 3-18Illustrationofelectromagneticshowering ......................41 9

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3-19 PhotographsofPbWO 4 crystalsforECAL .....................42 3-20DesignofECALBarrel(EB) .............................43 3-21PhotographofpartiallycompletedECALBarrel(EB)module ..........43 3-22PhotographsofECALBarrel(EB)moduleandasupermodule .........44 3-23DesignofECALEnd-cap(EE) ...........................44 3-24PhotographofECALEnd-cap(EE)supercrystals .................45 3-25PhotographofanECALpreshowermodule ....................45 3-26Illustrationofhadronicshowering ..........................47 3-27PhotographofHCALBarrel(HB)wedgesbeforeandafterassembly ......47 3-28PhotographofHCALEnd-cap(HE) .........................48 3-29PhotographofwedgesoftheForwardCalorimeter(HF) .............49 3-30Quarterviewshowingthemuonsystem. ......................50 3-31Muonmomentumresolution .............................51 3-32PhotoofDriftTube(TD)chambers .........................52 3-33PhotographofanEnd-CapMuon(ME)diskloadedwithchambers .......54 3-34PhotographofthecosmicteststandbuiltatUF ..................54 4-1Tracktypesusedinanalyses ............................59 4-2Effectofchargemis-assignmentonchargeratio .................59 5-1DTtriggermatching distributions ........................72 5-2PCAparameterdistributionsbeforeandaftertracksplitting ...........73 5-3Curvatureresolutionandchargeconfusionforselectiononthe cot( )betweentopandbottomtracks ............................73 5-4CurvatureresolutionandchargeconfusionforselectiononTOBhits ......74 5-5CurvatureresolutionandchargeconfusionforselectiononDThits .......74 5-6Curvatureresolutionandchargeconfusionforselectionon z -measuring(SL2) DThits ........................................75 5-7Distributionandselectionefciencyof 2 ofglobaltrackt ............75 5-8Comparisonofamountofunwantedcorrelationsformatchingon or cot z 76 10

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5-9 Symmetricacceptance ................................76 5-10Resolutionproxyvs.trueresolutioninMonteCarlo ................77 5-11RatioofresolutionestimatortoactualresolutioninMonteCarlo .........77 5-12ResolutioninMonteCarlo,binnedinMomentum .................78 5-13Realisticspreadofenergylossesforpropagationsthroughthedetectorcomparedwithanalyticalresult .............................79 5-14Migrationin q = p bins .................................80 5-15Migrationin q = p cos z bins .............................80 6-1Chargeratiopullsdistributionsfor500experiments.(Left)Pullsmeans.(Right) Pullswidths.(Top)In p bins.(Bottom)In p cos z bins. ..............94 6-2Chargebiasfromhardwaretrigger .........................95 6-3ChargebiasfromDThitsselection .........................95 6-4Chargebiasfrom z -hitsselection ..........................96 6-5ChargebiasfromTOBhitsselection ........................96 6-6Chargebiasfrom 2 track ..............................97 6-7Chargebiasfromalignmentuncertainty ......................97 6-8Chargebiasfrommagneticelduncertainty ....................98 6-9Chargebiasfromasymmetricenergylossbetweenpositiveandnegativemuons 98 6-10Chargebiasfrommuonrateuncertainty ......................99 6-11Chargebiasfrommolasseuncertainty .......................99 6-12Relativefractionofpositiveandnegativemuonsvs.impactparameter .....100 6-13Relativefractionofpositiveandnegativemuonsvs.varioushitrequirements .101 6-14Relativefractionofpositiveandnegativemuonsvs.pathtraveledthroughearth 102 6-15Pullsofchargeratioduetounfoldingprocedure ..................103 7-1Individualsystematicuncertaintiesforglobalmuonanalysis ...........108 7-2Statisticalandsystematicuncertaintiesforglobalmuonanalysis ........108 7-3Chargeratiomeasurementfromglobalmuons ..................109 8-1Muonchargeratiofrom2006MTCCanalysis ...................114 11

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8-2 CosmicmuonchargeratioatPCAin2008undergroundanalyses ........114 8-3Cosmicmuonchargeratiofrom2008undergroundanalyses ..........115 8-4Combinedresultofchargeratiofromallanalyses .................116 A-1ComparisonsofresolutionestimatorforGaussiansmearing ...........121 A-2Comparisonsofresolutionestimatorforexponentialsmearing ..........121 A-3ComparisonsofresolutionestimatorforacombinationofGaussianandexponentialsmearing ...................................122 A-4Comparisonsofresolutionestimatorwithdifferenttopandbottomresolutions .123 A-5Testsofthevalidityoftheresolutionestimatorwhenthesignofcurvatureis usedforaselection .................................124 A-6Testsofthevalidityoftheresolutionestimatorwhenrelativecurvatureisused foraselection .....................................125 A-7Resolutionts,datavs.MonteCarlo ........................126 A-8Momentumresolutionandscale,datavs.MonteCarlo ..............127 A-9Correlationbetweentopandbottomindividualtrueresolutions,inbinsoftrue transversemomentumatthePCA. .........................128 B-1AirdensitiesasafunctionofaltitudeduringCRAFT08usingNRLMSISE-00. .132 B-2Airdensitiesatgroundlevel:measuredfromGenevaInternationalAirportdata andsimulatedusingNRLMSISE-00. ........................132 B-3TheeffectiveelevationofgroundlevelaboveCMSduringthetimeoftheexperiment,usingdatapublishedbytheGenevaAirport. ..............133 12

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Abstr actofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy MEASUREMENTOFTHECHARGERATIOOFATMOSPHERICMUONSATTHE COMPACTMUONSOLENOIDINEVENTSWITHMOMENTABETWEEN5GEV/CAND 1TEV/C By MichaelHoustonSchmitt August2010 Chair:PaulAvery Major:Physics Theratioofpositivetonegativechargesinthesecondarycosmicmuonuxis measuredattheCompactMuonSolenoidexperiment.Muonswithmomentabetween 5GeV/cand1TeV/careobservedindatacollectedatgroundlevelor89munderground;andfoundtobeaconstant1.2766 0.0032(stat .) 0.0032(syst .)formomenta below100GeV/c,andrisingwithhighermomenta.Thefractionofchargedpionsand kaonsinthesecondarycosmicuxresultinginpositivemuonproductionhasbeenestimated,with f + =0.553 0.005and f K + =0.66 0.06,respectively.Theresultspresented hereinareingoodagreementwithcosmicrayshowermodels,consistentwithprevious measurements,andrepresentthemostprecisemeasurementtodateforatmospheric muonsupto500GeV/c.Thisisalsotherstphysicsmeasurementinvolvingmuonsat thecompletedCMSdetector. 13

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CHAPTER 1 COSMICRAYS 1.1History IndirectevidenceforthepresenceofextrasolarradiationonearthwasrstdiscoveredbyTheodorWulf;theJesuitpriest-turned-physicistoftheearly20thcenturywho,in 1910,climbedtheEiffeltowerwithhisnewlyinventedradiation-detectingelectrometer andfoundasurprisingabundanceofradioactivityatthetop[ 1];moreeventhanatits base.Theresultwascertainlyunexpectedatthetime,sinceionizingradiationwas believedtobecausedentirelybyradioactiveelementsintheground,orbyheavygases suchasRadon(discoveredadecadeearlier[ 2 ])intheair;anditwasthereforeassumed radiationshoulddecreasewithaltitude. Wulf'sresultwasconrmedandexpandeduponbyVectorHess;who,in1912, conductedasimilarexperimentatvariousaltitudesusingballoons;andfoundthat, above1km,aclearinverserelationshipexistedbetweenaltitudeandtheintensityof ionizingradiation.Hesseliminatedthesunasthesourceofthisradiation(byperforming hisexperimentduringasolareclipse),anddeducedthat`aradiationofverygreat penetratingpower(likely)entersouratmospherefromabove'[ 3 4].Meanwhile,the rstevidencefor showering ofthismysteriousradiationwasuncoveredbyDomenico Pacini,whoobservedthationizationintensityseemedtobecorrelatedacrossspansof distance[ 5 ]. Despitemountingevidencethattheradiationphenomenonwasextrasolarinnature, doubtsremained,andinfactthetermcosmic-raydidnotcomeintousageuntil1931, whenRobertMillikanrstpositedthathighenergygamma-rayphotonradiationmaybe incidentupontheearthfromdeepspace[ 6 ].In1935,ArthurComptonusedcorrelations betweencosmicrayintensityonearthandgalacticrotationtoprovidecompelling evidencethatatleastsomeoftheobservedcosmicraysoriginatedbeyondourown galaxy[ 7 ]. 14

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By theendofthedecade,itwasknownthatcosmic-raysweremadeupof particles ratherthanphotons;howevertheraynomenclaturestuck[ 9, 10 ].In1948,examination ofparticletracksfromcosmicrayeventscapturedinnuclearemulsionphotographs takeninballoonsathighaltituderevealedthat primary cosmicrays(thoseincident upontheatmospherefromspace),werecomposedofprotons,alphaparticles,anda smallfractionofheavieratomicnuclei(suchasiron).Bythen,ithadbeenestablished thatthe secondary cosmicrays(producedbycollisionsbetweentheprimarycosmic particlesandgaseswithintheearthsatmosphere)consistedofpions(whichwereonly justdiscovered[ 11]),muons,electrons,andphotons[12 ]. Althoughitwaswidelyconjecturedasearlyasthe1960'sthatcosmicrayswere producedinsupernova[ 13 14],itwasdifculttoaccountfortheveryhighestenergies observedinthecosmicrayspectrum;andtheoriginofsuchcosmicrayeventsremained amysteryformanyyears.Roughlyfourdecadeslater,in2007,aJapaneseteamledby YasunobuUchiyamastudyingasupernovausingNASA'sChandralaboratoryconrmed thataprocessofamplicationofthemagneticeldinyoungsupernovaremnantscan occur,leadingtosignicantcosmicrayenergies[ 15].Meanwhile,thePierreAuger Collaborationreleasedndingswhichshowedthatthevery highest momentacosmic raysarriveonearthfromdirectionshighlycorrelatedwithnearbyactivegalacticnuclei wheresuper-massiveblackholes,withcorrespondinglyenormousmagneticelds, arebelievedtoexistandareabletoaccelerateparticlestoultrahigh(PeV-scale) energies[ 16 17],thoughthislinkisstilltentative[ 18 ]. 1.2Theory Cosmicrayparticlesmaybeproducedinmanypotentialastrophysicalprocesses. Solarares,supernovae,andblackholesemitandacceleratetheseparticlesoutinto thecosmos;wheretheyarelikelytocontinueacceleratingundertheactionofthe turbulentmagneticeldsoftheinterstellarmedium[ 19].Thespectrumiscomposedof 15

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atomic nuclei,mostlyhydrogen(bareprotons)andhelium;inanapproximateratioof7915-6(hydrogen,helium,andallothers)above10GeV/nucleon,withtherelativefraction ofheavynucleiincreasingsomewhatwithenergy[ 20 ].Theuxofprimarycosmicray particlesincidentupontheearthfollowsasimplepowerlaw: b = b 0 E )Tj /T1_5 7.97 Tf 6.59 0 Td (r (1) Thespectrum[21]isplottedinFigure 1-1.Thespectralindex, r ,isfoundtobe2.7 above10GeVandbelow1PeVmultiplyingtheobservedrawspectrumby E 2.7 yields adetailedlookattheenergydependentshapeofthespectrum[ 22],whichmaybeseen inFigure 1-2.Theeffectsofsolarwinds,andeventheearthmagneticeld,provide shieldingfromlowenergycosmicrays;resultinginasuppressionofthespectrum below10GeV.Atthehighestenergies(above1PeV)thespectralindexincreases from2.7toabout3.0.Itisspeculatedthattheeffectivenessofcosmicrayproduction mechanismstoaccelerateparticlesdiminishes. Theprimarycosmicraysbombardstheupperatmosphereofearth;producing ashowerofpionandkaonmesonsastheycollidewithatmosphericgases.Muons areproducedwhenthepionsandkaonsdecaybeforetheythemselvescollideinthe atmosphere.Thespectrumofthesemuons[ 20, 23]depends,ofcourse,ontheprimary spectrum;butalsoonthetwo-bodydecaykinematicsofpionsandkaons( K + ) andontheirinteractionsitisplottedagainstmomentuminFigure 1-3;again,withthe spectralindexfactor( p r ,again,with r =2.7)appliedtohelpaccentuatetheshape. Aparameterizationforthespectrumofmuonshasbeenderived[25]according totheinteractionsofprimarycosmicrayparticlesintheearthatmosphere,andonthe 16

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Figure 1-1.Thetotaluxoftheincidentprimarycosmicrayspectrum[ 21]. decaysofthesecondarymesons;ofwhich,pionsandkaonsarethemostimportant contributors.Accordingtothisparameterization,theuxmaybewritten: dN dp d n = 0.14p )Tj /T1_0 7.97 Tf 6.59 0 Td (2.7 1 1 + 1.1 p cos 115 GeV =c + 0.054 1 + 1.1p cos 850 GeV =c cm )Tj /T1_0 7.97 Tf (2 s )Tj /T1_0 7.97 Tf 6.59 0 Td (1 c GeV )Tj /T1_0 7.97 Tf 6.59 0 Td (1 (1) ChargeRatio. Ofprimaryinteresttothisworkisthechargeimbalanceinthe cosmicmuonspectrum,expressedasthe chargeratio ofpositivetonegativemuons,as afunctionofmomentum.Becausetheprimarycosmicraysarenearlyentirelypositively charged,thechargeratiooftheincidentprimariesisveryhigh,andpositivemeson productionisfavored;however,asadditionalpionsandkaonsareproduced,theinitial chargeimbalanceisspreadoutoverlargerandlargermultiplicities,resultinginamore 17

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Figure 1-2.Thetotaluxoftheincidentprimarycosmicrayspectrum;scaledbythe spectralindexfactor E r with r =2.7.Adaptedfrom[ 22]. Figure 1-3.Thetotaluxofverticallyincidentmuonsinthesecondarycosmicray spectrumatgroundlevel;scaledby p r ,with r =2.7.Adaptedfrom[ 20 ]. 18

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unif ormchargedistribution.Thus,theexactnatureofthechargeimbalanceinmuons issensitivetotheproductionandinteractioncross-sectionsofpionsandkaonsinthe gaseousearthatmosphere,aswellastheirdecaylengths. Modelsofcosmicrayshowerspredictariseinthechargeratioathighermuon momenta;inpartbecausesuchmuonsarelikelyproducedwhentherearefewergenerationsbetweentheparentmesonandtheincidentprimarycosmicray;andalso becausekaonproduction,whichproducesrelativelymorepositivemuonsthanpions, becomesmuchmoreimportantathigherenergies.Thereisalsosomedisagreement amongstthemodelsatmomentaaboveseveralTeV/c;mostlyduetotheuncertaintyassociatedwithinteractionsofhighlyenergeticpionsandkaonswithatmosphericprotons andneutrons.Severalofthesemodels,alongwithrecentexperimentalresults[ 24],are displayedinFigure 1-4. Figure 1-4.Resultsofthecosmicmuonchargeratiofromvariousrecentexperiments, alongwithshowermodelpredictions[24 ]. 19

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F romtheparameterizationwritteninEquation 1,thechargeratiomaybewritten[ 26 ]asafunctionofthefractions f + and f K + oftheensembleofallchargedpion andkaondecaysthatyieldpositivemuons: N + N )Tj /T1_0 11.955 Tf 11.26 7.9 Td (= f + 1 + 1.1p cos 115 GeV= c + 0.054 f K + 1 + 1.1p cos 850 GeV =c # = 1 )Tj /T1_1 11.955 Tf 11.96 0 Td (f + 1 + 1.1p cos 115 GeV= c + 0.054 (1 )Tj /T1_1 11.955 Tf 11.95 0 Td (f K + ) 1 + 1.1p cos 850 GeV= c # (1) Thesefractionsarenotknown apriori ,andmustbeobtainedbyttingthemeasureddata.Obtainingthesefractionsisoneofthechiefmotivationsofmeasuringthe chargeratiointhesub-TeVregimeinparticular,becauseadditionaldataisrequired inordertodetermineifthesefactorswillhavetheirown(higherorder)momentum dependence.Thechargeratioofpioncontributionsispredicted[ 27]tobearound 1.27( f + =0.56);andhigherforkaons,duetoroughlyanorderofmagnitudesmaller likelihoodofinteractionbeforedecay 1 andbecauseofassociatedproduction. Thetermassociatedproductionreferstoaparticularsortofinteractioninvolving theproductionofstrangeparticles.Strangeparticlesareproducedonlyinpairsin strongnuclearinteractions,suchthatapropertydubbedstrangenessisconserved, butdecayonlyviatheweaknuclearforce.Anexampleofanassociatedproduction eventisillustratedinFigure 1-5,inwhichacosmicprotoninteractswithanatmosperic protonorneutron,producinganeutralstrangehadron(the )andapositivelycharged kaon.Thelambdamostlikelydecaysbackintoaprotonplusanegativepion;thus, associatedproductioneventssuchastheonedepictedwillincreasethechargeratioup inkaons. 1 This isdueto:ashorterlifetime(roughlyhalfthatofpions,about12nscompared with26ns);asmallerprobabilityofinteractingwithprotons(about25%);andahigher mass(roughlythreetimesthatofpions),whichcauseskaonstoexperiencelesstime dilationthanpionsforagivenamountofkineticenergy,andtherefore,ashortereffective lifetime. 20

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Figure 1-5.Exampleofanassociatedproductioneventresultingfromprimarycosmic rayinteractionsintheatmosphere,whichtendstofavorpositivekaon production. 1.3Scope Thisworkisbasedonameasurementofthecosmicmuonchargeratio,representativeoftherelativedensitiesofpositiveandnegativemuonuxes,attheCompact MuonSolenoid(CMS);aparticledetectorbuiltfortheLargeHadronCollider(LHC).The LHC,thoughnotusedforthismeasurement,isnonethelessimportantforthiseffort 2 fromthestand-pointoftheconstraintsitputsondetectordesignandoperation.Abrief introductiontotheLHCisprovidedinChapter 2 ;whiletheCMSdetectorisdescribedin Chapter 3 Atotalofthreeanalyseshavebeenconductedaspartofthecosmicmuoncharge ratiomeasurement:one,ondatacollectedwhilethemachinewaspre-assembledonthe earthsurface,andtwoondatacollectedafterthemachinewasinstalledunderground. Thenalresultofthechargeratiomeasurementisaproductofallthreeanalyses, andsoeacharebrieyintroducedinChapter 4;howeverjustoneofthemisthemain 2 As wellasamatterofcurrentinterest;asitisnow,atthetimeofthiswriting,operational;andsuccessfullyproducingcontrolledcollisionsatheretoforeunseenenergies. 21

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f ocusofthisdissertation. 3 ThemethodologyofthisanalysisispresentedinChapter 5 ; andestimationsontheerrorareprovidedinChapter 6 .Adetailingoftheresultfrom themainanalysisisprovidedinChapter 7,whilethecombinedresultsofallthreeare presentedinChapter 8. 3 As shallbedetailedinthenextchapterthisonebeingbasedontheunderground dataandusingboththesilicontrackerdataandthemuonspectrometerdata,asopposedtosolelymuonspectrometerdata. 22

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CHAPTER 2 THELARGEHADRONCOLLIDER TheLargeHadronCollider[28 29 ]isaproton-protonsynchrotronbuiltintothe existing27kmlongLargeElectronPositronCollidertunnel;situatedapproximately 100mbeneaththegroundalongtheborderbetweenFranceandSwitzerlandnearthe cityofGeneva.AmapoftheLHCringandassociatedsitesisgiveninFigure 2-1. Figure 2-1.MapoftheringandassociatedCERNsites[ 30](CMS,whichwillbe discussedinChapter 3,islocatedatPoint5nearthevillagesofCessyand S egny,inFrance). 2.1MemberExperiments TheLHCishosttoatotalofsixexperimentswithfourbeamcrossings(wherethe collisionsareproduced);thelayoutoftheseexperimentsmaybeseeninFigure 2-2. 23

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At Points5and1,respectively,aretheCompactMuonSolenoid(CMS)[ 31, 32]and ATLAS(AToroidalLHCApparatus)experiments[ 33]whicharelarge,generalpurpose detectors,withcollaborationsnumberinginthethousands.TOTEM[ 34](TotalCross Section,ElasticScatteringandDiffractionDissociation)isasmall,forward 1 physics experiment;whichsitsnestledpartiallywithin,andsharingthecollisionsproducedfor, CMS.Thesmallestoftheexperiments,LHCf[ 35](LargeHadronColliderforward),is designedtostudybeamremnants 2 andstraddlestheATLASexperiment,withdetectors placed140mineitherdirectionawayfromPoint1.ALICE[ 36 ](ALargeIonCollider Experiment)isadedicatedheavy-ionexperiment 3 locatedatPoint2.TheLHCb[37 ] (LargeHadronColliderbeauty)isaspecializedb-physicsdetectorlocatedatPoint8. 2.2Acceleratorchain BeforetheLHCcanbeginacceleratingbeamsofprotonstohighenergies,a complexsequenceofmustoccurinordertodeliverthebeamstothecolliderring. Thebeambeginsashydrogengas;fromwhichaduoplasmatronsourceionizesand extractsprotons.Theseprotonsarethenacceleratedinbunchesto50MeVbyLinac2, alinearaccelerator,andfedintooneofthefour(overlapping)50mdiameterProton SynchrotronBooster(PS-Booster)rings,whichacceleratesthebeamsto1.4GeV.The boostersdeliverthebeamsintothe200mProtonSynchrotron(PS),whichcombines theprotonbunchesandacceleratesthebeamsto26GeV.Atthispoint,thebunchesare structuredsuchthattheyareseparatedby25nsintime(orabout8.3mindistance), andinjectedintotheSuperProtonSynchrotron(SPS),thelarge6.9kmacceleratorring 1 Such assoftelasticscatteringanddiffractiveprocesses. 2 Whichcanbeused,forexample,tomodeltheinteractionsofcosmicraysintheatmosphere. 3 TheLHCisactuallyadualpurposemachine,abletobeconguredforioncolliding aswellasforprotons. 24

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Figure 2-2.LocationsofmemberexperimentsalongtheLHCring. (whichwasonceagreatcolliderinitsownright;havingdeliveredthecollisionsthatled tothediscoveryoftheWandZbosons)whichacceleratesthebeamsfrom26GeVup to450GeVreadyforinjectionintoLHC. NewstoresofprotonsmustbedeliveredtotheLHCuptoseveraltimesperday (roughlyonceeverytenhoursisexpected);sincethebeamgraduallylosesparticles duetobeam-gascollisions,crossingdeectionsattheinteractionpoints,andother largelyunavoidableinefcienciesinvolvedinkeepingsuchabeamintactoverseveral hundredsofmillionsoforbits.Oncefullyoperational,itisanticipatedthatacceleration frominjectionenergy(450GeV)to7TeVmayoccurinaslittleas20minutes. 2.3CurrentOperationalStatus TheLargeHadronCollidersuccessfullycirculatedbeamsatitsinjectionenergy of450GeVforthersttimeonSeptember10th2008,andproduceditsrstcollisions onNovember23rd,2009.Justaweeklater,onNovember30th,2009;theLHCbegan acceleratingprotonbeamsupto1.18TeV(for2.36TeVtotalcenter-of-massenergy 25

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collisions): surpassingtheTevatronatFermiNationalLaboratory(withprotonandantiprotonbeamsof0.98TeVforatotalof1.96TeVcenter-of-mass)tobecometheworld's highestenergyparticleaccelerator,andthemostpowerfulparticlecollidereverbuilt. OnMarch30th,2010;theLHCsuccessfullycollidedprotonsat7TeVcenter-of-mass, whereitisexpectedtoholdsteadyfor18to24months.Eventually,theLHCwillbe abletoproduceproton-protoncollisionsatupto14TeV;andisexpectedtodeliveran instantaneousluminosityof10 34 cm )Tj /T1_0 7.97 Tf (2 s )Tj /T1_0 7.97 Tf 6.59 0 Td (1 atthatenergy. 26

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CHAPTER 3 THECOMPACTMUONSOLENOID 3.1Introduction TheCompactMuonSolenoid(CMS)[ 31]isageneralpurposediscoverymachine builttostudycollisionsproducedbytheLargeHadronCollider(LHC),partofthe EuropeanOrganizationforNuclearResearch(CERN). Thedetectoriscylindricallyshaped;withadiameterofalmost16mandalengthof approximately21.6m.Intotal,ithasamassofapproximately12,500metrictons. 1 The CMSdetectorisillustratedinFigure 3-1. Figure 3-1.CutawayviewoftheCMSdetector. Itisimpossibletodirectlyobservemanyoftheinteractionsgoverningsubatomic physics,particularlywhenstudyingexoticnewformsofmatterandenergyinacollider environment.Mostoftheobservableparticlesproducedinahighenergycollision 1 That is,nearlyaquarterasmuchastheRMSTitanic,whichdisplacedabout 52,000metrictons[ 38].The6000passengerOasisoftheSeasthelargestcruiseship everbuiltatthetimeofthiswritingdisplacesapproximately100,000metrictons[ 39]. 27

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are not,infact,directparticipantsinacollision;nevertheless,sufcientlyprecise measurementsontheobservablesofthoseparticles(energy,position,mass,etc.) allowsforsomeinfererencesintothelikelynatureoftheunderlyingphysics.Thegoal oftheCMSdetector,then,istoreconstructthephysicsofacollisionstep-by-step;with eachlayerofsubdetectorsoptimizedtoperformaparticularkindofmeasurement,while affectingotherattributesoftheparticipatingparticlesasminimallyaspossible(soasnot tobiasanyothermeasurements). Attheheartofthemachineisahelium-cooledsuperconductingsolenoid,which bendsthepathofchargedparticles;allowingthemomentaofindividualchargedparticlestobeestimatedpreciselyfromtheircurvaturethroughtheinnertrackerandmuon spectrometerregions.ThedetectionelementsofCMS(workingoutwardfromthe beam-line)are:aninnertrackerconsistingofpixelsandsiliconstrips,ascintillatingelectromagneticcalorimeter,asamplinghadroniccalorimeter,and(ofparticularimportance totheuxmeasurement)muonspectrometers.Alsoindicatedinthegurearetheforwardcalorimetersacombinedelectromagneticandhadroniccalorimeterforparticles producedclosetothebeamlineandthepreshowerdetector,whichisconsideredpart oftheelectromagneticcalorimetersystem.ThesesystemsareillustratedinFigure 3-2. Figure 3-2.AsmallsliceoftheCMSdetector.Thelegendindicateswherevarioustypes ofparticlescanbedetectedinCMS. 28

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3.1.1 CoordinatesandGeography Thedetectorislocatedat46 18.57 0 northlatitudeand6 4.62 0 eastlongitude. Thecoordinatesystemusedwithinthedetectorenvironmentaredenedbythecollider ring:the x -axisofCMSisdenedtopointtowardsthecenteroftheLHCring,the y -axis pointsupward(itisactuallyoffsetbyabout0.8 ),andthe z -axisisdenedtobeparallel withthebeamlinesuchthataright-handedcoordinatesystemisformed.Sincethe detectorislocatednearthenorthern-mostextentofthering,the x -axispointsroughly southandthe z -axispointsroughlywest. CommoncoordinateanglesinCMSgeometryaretheazimuth(anglewithrespect tothe x -axisinthe xy -plane),denotedby ,andthepolarangle (awayfromthe z -axis).Pseudorapidity, ,isfrequentlyusedasanapproximationoftherelativisticrapidity[ 40 ]withrespecttothebeamline(formasslessparticlesoriginatingatthegeometric centerofthedetector);andasaconvenientreplacementfor ( = )Tj /T1_1 11.955 Tf 11.29 0 Td (ln(tan = 2),since particlesproducedinbeamcollisionstendtobedistributeduniformlyin .Figure 3-3 showsacrosssectionofthemachineinthe xy -plane,andFigure 3-4 illustratesone quadrantofthe yz -plane. 3.1.2CavernGeometry Locatedapproximately100munderthesurface,themainCMSdetectorcavern measures51mlong,27macrosswitha24mhigharchedceiling.Separatedbymore than7mofconcretereinforcements(whichalsoactsasradiationshielding),asecond cavernwasbuilttohousethecomputingfacilitiesandsupportpersonnel.Thelayoutof thecavernsandaccessshaftsconstructedforCMSisindicatedinFigure 3-5. CMSisunliketheothermajorexperimentsattheLHCinthatitwasconstructed andtestedabovegroundandthenloweredbysectionintothecavern;ratherthanbeing assembledunderground.WhiletheATLAScavernwasreadyin2003,thecavernsfor CMSwerenotcompleteduntil2005[ 41 42].Pre-assemblingthedetectoraboveground allowedCMStoremainonschedulegiventhe(thenanticipated)2007startdatefor 29

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Figure 3-3.BarrelproleofCMSinthe xy -plane,showingthe coordinate.The changingcurvatureofthe trackindicatestheradius-dependentmagnetic eld(whichreversesdirectioninthereturneldoutsideofthesolenoid). Figure 3-4.QuarterproleofCMSinthe y -z plane,showingthe coordinate. isa simplefunctionofthepolarangle: = )Tj /T1_0 11.955 Tf 11.29 0 Td (ln(tan =2). 30

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Figure 3-5.ThelayoutofcavernsandshaftsbuilttohousetheCMSexperiment[28 ]. LHC.Photographsofthebarecavern,andofadetectorsectionbeinglowered,aregiven inFigure 3-6. Figure 3-6.Left:thecavernandshaft,justcompleted.Right:TheYE+1endcapbeing loweredthroughtheshaft;oneoffteenindividuallyloweredsectionsof CMS(CopyrightCERN[ 43]). 3.2SolenoidMagnet AstrongmagneticeldisacriticalfeaturerequirementofCMS;asitcauses chargedparticlestocurveproportionallytotheirmomenta.The3.8Teslamagnetic 31

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eld 2 of CMSwillcausemeasurablecurvatureoftracksuptoparticlemomentaof severalTeV. TheLN 2 cooledsuperconductingsolenoidmagnetislocatedbetweenthehadronic calorimeterandthemuondetectorsitis12.9mlong,andhasadiameterof5.9m. Thewindingsofthemagnethaveatotalinductanceof14Handcarryapproximately 18,160Aofcurrent.Approximately2.3Gigajoulesofenergyarestoredinthemagnetic eldwhileitisrunning[ 44]. 3.3InnerTrackingSystem Thesilicontrackersystems[ 45]providehighprecisionmeasurementsofparticle momentumandpositionclosetotheinteractionpointforcollisionevents.Thediameter ofthetracker,includingbothsubdetectors(pixelsandstrips),isapproximately2.5m; andincludes76milliondetectorchannels.Intotal,itisthelargestsiliconparticle detectoreverbuilt;withapproximately205m 2 ofactivedetectionarea.Thelayoutofthe trackersystemsisillustratedinFigure 3-7. Figure 3-7.QuarterproleschematicoftheCMSinnertracker. 2 The eldstrengthwasdesignedforandisnominallyreferredtoas4T,howeverhas beenreducedto3.8Tinordertoextendthelifetimeofthemagnet. 32

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The smallestmasspossibleispreferableinthissystem,sinceaddedmaterial increasesthelikelihoodofparticleshowering(whichconfusesthesystem'sabilityto resolveindividualtracks,andotherwisecomplicatespossibleinterpretationsofthe event)andalsoabsorbsenergythatwouldhaveotherwisebeenmeasuredinthe calorimeters. Certainheavyparticlesthatareproducedincollisions,suchasCharmandBeauty mesons,haverelativelylonglifetimes;andparticlesproducedinthedecayofsuch particlesmayoriginatefromapositionthatisdisplacedfromtheprimaryinteraction point.Thetrackershouldbeabletomakemeasurementspreciseenoughtoallowus todeducethepointoforiginofanobservedparticle;soastobeabletodistinguishthe decayproductsofsuchlong-livedparticlesfrompromptlydecayingparticles.Thisisof particularimportancewhenconsideringisolatedleptons.Isolatedleptonsareproduced sparinglyaccordingtotheknownlawsofphysics,howeverareafeatureofsome theoreticalmodelsofnewphysics.Therefore,inadditiontobeingabletodetermine whethertheleptonoriginatesattheinteractionpoint,thetrackershouldalsobesensitive enoughtodistinguishasingle,isolatedparticlefromtwoormoreparticleswithhighly correlatedtrajectories. Finally,andmostimportantly,thetrackermustbedesignedtooperateproperlywith therequirementsofLHCconditions.Itneedstoworkproperlywithinanintensemagneticeld,anditabsolutely must beradiationhard,sinceitisinsuchcloseproximity totheLHCcollisionpoint.Whenoperatingatdesignspecications,LHCcollisionswill produceapproximately1000energeticparticlestraversingthetrackervolumeevery 25ns,comingfrommorethan20proton-protoninteractionsineachbeambunchcrossing.Intotal,anaverageof40billionindividualhighlyenergeticparticleswilltraversethe trackervolume everysecond.Inadditiontosensortoughness,theLHCenvironment alsoplacestoughconstraintsontheminimumreadoutspeedandsensoroccupancyof 33

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the trackertheremustbesufcientchannelsandrapidenoughread-outtoavoidtrack confusionandsaturation. Theinnertrackersub-detectoristhemostcrucialsub-detectorforprecisionmeasurementsofthechargeratio,particularlyathighermomenta,sinceitprovidesextremelyaccuratetrackinginastronguniformmagneticeld. 3.3.1PixelDetector TheCMSPixelsub-detectorisanextremelycompactsystem;ttingentirelywithin acylinderofabout40cmdiameterand1mlong.Despitethissmallsize,pixelsaccount forabout65millionofthetotal76millionchannelsoftheentireinnertracker.Pixels providehighprecisionpositionalinformationinthreedimensions;allowingextremely accuratetracking(resolutionsof10 min r and20 min z arepossible)closetothe beamline.Pixeldataisextremelyusefulformeasuringcollisionanddecayvertices (necessarytoidentifylonglivedmesons)aswellasforfastdeterminationsofparticle isolation. Thetrackerpixeldetectorsarearrangedintoseparatebarrel(TPB)andend-cap (TPE)regions;withthreesensorlayersinthebarrel(atradiiof4.4cm,7.3cm,and 10.2cmawayfromthebeamline)andtwolayersintheend-cap(extendingfrom6cmto 15cmindiameterandlocatedat 34.5 cm and 46.5 cm onthe z -axis),asillustrated inFigure 3-8. Anindividualpixelis100 mby150 minsize.Apixelmodule,depictedinFigure 3-9,consistsof5253pixelsinasensorarraymountedontoabufferedreadoutcircuit. Thereareatotalof1440pixelmodulesinthedetector;768inTPBand672inTPE.In total,thereareatotalofroughly40millionpixels,providing0.92m 2 ofactivedetector coverage. Inthebarrelregion,thedetectorsurfacesareparalleltothedirectionofthemagneticeld.BecauseCMShassuchapowerfulmagneticeld,accumulatedcharges spreadoutandaresharedamongstpixelchannels(theLorentzEffect).Thisenhances 34

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Figure 3-8.SchematicdrawingofthePixelsub-detector. Figure 3-9.Left:diagramofapixelmodule.Right:aphotographofaconstructed module(CopyrightCERN). 35

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position resolutionbeyondthepixelsize,becauseitallowsacentroidtobetfrom severalneighboringpixels(ratherthanabinaryyesornoforasinglepixel).Intheendcap,themagneticeldisperpendiculartothedetectorlayer;therefore,inordertotake advantageoftheLorentzEffect,eachoftheendcaplayersiscomposedof24wedgesin aturbinegeometry;witheachwedgerotatedintothedirectionoftheeldby20 Figure 3-10.Left:photographofhalfofoneendofTPEbeforeinstallationintoCMS (CopyrightFermilab[46 ]).Right:illustrationofhalfofanindividualpixel endcapdisk,alongwithoneofthewedges.Byrotatingthewedgesoutof the x -z plane,theLorentzEffectmaybeutilizedtoimproveresolutions beyondthepixelsize. 3.3.2SiliconStripDetector Furtherawayfromtheinteractionpoint,wheretheuxofparticles(duringcollisions) islower,morecoarsedetectionelementsmaybeused.Thestripdetectorisdivided intoinnerandouterbarrel(TIBandTOB,respectively)andend-cap(TEC)regions.The layoutofthestripsdetectorisgiveninFigure 3-11. TrackerInnerBarrel. TIBrangesbetweenaradiusof20cmand55cminfour layers(thersttwoofwhichprovidea100mradstereomeasurement);andextends to z = 65cm.Thecellsizesvary,butarearelativelylengthy7-12.5cmby80 m. 36

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Figure 3-11.Cutawayviewshowingonehalfofthesiliconstripsubdetector. Figure 3-12.Examplesoftrackerstripmodulesfromtheouterbarrelandend-caps (CopyrightCERN[43]). 37

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The inter-stripdistance(strippitch)ofTIBvariesfrom80-120 m.Despitehaving sensorsroughly100timesaslargeasthepixels,duetoitsincreaseddistancefromthe interactionregion,TIBisabletomaintainnomorethanabout3%occupancyperbunch crossing(atLHCdesignluminosity)andboastsapositionalresolutiononlyslightly worsethanthepixels,at23-34 min r )Tj /T1_1 11.955 Tf 11.95 0 Td ( and23 min z Figure 3-13.Aphotographofamock-upofalayerofthetrackerinnerbarrel (CopyrightCERN[43]). TrackerOuterBarrel. ThesixlayersofTOBsitbetweenaradiusof55cmand 120cm,withtheirfurthestextentto z = 110cm.Aswiththeinnerbarrel,thersttwo layersofTOBprovideastereomeasurement.Thecellsizeofanindividualdetector elementis25cmby180 m;howeverdespiteit'slargesize,atthisdistancefromthe interactionpoint,sensoroccupancyissub-percent.Positionalresolutionintheouter barrelisapproximately35-52 min r and52 min z TrackerEnd-Cap. TECconsistsofninedisks,arrangedalongthe z axisbetween 120cmand280cm.Eachcellintheend-capisupto20cminlengthwithastrippitch ofupto200 m.EachTECdiskhassixteenpetalsofsensorelements(eightoneach 38

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Figure 3-14.AphotographofthetrackerouterbarrelreadyforinsertionintoCMS (CopyrightCERN[43]). side),asshowninFigure 3-15 ,whicharedistributedintosevendistinctrings(denedby arangeofradii). Figure 3-15.Left:illustrationoftwoTECdisks(inseries);eachisequippedwitheight petalsperside.Right:photographofatestbenchassemblywiththree ringsofpetals(CopyrightCERN). 3.4Calorimetry Beyondthesilicontracker,thoughstillwithinthesolenoid,areseparateelectromagneticandhadroniccalorimetersub-detectors.Becausethesesystemsarecompletely 39

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Figure 3-16.Aphotographofoneofthetwotrackerend-caps(TEC),installedina rotatingcradle(CopyrightCERN). containedwithinthesolenoid,theymustbeextremelyresistenttomagneticeldsa non-trivialrequirement,particularlyforelectronics. Unlikethetrackersystemwhichisdesignedtobelight-weight,thecalorimetersare asdenseaspossibleinordertoabsorbthemaximumamountofenergy;this,ofcourse, alsoimpliesthattheymusthaveagreatdealofradiationhardness.Althoughthereare farfewerchannelsinthecalorimetersthanintheinnertracker,calorimetertechnology musthaveaveryquickresponseinordertokeepupwiththeLHCcollisionrate. 3.4.1ElectromagneticCalorimeter Theelectromagneticcalorimeter(ECAL)[47 ]consistsoftwotechnologies:crystal scintillatorsinthebarrelregionandbothcrystalsandacomplementarysiliconstrip preshowersystemintheend-cap.Intotal,thesub-detectorcontainsnearly90tonsof scintillatingleadtungstate(PbWO 4 )crystal(approximately80,000individualcrystals). ECALprovidesexcellentenergyresolutionforelectronsandphotonsof = E = 3%= p E b 0.3% (typical),andgranularitiesofaround2cm.Eachcrystalusedin 40

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CMS is23cmlong;crystalsinthebarrelregionhaveacross-sectionalfootprintof 2.05cm 2.05cm,whilethoseintheendcaprangeinsizefromabout1.8cm2.0cmto 2.7cm 2.9cm.ThelayoutofthedetectorisindicatedinFigure 3-17 Figure 3-17.QuarterviewofECALlayout. Figure 3-18.Withsufcientenergyandinthepresenceofahigh-Z medium(suchas leadtungstate),ionizingparticles(suchaselectrons)willreadilyradiate photons;whilephotonswilldecayto e + /e )Tj /T1_0 11.955 Tf 10.41 -4.34 Td [(pairs. Drawingnottoscale Detectortechnology. Whenphotonsorchargedparticlespassthroughhigh-Z materials,anelectromagneticshowermaydevelopfromColoumbinteractions,inducing theradiationofphotonsande + -e )Tj /T1_0 11.955 Tf 10.41 -4.34 Td [(pairs(whichinturnalsoshower).Thisprocess repeatsuntiltheenergyofeachproducedparticlefallsbelowthethresholdfornew pair-production;atwhichpoint,theremainingsoftelectronsandphotonsareabsorbed 41

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b ythecrystal.Asthecrystalabsorbsenergy,itemitslightwhichisthencollectedby photodetectorsonthebackofthecrystal.Thetotalamountoflightmeasuredinthe photodetectorsisthenproportionaltotheenergyoftheincidentparticles. Figure 3-19.Left:photoofasingleECALcrystalwithsensors(nexttoahousekeyfor scale).Right:photoofECALcrystalswithsensorsinstalled (CopyrightCERN). Leadtungstatecrystalshaveashortradiationlength, X 0 =0.89cm,sothat evenhighlyenergeticshowerswillbestoppedwithintheirlength;andaMoliereradius (indicatingthecharacteristic spread ofanelectromagneticshowerinthematerial)ofjust 2.2cm,whichishelpfultolocalizethelikelyentrypointoftheparticles. Thematerialisafastscintillator;emittingapproximately85%ofitslightyieldwithin therst20nsofaparticletraversingit.Althoughthetotallightyieldofthecrystals willdecreaseasitisexposedtoradiationfromLHCcollisions;thephotodetectors aresensitiveenoughtoallowrecalibration,andresolutionsarenotexpectedtosuffer becauseofit. ECALBarrel. WithinEB,thereare61,200individualECALcrystalsarrangedby5 5arraysinto144modules.Fourmodulesmakeupaunitcalledasupermodule;there areatotalof36supermodulesinECALeachoneproviding20 ofcoverageoverone halfofthebarrel.AschematicoftheEBsub-detectorisgiveninFigure 3-20. PhotographsofasingleEBmodule,asupermodule,andanentirehalf-barrel assemblyareshowninFigures 3-21 and 3-22. ECALEnd-cap. Insteadofmodulesandsupermodules,thetwoECALend-caps areconstructedfromfourdee(half-moon)structures;twoperside.Eachdeecontains 42

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Figure 3-20.DesignofECALBarrel(EB) Figure 3-21.PhotoofapartiallycompletedEBmoduleonatestbench (CopyrightCERN). 43

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Figure 3-22.Left:photoofasingleEBmoduleonatestbench.Right:severalmodules combinedtoformasupermodulemountedontoarotatingcradle (CopyrightCERN). 1385 5supercrystals,foratotalof3450crystalsperdeeand14,950forallofEE.The layoutofEEisindicatedinFigure 3-23.Adee,withseveralEEsupercrystalsinstalled,is showninFigure 3-24. Figure 3-23.DesignofECALEnd-cap(EE) Pre-ShowerDetector. Inordertoimprovedistinguishabilitybetweenneutralpions fromphotons,apre-showerdetectorisinstalledinfrontoftheendcapcrystals.Thepreshowerdetectorcontainstwolayersofleadconvertersandsiliconstripdetectors.Since 0 mesonsdecaytodi-r 0 'smaybedistinguishedfrompromptphotonsbybroader chargedistributionsonthestrips. 44

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Figure 3-24.FourECALEnd-cap(EE)supercrystalsmountedonadee.Eachdeehas 138suchsupercrystals(CopyrightCERN). Figure 3-25.PhotographofanECALpreshowermoduleonatestbench (CopyrightCERN). 45

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3.4.2 HadronicCalorimeter Thehadroniccalorimeter(HCAL)[48]consistsofaaconventionalsamplingtypecalorimeterthroughoutthebarrel(HB)andforwardend-cap(HE)regions,and aquartzbersub-detectorunitinthe very forwardregion(HF).Itisdesignedtobe as hermetic aspossiblethatis,havingthelargestpossiblecoverage.Havinga hermeticcalorimeterallowsfortheindirectobservationofundetectableparticlessuchas neutrinos(bybalancingthetotalamountoftransverseenergymeasuredintheproducts ofacollision). Thecalorimeterusesthicksteelandbrassabsorbersinterleavedwithplasticscintillatortiles.Particlespassingthroughtheabsorptionlayersmayinteractwiththeheavy nucleiofthedensematerialsandwillshower;theresultingsprayofparticlespassing throughthescintillatorlayerscausethemtoemitultra-violetlight.Thislightproduced inthescintillatorsisconvertedtovisiblelightby1mmdiameterwavelength-shifting bersandcarriedtohybridphotodiodestoprovideread-out.Ahybridphotodiodeisa photocathodeheldathighvoltage(-8kV)ashortdistance(3.3mm)awayfromasilicon photodiode;thehighvoltageacceleratesphotoelectronsproducedbythescintillatorlight andresultsinatotalsignalgainofapproximately2000. Brass 3 waschosenasthemainabsorbermaterialforHCALbecauseitprovides sufcientdensity(8.53g/cm 3 ,yieldinganinteractionlengthof16.42cm)whilehaving excellentmachinability. HCALBarrel. HBconsistsofbrassabsorber(either5.05cmor5.65cmthick), andfrontandbackplatesofsteel,4.0cmand7.5cmthickrespectively,whichprovide additionalrigidityandstrength.Fourteenofthescintillatorlayersare3.7mmthick, howevertheinnerandouterlayersare9mm(16layerstotal).Itisconstructedfrom 3 Specically ,70%Cu,30%ZnC26000/cartridgebrassmuchofitmelteddownfrom artilleryshellscontributedbytheRussianNavy. 46

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Figure 3-26.Whenhighlyenergetichadronsscatteroffofnucleiinmatter,thecollision producesasprayofparticlesincludingmorehadronssuchasneutral pions(dashedlines);chargedpionsorkaons(solidlines),whichmay collidewithmorenuclei,creatingacascadeeffect.Asitdevelops,the resultingshowerwillproducelightwithinthescintillatortilesproportionalto thenumberofparticlesinthecascade,whichisinturnproportionaltothe energyoftheoriginalhadron. 36wedgesformingtwohalf-barrels;eachwedgeisboltedtogether,leavingagapofat most2mmbetweenadjacentwedges.Thescintillatorsarereadoutin16 regions. ThegranularityofHCALissquareinthebarrelregionin and ,with = 0.087 0.087.Itprovidescoverageupto j j =1.3. Figure 3-27.Left:aseriesofHBwedgesawaitingassembly.Right:mergedtogetherto formtheHBsub-detector(CopyrightCERN). HCALEndcap. TheHEsub-detectorcontains7.9cmthickbrassabsorberand 9mmscintillatortiles.Thelayersareafxedtoa10cmthicksupportplate,whichis mountedtotheironreturnyoke.GranularityinHEvariesfrom =0.087to0.35and 47

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from 0.087to0.175radians,andthesub-detectorprovidescoveragefrom j j =1.3 to j j =3. Figure 3-28.PhotographoftheHCALEnd-Cap(CopyrightCERN). OuterHadronicCalorimeter. Theouterhadroniccalorimeter(HO)isasampling calorimeterplacedoutsideofthesolenoidwhichactsasatail-catcherforextremely highenergyjets;thatis,forparticleswhichcouldnotbecompletelyabsorbedwithinthe bulkoftheinnersystem.Ratherthanahalf-barreldesignliketheinnercalorimeters, HOismountedtotheringsoftheironreturnyoke;itisthereforeseparatedintove sections(oneforeachofthevewheelsofCMS).Itconsistsofasinglescintillator layerat r =4.07 m mountedontopofa19.5cmironabsorberforthefull range,and anadditionalscintillatorlayermountedontheundersideoftheironintheverycentral region.BecauseitismeantasacomplementarydetectortoHB,itsgranularityand and parametersarematchedtothoseofHB. ForwardCalorimeter. HFprovidescoverageuptoan =5.0,withagranularity of =0.175 0.175.Becauseoftheextremeradiationlevelsnearthebeam lineandintheforwardregion,traditionalshowersamplingcalorimetersarenotsuitable; aCherenkovlightcountingcalorimeterisusedinstead.Inthissub-detector,ironis usedasanabsorbermaterial;whenchargedparticlesinteractwiththeiron,theywill beginshowering(eitherelectromagneticallyorhadronically).Theresultingshowerwill 48

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r adiatephotonsastheypassthroughthequartzbers(sincequartzhasahighindexof refraction,chargedparticleswillemitCherenkovlightastheypassthroughthebersif theyaretravelingfasterthanthelocalspeedoflight)whicharearrangedparalleltothe z -axis.ThethresholdforCherenkovemissioninquartzisonly190keVforelectrons. Becauseelectromagneticshowersdevelopmuchmorequicklythanhadronic showers,itispossibletodistinguishincidentelectromagneticparticlesfromhadronic particlesbyhavingbersofdifferentlengthsinHF.TwoberlengthswerechosenforHF, calledlongandshort,whichare1.65mand1.43minlength,respectively;withthe shorterberbeingdisplacedawayfromtheinteractionregion.Theratioofmeasured energyinthetwolengthsofbers(longtoshort)givesagoodindicationofwhetherthe showerishadronicorelectromagnetic;asanelectromagneticshowerwillleavemuch moreenergyinthelongberthanintheshortber. Figure 3-29.PhotographofwedgesoftheForwardCalorimeter(HF)awaitinginstallation (CopyrightCERN[43]). 3.5MuonSpectrometers GoodmuonresolutionisakeydesigngoaloftheCMSdetector;asmuonsarea featureofmanytheoreticalmodelswhichwillbestudiedatCMS(suchasSupersymmetry,UniversalExtraDimensions,etc.).Forthisanalysis,themuonspectrometer 49

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systems [ 49]ofCMSareusedtoprovidetriggeringcapabilities,aswellastracking,to supplementtheinnersilicondetectors.Themuonsystemsaredividedupintoaseries ofvewheelsinthebarrelregionandtwoend-caps,asmaybeseeninFigure 3-30 Figure 3-30.Quarterviewshowingthemuonsystem. Themuonsub-detectorconsistsofthreeseparatetechnologies:ResistivePlates (RPC),DriftTube(DT),andCathodeStrips(CSC).Drifttubesprovideaninexpensive solutionwhichworkswellwithlowoccupanciesandinuniformmagneticelds;sothey areusedinthebarrelregion.Thecathodestripchambersfunctionwelleveninrapidly changingmagneticeldsandwithhigherparticleuxes;hencetheyareinstalledinthe end-caps.Resistiveplatechambersareasimplertechnologyusedinboththeforward (RPCf)andbarrel(RPCb)regions,andprovidesacomplementarysystemfortimingand triggeringpurposes.Thechambersareinstalledinfourseparatestations,orlayersof chambers;onestationoneachofthevewheelsofCMSinthebarrelregionandfour stationsdeepintheend-caps.Eachofthestationsismountedtotheironyokes.The 50

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combined resolutionformuons,includingboththemuonspectrometersandtheinner tracker,isindicatedinFigure 3-31. Figure 3-31.Muonmomentumresolution,includingboththeinnertrackerandthemuon spectrometers.Left:thebarrelregion.Right:theend-capregions[61 ].This resultisfordesignusageoftheCMSdetector(thatis,muonsproducedin collisions).Thesituationisn'tassimpleforcosmicmuons,wherethe resolutionhascomplexdependenciesonthelocationandanglesofparticle incidence. 3.5.1DriftTubeChambers Thedrifttubechambersareconstructedfromaluminumcathodetube(1.3cm4.2cm) withacentralgold-plated,50 mstainlesssteelanodewire,andlledwithAr/CO 2 gas ina85-15mixture.Thereareeithertwoorthreesuper-layers(SL)inaDTchamber; twoprovide r )Tj /T1_3 11.955 Tf 12.47 0 Td ( measurementsandathirdone,presentonlyfortheinnerthreestations,providesameasureofparticle z .AsingleSLismadeupoffourlayers(consisting ofawireandatube).Intotal,therearethereforeeither8or12detectionlayersina singleDTchamber.BecausetheDTadoptedanessentiallyframelessdesign,rigidity andstructureisprovidedbyanaluminumhoneycomblayerinthecenterofthechamber. Thereareatotalof250DTchambersinstalledatCMS,dividedupintothe5wheelsand 12 sectors. 51

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Figure 3-32.Left:photoofDriftTube(DT)chambersawaitingshipmenttoCERN.Right: asinstalledinthebarrelregion(CopyrightCERN). Whenchargedparticles(typicallymuons,sincemostotherparticleswillbetrapped withinthecalorimeters)passthroughthegas,theywillknockelectronsfreefromthe gas.Ahighvoltagebetweenthewireandthetubewillcauseanelectronavalanche; astheelectronwillfreeadditionalelectronsonitspathtowardstheanodewire.The resultingchargebuild-uponthewirecanberead-outtoprovideasignalforthechamber.TypicalspatialresolutionfortheDTsystemis250 m(aslowas100 min r )Tj /T1_1 11.955 Tf 12.25 0 Td (), withatimingresolutionof5nswhichiswellmeasurablebecausethedriftvelocityfor electronsinAr/CO 2 isknownprecisely(5.4cm/sat1.8kV;foramaximumdrifttimeof 380ns). 3.5.2ResistivePlateChambers TheRPCchamberareadouble-gapresistiveplatetechnologywhichprovides ultra-fast(1ns,muchlessthanthe25nscollisionfrequency)timinginformation.Anode strips(runningparalleltothebeam)separatethetwogapsandprovideacommon readout.Thereareatotalof480RPCchambers;dividedupintosixlayersinthebarrel region(whicharedistributedamongstthefourmuonstations)andthreelayersinthe end-capregion.TheRPCchambers,thoughlessaccuratethantheDTchambers, 52

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pro videaninvaluablesourceofinformationregardingtheoverallmuontriggering performanceofCMS. 3.5.3CathodeStripChambers TheCSC'saremulti-wireproportionalchambersconsistingofsevencathode layers,milledtohaveaconstant alongthelengthofthetrapezoidalchamber, interleavedwithsixgold-platedtungstenanodewirelayers.Thechambersarelledwith Ar/CO 2 /CF 4 gasina40-50-10mixture.Thereareatotalof468chambersdistributed betweenthetwoend-caps,withanadditional72chambersplannedforafutureupgrade. Eachstationprovideseither10 or20 ofcoveragein andtheentiresystemcovers 0.9 < j j < 1.2.Spatialresolutionsof100-200 marepossibleintheCSC's.Asin theDTchambers,chargedparticlestraversingtheCSC'swillionizethegasandfree electrons,whichavalancheinthepresenceofahighelectriceldtowardstheanode wires.Thechargescollectedontheanodewiresinduceareectedimagechargeon thestrips,whichcanbeintegratedinordertondthecentroid(mostlikelypositionof theparticleposition)foranaccuratemeasureofthe positionoftheparticle;while thedifferentialsignalobtainedfromtheanodewiresyieldafastresponsefortiming purposesaswellasameasureofthemuon CommissioningwithCosmics. AlthoughtheCSCdetectorsarenotsuitablefor useinthismeasurement(incidentcosmicmuonsareprimarilyvertical,andtherefore paralleltotheiractivedetectionsurfacesleadingtounpredictablebehaviorandpoor efciencies),theyhavebeenpartiallycommissionedoncosmicmuonsbefore.In2004, severalCSCchamberswereusedinacosmicmuontestattheUniversityofFlorida. Ateststandwasconstructed,andCMS-liketriggeringlogicwassimulated. 4 Withthe 4 The authorcontributedtobothefforts;machiningthenecessarysteelextenderarms forthestand,helpingtoinstallandcablethescintillatorpanelsusedtoprovidethetriggeringsignal,andalsodesigningandassemblingtheNIMcrateusedtoprovidetriggeringlogic. 53

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absence ofbeam,cosmicmuonsprovidedausefulsourceoftracksfortestingand calibratingthechambers.TheteststandisillustratedinFigure 3-34. Figure 3-33.Photographofadiskintheend-capmuonsystem(CopyrightCERN). Figure 3-34.ThiscosmicteststandwasconstructedattheUniversityofFloridain supportofCSCcommissioning. 54

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CHAPTER 4 CHARGERATIOANALYSES Thecosmicmuonchargeratioisameasureoftherelativenumberofpositiveand negativemuonspresentwithinthecosmicmuonspectrum.Becausefewmachines existthatcanprovideprecisionmeasurementsofthemomentaofindividualcharged muonsintheGeVtoTeVenergyrange, 1 themeasureofthisquantityremainsanarea ofsomeinterestintherangesofenergiestowhichCMS,withitslargesizeandpowerful magneticeld,hasthecapabilitytoaccess.Threeseparateanalyseswereperformed tomeasurethechargeratioatCMSthoughjustoneisdescribedindetailinthis dissertation(theoneintroducedinSection 4.2.2).Inthischapter,allthreeanalysesare brieyintroduced. 4.1TheMTCCAnalysis Therstanalysis[ 50, 51]wasperformedondatacollectedfromtheMagnetTest andCosmicChallenge(MTCC)exercise[ 5254 ],conductedaspartofcommissioning onthepre-assembleddetectorattheendof2006,whileitstillsatonthesurfaceofthe earth.Around15MeventswererecordedduringMTCCinrunswithastablemagnetic eldofatleast3.67T. Duringpre-assembly,onlyasmallfractionofthedetectorwasinstrumented; assuch,onlythebottomsectorsoftwooutofthevewheelsofDTchamberswere availablefortrackreconstruction,asillustratedinFigure 4-1 (bottom).Evenwith thelimiteddetectorarea,theprobabilityofchargemisassignmentissmallforlowmomentummuons.Athighermomenta,resolutioneffectsincreasethechanceof randomchargemisassignment;resultinginanarticiallylowvalueforthecharge 1 The twocommonlystudiedregimesareformuonswithalowenoughenergytobe curvedinsmallorweakmagneticelds;andextremelyenergeticmuons,whichcanbe measuredusingcalorimetry. 55

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r atio. 2 Todemonstratethiseffect,theparameterizedchargeratio(Equation 1)has beenplottedalongwithvariousassumptionsontherateofchargemis-assignment at200GeV/cinFigure 4-2,assumingasimple,linearlyincreasingprobabilityformisassignment. Upto200GeV/c,therateofchargemis-assignmentislowenoughtobesafely estimatedandcorrectedforusingMonteCarlosimulations.Onlymuonsreconstructed withinasymmetricalducialvolumewereacceptedforanalysis.Approximately330k outoftheoriginal15Mcosmicmuoneventsremainafterallselectionrequirementshave beenapplied. 4.2TheCRAFTAnalyses TwoanalyseswereconductedondatafromCosmicRunatFourTesla(CRAFT) exercise[ 55],collectedbetweenOctober17thandNovember11th,2008.During CRAFT,theentiremachinewasinstrumentedandinstalledunderground.Oneofthe analysesusedonlymuonsystemhitsfortracking,whiletheotheranalysisusedboth muonsystemandtrackerhits.Thekindsoftracksusedinbothanalysesareillustrated inFigure 4-1. Cosmicmuoneventswerecollectedonanopen 3 muontrigger[ 56]path,with triggersoriginatingineitherofthebarrelsub-detectors(DTorthebarrelRPC).Approximately270Mcosmicmuoneventswererecordedonthesetriggers.Forbothanalyses, asymmetricselectionisappliedwithrespecttothe yz -plane;removingmuonsfromconsiderationiftheyhaveatrajectorythroughthetwoasymmetricauxiliaryaccessshaftsat 2 Since thechargeratioisgreaterthanone,therearemorepositivelychargedmuons thatcanbemis-reconstructedwithanegativechargethantherearenegativelycharged muonsthatcanbemis-reconstructedashavingapositivecharge. 3 Thatis,nomomentumrequirement. 56

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P oint-5,orthroughthemirrorimageofthoseshafts.Noselectionisappliedtothemain accessshaft(whichissymmetricinthe yz -plane). 4.2.1AnalysiswithStand-AloneMuons Inthisanalysis[57],muontrajectoriesarereconstructedusingonlyhitsfromtheDT andRPCbarrelsub-detectors.TrackswithanyhitsintheendcapCSCchambersare rejected,andhitsinthesilicontrackerareusedonlytoestimatemomentumresolution andsystematicuncertainties.Singlelegreconstructionisused,suchthathitsinboth theupperandlowerhalvesofCMSaremergedintoasingletrackobject;allowingfora longerleverarminthemagneticeld,andthereforeimprovedmomentumresolution.In ordertosuppressthebackgroundfrommulti-muonevents,exactlyonesingle-legtrackis requiredineachevent. Aminimumtransversemomentumof10GeV/ c isrequired;andaminimumof45 hitsintheDriftTubesarerequired,withnolessthan20hitseachineitherthetopor thebottomofthedetector.Furtherselectionsareappliedonthetrack 2 ,theimpact parameterinthe xy -plane(lessthan100cm,suchthatthesilicontrackermaybeused toestimatemuonsystemdetectorperformance),themaximumdistance(atthepointof closestapproach)fromthecenterofthedetectoralongthe z -axis(lessthan600cm) andtheangulartrajectories(verticalwithin42 in and60 in ).Approximately1.6M cosmicmuonsoutoftheoriginal270MCRAFTeventsareselected. 4.2.2AnalysiswithGlobalMuons Thisanalysis[5860],basedonglobalmuons,istheprimaryfocusofthisdissertation.ThetrajectoryforaglobalmuonisreconstructedusingbothDTandTOBhits. Inparticular,forthisanalysis,eachcosmicmuonisrequiredtobereconstructedastwo separatetracksegmentsoneaboveandonebelowthepointofclosestapproach eachhavingunsharedhitsinbothDTandTOB.Eachofthetwotracksegmentsmust haveatleastvehitsinTOBandatleast20hitsintheDTsystem;ofwhich,atleast threemustprovideameasurementofthe z coordinate(soastoobtainanaccurate 57

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measurement ofthezenithangle).TheanalysisisrestrictedtothebarrelregionofCMS; therefore,themuontrackmaycontainnohitsineitherthemuonortrackerendcaps.A looserequirementisappliedtothenormalized 2 ofeachofthetwoglobal-muonts. Inordertoeliminatethesmallbackgroundduetomulti-muonshowerevents;exactly twotrackhalvesmustbeintheevent,andthezenithanglebetweenthemisrequired tomatchwithin j cot j < 0.2.Finally,theaveragetransversemomentumofthetwo trackhalvesisrequiredtobegreaterthan10GeV/ c .Outof270M,approximately245k muonspasstheselectionrequirements. 4.3Summary Forthenalmeasurementofthecosmicmuonchargeratio,theresultsofallthree analysesarecombined.TheMTCCdata(sinceitwascollectedonthesurface)provides agoodresultforthelowestenergies;whicharedifculttoobtaininthelaterdata duetoshieldingbytheearth.Forhighermomenta,thetwoCRAFTanalysesprovide complementaryresults.TheresultsofallthreeanalysesarecombinedinChapter 7. 58

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Figure 4-1.Typesoftracksusedineachofthethreeanalyses.Upperleft:the stand-alonemuonanalysisutilizeshitsfrombothhalvesofthemuonsystem. Upperright:theglobalmuonanalysisrequireshitsinboththesilicontracker andthemuonsystem.Bottom:theMTCChadonlyasinglesectoroftwo wheelsinthebottomofthedetectortousefortracking. Figure 4-2.Theeffectofmis-assignmentonthechargeratio.Amis-assignmentrateof 1%,2%,3%,and5%atmuonmomentaof200GeV/cisshown,increasing linearlywithmomentum.ThedetectorperformanceinMonteCarloisused toestimatetheactualformandmagnitudeofchargemis-assignment. 59

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CHAPTER 5 THEGLOBALMUONANALYSIS Thischapterprovidesadescriptionoftheanalysisperformedusingglobalmuon trackscollectedduringCRAFT.Thenalresultsofallthreeanalysesareultimately combinedtoformtheofcialCMSmeasurementofthecosmicmuonchargeratio. 5.1AnalysisOverview Theanalysisisperformedbyrstapplyingselectionrequirementsonthemuons observedwithinthedetectortoensuregoodtrackobjects.Thecollectionofobjects splitatthepointofclosestapproach(PCA)tothe z -axisareindividuallypropagated tothesurfaceoftheearthinordertoestimatetheenergylossesthroughtheearthand detectormaterial.Anunfoldingprocedureisused,whichconsistsofapproximatingthe migrationmatrixwhichactstoconvertatruecountofmuonsattheearthsurfacetoa measuredcountwithinCMSandinvertingit,inordertoderiveanalcountofpositive andnegativemuonsineachbinafteraccountingforallresolutioneffects.Unfoldingis handledseparatelyfortwocases:muoncountsbinnedbytheirmomentum( p )andthe verticalcomponentoftheirmomentum( p cos z ),alwaysasestimatedatthesurfaceof theearth. 5.2SelectionRequirements 5.2.1EventSelection Approximately270millioncosmicmuoneventswerecollectedovertheduration ofCRAFT.Thisanalysisisbasedonasubsetofthatdata;inparticular,eventswere skimmedfortrackerpointingmuontracks:tracksreconstructedintheoutermuon chamberwhichpropagateintoa260cmlong,90cmdiametercylinderattheheartof CMS.Thispropagationcylindersitswellwithinthevolumeofthesilicontracker.Events wererequiredtohavebeencollectedduringrunswithastable3.8Tmagneticeld. Trigger. Anopentriggerpathwasusedathardwarelevel,whichpromotes anyvalidmuontriggercandidates(becausethetriggerestimatesmomentumusing 60

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look-up tablesdesignedfortheLHC,momentum-basedtriggeringisnotpossiblewith cosmics).Becausethisanalysisisbasedonbarrelmuonevents,thetriggeredsample wasfurtherrequiredtohaveatleastonetriggercandidatefromeithertheDTorRPCb sub-detectors. ThemuontriggersystematCMSreportsan and coordinateasmeasuredat aparticulartriggersurface,nominallylocatedatthecenterofachamberinstation two[ 61].ForLHCconditions,thisdataisintendedtorepresentthe and ofthe momentumvectorasitpassesthroughthechambers;howeverforcosmicmuons(since theyarecomingfromabove,andnotconstrainedtopassthroughthegeometriccenter ofthedetector),thiscoordinaterepresentsapointinspacewhichistheintersection ofthe and vector(inCMSdetectorcoordinates)andthesurfacerepresentingthe centerofstationtwo,whichisapproximatedasacylinderwitharadiusof5m. Todeterminewhetheramuontriggercandidatecanbematchedtoatrackfor analysis,thestand-alonemuontrack(theportionoftheglobalmuontrackconsisting onlyofMuonSpectrometerdata)ispropagatedtothecenterofstationtwooftheDT system.Matchingrequiresthat j j< 0.2betweentherecordedpositionofthetrigger andthepositionofthepropagatedstand-alonemuonatstationtwo.Theshapeofthe distributionataradiusof5misdisplayedinFigure 5-1 fordifferenthalves(topand bottom)ofthedetector,andalsoforpositiveandnegativemuons. 5.2.2PhysicsObjectSelection AsdescribedinSection 5.2.1,thepresenceofareconstructedtrackinthemuon spectrometerenteringthetrackervolumeisassumed.Globalmuonsarereconstructed[ 62, 63]fromthecombinedhitsinthesilicontrackerandmuonspectrometers; andonlytracksconsistingofbothkindsofhitsareutilizedintheanalysis.Inparticular,splittracksareused;meaningthatthehitdataisdividedupintoseparatetopand bottomtrackhalves(eachofwhicharealsoglobalmuontracks). 61

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Only muonsinthebarrelregionofCMSareconsidered;therefore,anytracks containinghitsintheTrackerEndcapsorCathodeStripChambersareremoved.Muons musthaveatransversemomentumofatleast10GeV,andbetravelingdownwardalong thedetectory (approximatelypointingdown,intotheearth);suchthatthe oftheir momentumvectorisnegativeatthePCA. 1 Splitting. InSection 5.4,themethodologyforobtainingadata-drivenestimate fordetectorresolutionisdescribed.Aspartofthismethodology,thetrackmustbefully splittablewithinthesilicontracker;inotherwords,theremustbeatleastonehitinthe siliconbothabove and belowthePCA,inordertoconstructseparateupperandlower trackswith unshared trackerhits. 2 Thesplitrequirementismostefcientfortracks passingclosetothegeometriccenterofCMS(andtherebypassingthroughamaximum amountoftrackermaterial),withefciencyrapidlydroppingfordistanceslargerthan about50cm,asmaybeinferredfromFigure 5-2.ThecomponentsofthePCAarethe cosmicmuonanalogsofthe impactparameters traditionallyusedincolliderphysics. Thus,inFigure 5-2 thetraditionalnotationforimpactparametersisused; d 0 referstothe shortestdistancebetweenthetrajectoryoftheparticleandthe z -axis/beam-line,and z 0 referstothedisplacementofthatpointfromthecenterofthedetectoralongthe z -axis. 5.2.3QualitySelection Eachoftheselectionqualityrequirementsareappliedindividuallytothetopand bottomlegsofthereconstructedtracks.Aminimumof20hitsintheDTchamberswere required.AtleastthreeoftheDThitsmustbeinSuperlayer-2,whichmeasuresthe 1 Although cosmicmuonreconstructionisseededassumingdownwardmomentum, occassionallynon-downwardtrajectoriesresult,mosttypicallybecausethemuonhas lowmomentumandisactuallyturnedaroundbythemagneticeldofCMS,orhasbeen back-scatteredoffofmaterialbelow.Moreexoticexplanationsarealsopossible,but exceedinglyunlikely[ 64 ]. 2 StandardsplittracksinCMScosmicmuonreconstructiondonotrequirethelegsto haveunsharedsiliconhits,thusthisisamorestrictselectionrequirement. 62

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z -component ofthelocaltrajectory;whichisnecessaryinordertoobtainasatisfactory measurementofthetrack .WhiletwoTOBhitsareimpliedbythesplittrackrequirement,additionalhitsareeffectiveatreducingchargeconfusion.Sufcientsuppression ofchargeconfusionisobservedwithveormorehitsintheTOB(withdiminishing returnscoupledwitharapidlossofefciencyifmorethanvehitsarerequired).An extremelylooserequirementonthe 2 (1500)isappliedtotrackts,inordertoreject poorlyreconstructedtracks.Thisrequirementwasfoundtoefcientlyremoveevents inwhichtheglobalmuontwouldincorrectlyipthechargeofthemuon. 3 Figure 5-7 showstheefciencyofthe 2 requirementasafunctionof p T ;itisnearly99%forall momentaconsideredinthisanalysis. Withsplittracks,itisnecessarytoverifythatthetwotrackhalvesareindeed consistentwiththesamemuon.Thisnecessitates,rstofall,thatmulti-muonevents (withtheirunavoidableambiguities)aresuppressed,byrequiringexactlytwosplittracks intheevent;oneinthetopandoneinthebottomofthedetector.Evenaftertheremoval ofobviousmulti-muons,itisoccassionallythecasethattwounrelatedtracksmaybe incorrectlybeassociatedwithoneanother;soadditionalmatchingisrequired.Alogical variableisthedifferenceinthe oftheirtrajectoriesatthePCA;howeverthisishighly sensitivetotheestimatesoftheparticlecharge,andwouldhencebiastheestimation ofdetectorresolution.Infact,theonlywaytoavoidbiasingthismeasurementisto restrictthematchingtotrajectoryalongthe z -axis;becausethemagneticeldinthe barrelregionishighlyuniformandparallelto z ,andthusthedetectordoesnotuse thisinformationtoestimatethemomentumorchargeoftheincidentmuontrack.In particular,aselectionrequirementonthecotangentofthetrack (angleoftrajectoryin the rz -plane)isused. 3 This wasoriginallynecessaryduetoabuginthereconstructionalgorithm,since corrected. 63

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The correlationbetweentheestimatorofthecurvatureresolution(d C ,described inSection 5.4)isshownfortwopotentialmatchingrequirements, and cot( ),in Figure 5-8.Whileastrongcorrelationwith isobserved(asexpected),thecorrelation with cot( )isfoundtobeanegligible0.7%.Therefore,norequirementon isused andonlyalooserequirementoflessthan0.2isappliedon cot( )inordertosuppress mismatchesbetweenthetopandbottomlegs.Theperformancedistributionsfor transversecurvatureandchargeconfusionagainstthisvariableareshowninFigure 5-3. 5.2.4SymmetricalAcceptanceSelection BecausecosmicmuonstravelthroughCMSfromtoptobottom,themagneticeld ofCMSalwayssplitsthetrajectoryoftracksaccordingtotheircharges;positivemuons willalwayscurvetooneside,andnegativemuonstotheother.Thus,anyasymmetries arisingfromthedetectororcaverngeometrycanbiasthenalmeasurementofcharge ratio. WhilethemainaccessshaftiscenteredalongtheaxisofCMS,andthusdoesnot contributetoabias,therearetwootheraccessshaftswhichare not centered;giving risetoanunbalancedgeometricacceptance.Inordertoeliminatethebias,asetof parabolicselectionshavebeenappliedwhichvetomuonsprojectedtohavepassed nearorthroughtheseshafts aswellas muonswhicharrivefromthepreciseopposite direction.Theresult,separatedaccordingtotheestimatedmeanenergylossthemuons experienceastheypassedthroughtheearthisindicatedinFigure 5-9.Thetwocases areformuonswhichloselittleenergy(becausetheypassatleastpartiallythrough ashaft)andthosewhichdonot;theselectionrequirementitselfdoesnotdependon energyorthemeanenergyloss. 5.2.5SelectionEfciencySummary Thetotalselectionefciency,beginningfromallmuonspassingthepre-selection requirements(recordedinarunwithastablemagneticeld,hasaMuonSpectrometer trackinthevicinityoftheSiliconTracker),isindicatedinTable 5-1. 64

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The geometryoftheSiliconTrackeris,byfar,themoststringentselectioncriteriafor thisanalysis.Withrespecttoallofthe270Morsocosmicmuoneventscollectedduring CRAFT,thefractionofmuonswhichpropagateintothetrackerislessthanapercent; andonlyabout25%of those aresplittable.Allotherselectionrequirements,iftaken together,aremorethan40%efcientontheremainingsample. 5.3MonteCarloSimulation TheCMSCollaborationhasadaptedacosmicmuongeneratorcalledCMSCGEN (TheCompactMuonSolenoidCosmicGenerator[ 65])fromsoftwaredevelopedforthe L3+Cexperiment;whichgeneratessinglerandomcosmicraymuons(aboveanenergy thresholdof10GeV)atthesurfaceoftheearthbasedondistributionsofmuonenergy andanglesofincidencebasedontheCORSIKA[ 66]airshowerprogram. AmapdescribingthevariousmaterialsbetweentheEarth'ssurfaceandtheCMS detectorisusedtoobtaintheexpectedenergylossofsimulatedmuonsasafunction oftheirenergy,impactpoint,andincidencedirectionatthesurface[ 6769].Only meanenergylossthroughtheearthisconsideredfortheextrapolatedparticles,and nomultiplescatteringhasbeenmodeled;sincethespreadofanglesisconsidereda minoreffectontheincidentspectrumofcosmicmuons.Theresidualmagneticeld surroundingCMS(thoughitmayreachhundredsofgauss)isconsideredasmalleffect onthearrivallocationofmuonsincidentuponthedetector,andisnotincluded.The CMSdetectorresponseissimulatedusingtheGEANT4program[ 70 ],whichtakesinto accounttheeffectsofenergyloss,multiplescattering,andshoweringinthedetector. 5.4CurvatureMeasurement Curvature,denoted C = q =p ,isthemainobservableusedinthisanalysisto measurechargeratio.WithinCMS,however,curvatureoccursonlyinthetransverse plane;therefore,itismoreappropriatetoworkwiththetransversecomponentofthe 65

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momentum 4 instead. Theactualtransversecurvatureofthemuonisestimatedfromthe seperatemeasuresofcurvaturefromthetopandbottomlegsofthesplittracks,asin Equation 5: C T = q p T = 1 2 q 1 p T ,1 + q 2 p T ,2 (5) ..where q 1 and q 2 arethereconstructedchargesand p T ,1 and p T ,2 arethereconstructedtransversemomentaofthetopandbottomlegs,respectively,atthePCA. Becausethemagneticeldisuniformintheregionofthetrackervolume,thecurvatureofthetwotrackhalvesshouldbeidentical;providingtwo(nominallyindependent) measurementsofthesamequantity,andthereforeaperfecthandleforderivingthe resolutionofthemeasurementfromthedataitself.Theresolutiondistributionforthe curvatureinEquation 5 maybeestimatedbythehalf-differenceofthetwoquantities, aswritteninEquation 5. d C = 1 2 q 1 p T ,1 )Tj /T1_1 11.955 Tf 17.25 8.09 Td (q 2 p T ,2 (5) That thisestimatorisanaccuraterepresentationofthecurvatureresolutionmay betestedusingatoyMonteCarloofindependentvariables,centeredonzero.Thistest hasbeenconductedforvariousresolutioncasesintheAppendix,Section A.1 (however, notethatthesetestsapplytoonlytotallyuncorrelatedmeasures).Soastocheckthat nosignicantcorrelationshavebeenintroducedfromtrackttingandreconstruction; theestimatorhasalsobeentestedwitharealisticMonteCarlo,wheretheresolutionof thecurvaturemaybecompareddirectlywiththeresultfromtheestimator.Theresultis indicatedinFigure 5-10. 4 The curvaturediffersfromthetransversecurvaturebyafactorof 1+cot 2 ( ) )Tj /T1_0 5.978 Tf 7.78 3.25 Td (1 2 where is thetrajectoryinthe rz -plane. 66

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Neglecting simulationjitter, d C sim whicharisesfromachargedisagreementowingtoamismatchofsimulatedhitsthetrueresolution, C ,isfoundtobefairlywell modeledbytheestimator, d C ,fortheaggregatetotalMonteCarlosamplepresentedin Figure 5-10 .Dividingthesedistributionsupintobinsoftruetransversemomentum,however,illustratessomediscrepancies;asmaybeseeninFigure 5-12.Thedistributions aretwithGaussianresolutionfunctionsandtheratioofwidths, (d C )to ( C ),are obtained.Theseratios,depictedinFigure 5-11,areusedasacorrection, 5 d C ,tothe resolutionestimator: d C = (d C ) ( C ) d C d C d C (5) The measuredcurvatures, C 1 and C 2 ,arethenpredictedtoliewithinthe(now corrected)resolutionestimator, d C ,ofthetruecurvature.Therefore,theexpressions maybeassertedasinEquation 5. C true 1 2 ( C 1 + C 2 ) (5) C 1,2 = C tr ue d C NotethatthetruecurvatureofthemuonwithinCMSneednotbeestimatedatall forthenalmeasurementofchargeratio,sinceitisreportedontheearthsurface.In Section 5.5,themethodologyforextrapolatingthemeasuredcurvatureswithinCMSup totheearthsurfacewillbedescribed;anditisfromthesepropagatedmeasurements thatthetruecurvature,onthesurfaceoftheearth,isestimated. 5 In fact,thesecorrectionscanevenbepredictedanalytically(tosomeextent)based onthestrengthofthecorrelations,asshownintheAppendix,Section A.2. 67

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5.5 Unfolding VariousmethodsofunfoldingthespectrumincidentuponCMSinordertoarriveat measuresatthesurfaceoftheearthwereconsideredforthisanalysis[ 71 ],including SingularValueDecomposition(SVD)[ 72],Bayesiteration[ 73],andseveralother methods;thoughasimplematrixinversionwasthemethodchosenforthisanalysis. Themomentum-binnedcountsofmeasuredmuons, N measured ,maybeexpressed astheresultoftheactionofamigrationmatrix, M ,appliedtothebinnedtruenumber ofmuons, N true .Thetruebutunknownmigrationmatrixelement, M ij ,givesthe probabilitythatamuonwithatruecurvature C true ,whichbelongsinmomentumbin j ,will bemeasuredwithacurvature( C 1 or C 2 )locatedinbin i .Anestimateofthemigration matrix,denoted e M ,isconstructed(asdetailedinSection 5.5.2)fromthemeasured curvatures.Givenanapproximationforthemigrationmatrix,itispossibletoobtainan estimateforthetruenumberofmuons, e N true ,giventhemeasurednumbersbyaprocess ofmatrixinversion: N measured i = X j M ij N true j e M M (5) e N true i = X j e M )Tj /T1_1 7.97 Tf (1 ij N measured j Themomentumbinsarerepresentedonthesurfaceoftheearth.Thesebinsare chosenempirically,withthemainrequirementbeingthatthespill-over(transferofmuons betweenbinsduetooff-diagonalelementsinthematrix)isminimized: p = ( 30,50,70,100,200,400, 1 ) GeV = c (5) Oneobviousdifferencebetween M and e M isthenormalization,sincethetrue migrationmatrixinvolvesthelossofmuonsastheytravelthroughtheearth( N true 68

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N measured ), andtheapproximationofthemigrationmatrixisbuiltentirelyfromthemeasuredtracks.TheuncertaintyintheresultduetothiseffectisestimatedinSection 6.2.5. 5.5.1PropagationtotheEarth'sSurface Inordertoobtainanapproximationforthemigrationmatrix,itisnecessaryto transferthemeasuredcurvatureswithinCMStoameasureatthesurfaceoftheearth. ThetransversecurvaturesmeasuredatthePCA, C PCA T ,1 and C PCA T ,2 ,arerstconvertedto regularcurvatures, C PCA 1 and C PCA 2 ,asinEquation 5.Thenumericsubscriptindicates thatthetwotermsarenominallyindependentmeasuresonefromthereconstructed tracksegmentinthetophalfofthedetectorandonefromthetracksegmentinthe bottomhalfofthedetector. C PCA 1 = q 1 p T ,1 1 p 1 +cot 2 1 (5) C PCA 2 = q 2 p T ,2 1 p 1 +cot 2 2 ThemeasuredcurvaturesobtainedatthePCAareindividuallypropagatedtothe earthsurface.Thepropagationoccursintwosteps.First,astandardhelicalpropagator isusedtotransferthetracksoutoftheCMSvolume(toaradiusof8m),usingGEANT tosimulatethedetectormaterial,andaccountingforthemagneticeld.Oncethetrack ispropagatedoutofCMS,ananalyticextrapolationtakesthetrackthroughtheshaftand caverngeometry,uptothesurfaceoftheearth.Thisextrapolationislinear(astraight linetothesurface);whichisareasonableapproximation,sincethefringingmagnetic eldoutsideofCMSisfairlyweak(atmostafewhundredGauss),andothereffects (suchasmultiplescattering)produceonlynegligibleerrorsontheanglesoftrajectory, whichmaybeaccountedforinthesystematicuncertainty.Propagationtransformsthe 69

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cur vaturesmeasuredwithinthedetector, C PCA ,tomeasuresofcurvatureontheearth surface, C : C PCA 1,2 )347()222()222()223()222()347(! propagation C 1,2 (5) Tocompletethedeterminationofthemeasuredcurvaturesontheearthsurface, anadditionalresolutioneffectduetonon-uniformenergylossintheearthmustbe accountedfor.Onlymeanenergylossesareestimatedintheextrapolationtotheearth surface;thoughinrealitythereisawidespreadofenergies(referredtoasstraggling) thatmaybelostastheparticlespassthroughtheearth.Inordertoestimatethewidth ofthisspreadofenergylosses,theMonteCarlosimulationwasused,asitwasalready available.MuonswerepropagatedthroughtheCMSvolumeintwoways:onceusing thestandardGEANTsimulation,andonceusingananalyticalextrapolator(similarto theoneusedtotransportmuonsfromCMSuptothesurfaceoftheearth).Whileboth methodsagreedonthemeanenergyloss,GEANTalsoproducesarealisticspreadof energylosses.TherelativeenergyspreadwithintheCMSdetectorwascomputedas thedifferencebetweenthetwocomputedenergylosses,dividedbythemeanenergy lossfromGEANT.Figure 5-13 illustratestheresult:therelativesmearingisfoundtovary from10%uptomorethan20%.Sincetheactualmolasseisfairlyhomogeneousand uniformlydensethatis,comparedwiththeCMSdetector;whichhaslargepocketsof gas,particularlyinthedrifttubesthisislikelyanoverestimationofthetrueeffectof straggling.Thus,aspreadof10%isassumedtoapplytothemeanenergylossthrough theearth,whichisappliedasacorrectiontothedetectorresolution. 5.5.2ConstructionofMigrationMatrix Foreachmuon,thetwomeasuredvaluesforthecurvature, C 1 and C 2 ,arepropagatedindividuallyfromthedetector,asdescribedinSection 5.5.1.Eachofthemeasurementsproducesanentryforthemigrationmatrixtwopermuonwiththecorrespondingtruecurvatureestimatedfromthehalf-sumofthetwomeasurements.Theresulting 70

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histog rams,binnedin p and p cos z atthesurfaceoftheearth,arepresentedinFigures 5-14 and 5-15,respectively.Thecolumn-wisenormalizationofthesehistograms (calledtheresponsematrices)formanapproximation, e M ,ofthetruemigrationmatrix, whichtakesthetruecountofmuonsandconvertsittomeasuredcounts.Theresponse matricesarepresentedinTables 5-2 and 5-3. Table5-1.ThetotalnumberofmuonsinthebarrelregionofCMSsurviving,alongwith boththecumulativeandrelativeselectionefciencies. requirement N (%) rel. (%) good runs 2372101 )-4183()]TJ /T1_0 11.955 Tf -219.45 -14.44 Td (matched trigger 2343585 98.8098.80 twotrackertracks 579183 24.4224.71 N DT 20 463342 19.5380.00 N DT z -hits 3 442713 18.6695.55 N TOB 5 428458 18.0696.78 cot < 0.2 428204 18.0599.94 max 2 < 1500 415173 17.5096.96 p T > 10GeV/c 308390 13.0074.28 symmetricalacceptance 245218 10.3479.52 71

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Figure 5-1.DTtriggermatching distributionsbetweenthestand-alonemuontrack propagatedto5m,andallsimultaneousmuontriggers.Thedashedlineat 0.2marksthepositionofthecut.TopLeft:Upperlegdistributionfor )Tj /T1_0 11.955 Tf -376.41 -18.78 Td [(events.TopRight:Upperlegdistributionfor + events.BottomLeft:Lower legdistributionfor )Tj /T1_0 11.955 Tf 10.41 -4.34 Td [(events.BottomRight:lowerlegdistributionfor + events. 72

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Figure 5-2.PCAparameterdistributionsbefore(blackline)andafter(redhistogram)the removalofmuonswithoutasplittabletrackertrack.Left: j d 0 j.Center: z 0 Right:totaldisplacementofPCAfromgeometriccenterofCMS, q z 2 0 + d 2 0 The PCAfromthetopandbottomtracksarenearlyidentical;therefore,only themeasurementfromthetoplegisdisplayed. Figure 5-3.Left:curvatureresolutionmetric d C vs. cot( )betweentracklegs.Right: chargeconfusionvs. cot( )betweentracklegs.Aselectionrequirementof cot( ) 0.2isapplied. 73

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Figure 5-4.Left:curvatureresolutionmetric d C vs.minimumnumberofTOBhits.Right: chargeconfusionvs.minimumnumberofTOBhits.Aselectioncutofat least5TOBhitsisapplied. Figure 5-5.Left:curvatureresolutionmetric d C vs.numberofDThits.Right:charge confusionvs.numberofDThits.Aselectioncutof20ormoreDThitsis applied. 74

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Figure 5-6.Left:curvatureresolutionmetric d C vs.numberofDThitsinSL2.Right: chargeconfusionvs.numberofDThitsinSL2.SL2isthesuperlayer responsibleforprovidingmeasurementsofthe z -position.Aselectioncutof threeormoresuchhitsisapplied. Figure 5-7.Globalt 2 requirement.Left: 2 ofthepair.Aselectionrequirementof 1500orlessisapplied.Right:selectionefciencyvs p T 75

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Figure 5-8.Behaviorof vs. d C (left)and cot z vs. d C (right).Aselection requirementof cot z 0.2isapplied. Figure 5-9.Positionofincidenceofmuontracks(aspropagated)totheearthsurface; withtheoutlineofthedetectorcavern,shafts,CMS,andtheinnertracker indicated(orthographicview);alongwiththefourappliedparabolicselection requirements.Left:effectofselectionformuonswith E loss < 42GeV;right: effectofselectionformuonswith E loss > 42GeV. 76

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Figure 5-10.Comparisonoftheresolutionproxy d C (blackpoints)withthesimulation jitter d C sim (solidbluehistogram)andthetrueresolution C (hashedred histogram).Left:linearscale.Right:logarithmicscale. Figure 5-11. d C = C ratiosofwidthsfromtheGaussiantsofthecoredistributions,and ratiosofrms,inbinsoftruetransversemomentumatthePCA. 77

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Figure 5-12.Comparisonofthe(q =p T )resolutionestimator d C (blacksolidcircles)with thetruecurvatureresolution C (hashedredhistogram),inbinsoftrue transversemomentumatthePCA.Thecoresofboth d C and C distributionsarettedwithsimpleGaussians. 78

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Figure 5-13.Normalizedenergylossdistributionsformuonspropagatedthroughthe CMSdetector,fromGEANTMonteCarlosimulation.Thedistributionsare ttedwithaGausian(reddashed)andLandau(blue)andthe correspondingtqualitiesandparametersarereported 79

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Figure 5-14.Migrationhistogramwhichconnectsmeasuredcurvatureswiththe estimationsoftruecurvatureonthesurfaceoftheearthin q = p bins.(Left) Finebinningforillustration.(Center)Actualbinning.(Right)Off-diagonal spill-overbycolumn. Figure 5-15.Migrationhistogramwhichconnectsmeasuredcurvatureswiththe estimationsoftruecurvatureonthesurfaceoftheearthin q = p cos z bins. (Left)Finebinningforillustration.(Center)Actualbinning.(Right) Off-diagonalspill-overbycolumn. 80

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T able5-2.Responsematrixwhichtransformseventcountsinbinsoftrue p (x -axis)toeventcountsinbinsofmeasured p (y -axis).Matrixelementsthatremainsmallerthan10 )Tj /T1_0 7.97 Tf 6.59 0 Td (20 arenotrepresentedhere. )Tj /T1_0 11.955 Tf (30 0.9748 0.0231 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 530.08 -580.9 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 234.57 387.69 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 578.6 -580.9 cm 0 0 m 0 14.44 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 580.59 -580.9 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 234.57 438.2 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 629.1 -580.9 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 234.57 487.05 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 678.29 -580.9 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 234.57 536.24 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 727.48 -580.9 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 234.57 585.43 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 776.68 -580.9 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 234.57 634.62 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 825.87 -580.9 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 234.57 683.81 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 875.06 -580.9 cm 0 0 m 0 14.44 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 240.94 -581.1 cm 0 0 m 634.12 0 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 240.94 -595.75 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 249.41 91.57 Tm ()Tj /T1_0 11.955 Tf (50 0.0248 0.8925 0.0516 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 530.08 -595.75 cm 0 0 m 0 14.45 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 249.41 374.06 Tm (0.0003 0.0002 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 678.29 -595.75 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 249.41 536.24 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 727.48 -595.75 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 249.41 585.43 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 776.68 -595.75 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 249.41 634.62 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 825.87 -595.75 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 249.41 683.81 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 875.06 -595.75 cm 0 0 m 0 14.45 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 240.94 -595.95 cm 0 0 m 634.12 0 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 240.94 -610.59 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 264.26 91.57 Tm ()Tj /T1_0 11.955 Tf (70 0.0002 0.0843 0.9071 0.0377 0.0001 0.0003 0.0002 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 727.48 -610.59 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 264.26 585.43 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 776.68 -610.59 cm 0 0 m 0 14.45 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 264.26 620.65 Tm (< 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 875.06 -610.59 cm 0 0 m 0 14.45 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 240.94 -610.79 cm 0 0 m 634.12 0 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 240.94 -625.43 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 279.1 84.92 Tm ()Tj /T1_0 11.955 Tf (100 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 333.32 -625.43 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 279.1 191.27 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 382.51 -625.43 cm 0 0 m 0 14.44 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 279.1 226.83 Tm (0.0413 0.9500 0.0404 0.0003 0.0002 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 825.87 -625.43 cm 0 0 m 0 14.44 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 279.1 670.18 Tm (0.0001 )Tj /T1_0 11.955 Tf (200 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 333.32 -640.28 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 293.95 191.27 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 382.51 -640.28 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 293.95 240.46 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 431.7 -640.28 cm 0 0 m 0 14.45 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 293.95 276.02 Tm (0.0121 0.9468 0.0469 0.0005 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 825.87 -640.28 cm 0 0 m 0 14.45 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 293.95 669.84 Tm (< 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj /T1_0 11.955 Tf (400 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 333.32 -655.12 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 308.79 191.27 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 382.51 -655.12 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 308.79 240.46 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 431.7 -655.12 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 308.79 275.68 Tm (< 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 0.0125 0.9497 0.0016 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 678.29 -655.12 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 308.79 522.27 Tm (< 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 776.68 -655.12 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 308.79 634.62 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 825.87 -655.12 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 308.79 669.84 Tm (< 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 400 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 333.32 -671.96 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 325.63 191.27 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 382.51 -671.96 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 325.63 240.46 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 431.7 -671.96 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 325.63 289.65 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 480.89 -671.96 cm 0 0 m 0 14.45 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 325.63 324.87 Tm (< 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 0.0016 0.9463 0.0113 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 776.68 -671.96 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 325.63 634.62 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 825.87 -671.96 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 325.63 683.81 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 875.06 -671.96 cm 0 0 m 0 14.45 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 240.94 -672.16 cm 0 0 m 634.12 0 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 240.94 -686.8 cm 0 0 m 0 14.44 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 340.47 94.22 Tm (200 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 333.32 -686.8 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 340.47 191.27 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 382.51 -686.8 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 340.47 240.46 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 431.7 -686.8 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 340.47 275.68 Tm (< 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 0.0001 0.0003 0.0495 0.9463 0.0112 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 776.68 -686.8 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 340.47 634.62 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 825.87 -686.8 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 340.47 683.81 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 875.06 -686.8 cm 0 0 m 0 14.44 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 240.94 -687 cm 0 0 m 634.12 0 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 240.94 -701.65 cm 0 0 m 0 14.45 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 355.31 94.22 Tm (100 0.0001 < 10 )Tj /T1_0 7.97 Tf (4 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 530.08 -701.65 cm 0 0 m 0 14.45 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 355.31 374.06 Tm (0.0003 0.0009 0.0420 0.9517 0.0404 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 70 < 10 )Tj /T1_0 7.97 Tf (4 < 10 )Tj /T1_0 7.97 Tf (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 431.7 -716.49 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 370.16 289.65 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 480.89 -716.49 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 370.16 338.84 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 530.08 -716.49 cm 0 0 m 0 14.44 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 370.16 374.06 Tm (0.0003 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 629.1 -716.49 cm 0 0 m 0 14.44 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 370.16 473.42 Tm (0.0001 0.0369 0.9079 0.0875 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 50 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 333.32 -731.34 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 385 191.27 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 382.51 -731.34 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 385 240.46 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 431.7 -731.34 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 385 289.65 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 480.89 -731.34 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 385 338.84 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 530.08 -731.34 cm 0 0 m 0 14.45 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 385 387.69 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 578.6 -731.34 cm 0 0 m 0 14.45 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 580.59 -731.34 cm 0 0 m 0 14.45 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 385 424.57 Tm (0.0005 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 0.0517 0.8892 0.0253 30 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 333.32 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 399.85 191.27 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 382.51 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 399.85 240.46 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 431.7 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 399.85 289.65 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 480.89 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 399.85 338.84 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 530.08 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 399.85 387.69 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 578.6 -746.18 cm 0 0 m 0 14.44 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 580.59 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 399.85 438.2 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 629.1 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_3 11.955 Tf 0 1 -1 0 399.85 487.05 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 678.29 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 399.85 522.27 Tm (< 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 0.0233 0.9744 )Tj /T1_0 11.955 Tf (30 )Tj /T1_0 11.955 Tf (50 )Tj /T1_0 11.955 Tf (70 )Tj /T1_0 11.955 Tf (100 )Tj /T1_0 11.955 Tf (200 )Tj /T1_0 11.955 Tf (400 400 200 100 70 50 30 81

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T able5-3.Responsematrixwhichtransformseventcountsinbinsoftrue p cos z (x -axis)toeventcountsinbinsof measured p cos z (y axis).Matrixelementsthatremainsmallerthan10 )Tj /T1_0 7.97 Tf 6.59 0 Td (20 arenotrepresentedhere. )Tj /T1_0 11.955 Tf 9.29 0 Td (30 0.9743 0.0138 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 432.38 -580.9 cm 0 0 m 0 14.44 l S Q Q BT /T1_2 11.955 Tf 0 1 -1 0 234.57 276.36 Tm (< 10 )Tj /T1_0 7.97 Tf (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 530.08 -580.9 cm 0 0 m 0 14.44 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 234.57 374.06 Tm (0.0010 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 629.1 -580.9 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 234.57 486.71 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 677.62 -580.9 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 234.57 535.56 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 726.81 -580.9 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 234.57 584.75 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 776 -580.9 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 234.57 633.94 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 825.19 -580.9 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 234.57 683.13 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 874.38 -580.9 cm 0 0 m 0 14.44 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 241.62 -581.1 cm 0 0 m 632.76 0 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 241.62 -595.75 cm 0 0 m 0 14.45 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 249.41 92.25 Tm ()Tj /T1_0 11.955 Tf 9.29 0 Td (50 0.0254 0.9101 0.0692 < 10 )Tj /T1_0 7.97 Tf (4 0.0002 0.0020 0.0028 0.0001 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 776 -595.75 cm 0 0 m 0 14.45 l S Q Q BT /T1_2 11.955 Tf 0 1 -1 0 249.41 619.98 Tm (< 10 )Tj /T1_0 7.97 Tf (4 0.0001 )Tj /T1_0 11.955 Tf 9.29 0 Td (70 0.0001 0.0761 0.9036 0.0395 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 530.08 -610.59 cm 0 0 m 0 14.45 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 264.26 374.06 Tm (0.0010 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 629.1 -610.59 cm 0 0 m 0 14.45 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 264.26 486.71 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 677.62 -610.59 cm 0 0 m 0 14.45 l S Q Q BT /T1_2 11.955 Tf 0 1 -1 0 264.26 521.59 Tm (< 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 776 -610.59 cm 0 0 m 0 14.45 l S Q Q BT /T1_2 11.955 Tf 0 1 -1 0 264.26 619.98 Tm (< 10 )Tj /T1_0 7.97 Tf (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 874.38 -610.59 cm 0 0 m 0 14.45 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 241.62 -610.79 cm 0 0 m 632.76 0 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 241.62 -625.43 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 279.1 85.6 Tm ()Tj /T1_0 11.955 Tf (100 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 334 -625.43 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 279.1 191.94 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 383.19 -625.43 cm 0 0 m 0 14.44 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 279.1 227.51 Tm (0.0272 0.9517 0.0409 0.0030 0.0014 0.0002 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 776 -625.43 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 279.1 633.94 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 825.19 -625.43 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 279.1 683.13 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 874.38 -625.43 cm 0 0 m 0 14.44 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 241.62 -625.63 cm 0 0 m 632.76 0 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 241.62 -640.28 cm 0 0 m 0 14.45 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 293.95 85.6 Tm ()Tj /T1_0 11.955 Tf (200 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 334 -640.28 cm 0 0 m 0 14.45 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 293.95 191.94 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 383.19 -640.28 cm 0 0 m 0 14.45 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 293.95 241.14 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 432.38 -640.28 cm 0 0 m 0 14.45 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 293.95 276.7 Tm (0.0087 0.9466 0.0813 0.0021 0.0001 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 825.19 -640.28 cm 0 0 m 0 14.45 l S Q Q BT /T1_2 11.955 Tf 0 1 -1 0 293.95 669.17 Tm (< 10 )Tj /T1_0 7.97 Tf (4 )Tj /T1_0 11.955 Tf (400 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 334 -655.12 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 308.79 191.94 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 383.19 -655.12 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 308.79 241.14 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 432.38 -655.12 cm 0 0 m 0 14.44 l S Q Q BT /T1_2 11.955 Tf 0 1 -1 0 308.79 276.36 Tm (< 10 )Tj /T1_0 7.97 Tf (4 0.0120 0.9018 0.0028 0.0001 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 776 -655.12 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 308.79 633.94 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 825.19 -655.12 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 308.79 683.13 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 874.38 -655.12 cm 0 0 m 0 14.44 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 241.62 -655.32 cm 0 0 m 632.76 0 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 241.62 -657.32 cm 0 0 m 632.76 0 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 241.62 -671.96 cm 0 0 m 0 14.45 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 325.63 94.9 Tm (400 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 334 -671.96 cm 0 0 m 0 14.45 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 325.63 191.94 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 383.19 -671.96 cm 0 0 m 0 14.45 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 325.63 241.14 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 432.38 -671.96 cm 0 0 m 0 14.45 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 325.63 290.33 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 481.57 -671.96 cm 0 0 m 0 14.45 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 325.63 325.55 Tm (0.0002 0.0030 0.8927 0.0154 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 825.19 -671.96 cm 0 0 m 0 14.45 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 325.63 683.13 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 874.38 -671.96 cm 0 0 m 0 14.45 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 241.62 -672.16 cm 0 0 m 632.76 0 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 241.62 -686.8 cm 0 0 m 0 14.44 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 340.47 94.9 Tm (200 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 334 -686.8 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 340.47 191.94 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 383.19 -686.8 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 340.47 241.14 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 432.38 -686.8 cm 0 0 m 0 14.44 l S Q Q BT /T1_2 11.955 Tf 0 1 -1 0 340.47 276.36 Tm (< 10 )Tj /T1_0 7.97 Tf (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 530.08 -686.8 cm 0 0 m 0 14.44 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 340.47 374.06 Tm (0.0020 0.0922 0.9420 0.0086 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 776 -686.8 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 340.47 633.94 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 825.19 -686.8 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 340.47 683.13 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 874.38 -686.8 cm 0 0 m 0 14.44 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 241.62 -687 cm 0 0 m 632.76 0 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 241.62 -701.65 cm 0 0 m 0 14.45 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 355.31 94.9 Tm (100 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 334 -701.65 cm 0 0 m 0 14.45 l S Q Q BT /T1_2 11.955 Tf 0 1 -1 0 355.31 177.98 Tm (< 10 )Tj /T1_0 7.97 Tf (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 432.38 -701.65 cm 0 0 m 0 14.45 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 355.31 290.33 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 481.57 -701.65 cm 0 0 m 0 14.45 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 355.31 325.55 Tm (0.0002 0.0010 0.0034 0.0415 0.9509 0.0266 < 10 )Tj /T1_0 7.97 Tf (4 < 10 )Tj /T1_0 7.97 Tf (4 70 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 < 10 )Tj /T1_0 7.97 Tf (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 432.38 -716.49 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 370.16 290.33 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 481.57 -716.49 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 370.16 339.18 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 530.08 -716.49 cm 0 0 m 0 14.44 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 370.16 374.06 Tm (0.0010 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 629.1 -716.49 cm 0 0 m 0 14.44 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 370.16 473.08 Tm (0.0002 0.0402 0.9063 0.0771 < 10 )Tj /T1_0 7.97 Tf (4 50 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 < 10 )Tj /T1_0 7.97 Tf (4 < 10 )Tj /T1_0 7.97 Tf (4 < 10 )Tj /T1_0 7.97 Tf (4 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 530.08 -731.34 cm 0 0 m 0 14.45 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 385 374.06 Tm (0.0030 0.0028 0.0001 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 0.0670 0.9086 0.0263 30 )Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 334 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 399.85 191.94 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 383.19 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 399.85 241.14 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 432.38 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 399.85 290.33 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 481.57 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 399.85 339.18 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 530.08 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 399.85 387.69 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 578.6 -746.18 cm 0 0 m 0 14.44 l S Q Q q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 580.59 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_4 11.955 Tf 0 1 -1 0 399.85 438.2 Tm ()Tj ET q 0 1 -1 0 -342 -162 cm 0.398 w q 1 0 0 1 629.1 -746.18 cm 0 0 m 0 14.44 l S Q Q BT /T1_0 11.955 Tf 0 1 -1 0 399.85 473.08 Tm (0.0001 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 < 10 )Tj /T1_0 7.97 Tf 6.59 0 Td (4 0.0142 0.9735 )Tj /T1_0 11.955 Tf (30 )Tj /T1_0 11.955 Tf (50 )Tj /T1_0 11.955 Tf (70 )Tj /T1_0 11.955 Tf 9.29 0 Td (100 )Tj /T1_0 11.955 Tf (200 )Tj /T1_0 11.955 Tf (400 400 200 100 70 50 30 82

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CHAPTER 6 SYSTEMATICUNCERTAINTIESINTHEGLOBALMUONANALYSIS InthisChapter,thesystematicuncertaintiesfortheanalysisdescribedinChapter 5 areevaluated.Theuncertaintiesarecomputedseparatelyforeachmomentumbin(both p and p cos ( ))atthesurfaceoftheearth,bothrawandafterunfolding,andaredivided upintocontributionsfromthehardwaretrigger,qualityselection,misalignment,magnetic eld,muonrates,molassemodel,anddetectorresolution.Eachofthemisdesigned accordingtoEquation 6: 2 syst = 2 + 2 (6) ...where istheestimatedchargebiasinducedfromeachsource(equaltozero forthecaseofnobiasingerror),and isthestatisticaluncertaintyontheestimation ofthatbias.Notethat(inthisanalysis)niteMonteCarlostatisticssometimesprevents aprecisionestimationofthesystematicerror.Insuchcases,theobtainedcharge bias, ,isitselfactuallyconsistentwithzero(andthereforethetermitselfislikelyan overestimationoftheactualerror).Asaresult,thenalsystematicerror,onacaseby casebasis,issometimesassumedtobegivenby 2 syst = 2 6.1ErrorPropagationandUnfolding Inordertoincorporatethevarioussystematicuncertaintiesintotheunfolding procedureforerrorpropagation,theymustrstbedividedbetweentheindividual positiveandnegativemuoncountsforeachmomentumbin: R R = s + N + 2 + )Tj ET q 1 0 0 1 72 720 cm 0.478 w q 1 0 0 1 269.82 -532.58 cm 0 0 m 15.71 0 l S Q Q BT /T1_1 11.955 Tf 341.82 176.23 Td (N )Tj /T1_6 11.955 Tf 8.28 26.85 Td ( 2 (6) 83

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. ..wherethe N arethecountofpositiveandnegativemuons, R = N + = N )Tj /T1_0 11.955 Tf 7.09 1.79 Td [(,andthe termsarethetotaluncertaintiesonthecounts.Ifthesystematicuncertaintieson R arepresumedtobeequallydistributedbetween N + and N )Tj /T1_0 11.955 Tf 7.09 1.79 Td (: syst ,+ N + = syst )Tj ET q 1 0 0 1 72 720 cm 0.478 w q 1 0 0 1 215.79 -104.6 cm 0 0 m 30.84 0 l S Q Q BT /T1_1 11.955 Tf 295.35 604.21 Td (N )Tj /T1_0 11.955 Tf 19.16 9.99 Td (= syst R p 2 R (6) ..then,thetotaluncertaintyontheseparatecountsofpositiveandnegativemuons (permomentumbin)maybewritten: 2 tot N = 2 stat N + 2 syst N = N + N 2 2 syst R 2 R 2 (6) The truecountofpositiveornegativemuonsinthe i thmomentumbiniscomputed bymultiplyingtherawcountsfromthevarious j momentumbinsbythenormalizedand invertedmigrationmatrix.Theuncertaintiesontheunfoldedratiosarethencomputedas inEquation 6 2 i ,unfolded = X j e M )Tj /T1_0 7.97 Tf (1 ij 2 2 j (6) Therelativesystematicuncertaintieson R arereportedbothrawandafteraccountingfortheunfoldingprocedureineithercaseusingthesplitformdenedin Equation 6.Fortherawuncertainty,the termsarecomputedfromEquation 6; whilefortheunfoldedone,theyarecomputedfromEquation 6. 84

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6.2 SourcesofSystematicUncertainty 6.2.1Trigger Relativedifferencesintheefciencyofthehardwaretriggersystemformuons ofonechargevs.theothercancauseanoverallchargebias.Thisbias, trig ,maybe expressed: trig = + )Tj /T1_5 11.955 Tf 10.94 10 Td ()Tj /T1_1 11.955 Tf 11.96 0 Td (1 (6) The ter msinEquation 6 refertothetriggerefciencyfor any barreltriggerto reinresponsetoamuoneventofthegivencharge.Inordertoestimatethecharge bias,thesampleofrecordedeventsisrstdividedintoasetofpositiveandasetof negativemuons.Withineithersample,theprobabilityofatriggermaybeexpressed: = p ( or #)= p (")+ p ( # ) )Tj /T1_3 11.955 Tf 11.96 0 Td (p (" and # ) (6) ...wherethearrowsrefertowhetheratriggeroriginatedinoneofthesub-detectors ofthetoporbottomofCMS,andthe subscriptdenotingwhethertheefciencyisfor positiveornegativemuonshasbeendroppedforbrevity.Theefcienciesareestimated usingtag-and-probetests,whichareperformedbytaggingatriggerononesideofCMS andprobingfortheexistenceofatriggerontheoppositeside(usingthereconstructed tracktodeterminewhetheranymatchesexist).Forexample,theestimator p (")ofthe true uppertriggerprobability, p (" ),isconstructedfromtheratioofthenumberofprobes tothenumberoftags: e p (") n (" and #) n (#) p (" and #) p (#) = p (") p (#) p ( # ) = p (") ) p (") e p (") (6) 85

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. ..and,likewise, p (#) e p (#).Thesetestsgiveanaccurateestimateofthetrigger efciencyifthespectrumofmuonsselectedbythetagiswellrepresentativeofthe entireconsideredspectrumforwhichthetriggerefciencyisdesired. 1 Theprobabilityof bothkindsoftriggersacceptingtheevent, p (" and #),mayalsobeestimatedinasimilar fashion,withthecountoftriggersonbothsidesofCMSringcomparedwiththecount ofeventsinwhicheithertriggerred: e p (" and #) n (" and #) n ( or #) p (" and #) p (" or #) ) p (" and #) e p (" and # ) p (" or #) (6) Combining theresultsfromEquations 6 and 6;Equation 6 mayberewritten intermsoftheappropriateestimators: p ( or #)= p (")+ p (#) )Tj /T1_1 11.955 Tf 11.96 0 Td (p (" and # ) e p (")+ e p (#) )Tj /T1_3 11.955 Tf 12.12 1.33 Td (e p (" and # ) p (" or #) e p (")+ e p (# ) 1 + e p ( and #) (6) Fromtheseestimationsonthetriggerprobability,therespectivetriggerefciencies forpositiveandnegativemuonsarecomputed.Theresultingchargebias,previously denedinEquation 6,isillustratedinFigure 6-2. 1 Such isthecaseformuonsinthisanalysis,sincethesplitmuonrequirementguaranteesthattheconsideredtrackstraversetheentiredetector;and,further,because theyareconstrainedtothecenterofthemachine,andthereforehavesimilarrangesof incidentanglesastheycrossthroughtheMuonSpectrometer. 86

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6.2.2 Selection Theselectionrequirementsappliedinthisanalysiswerechosentobeascharge blindtothemeasurementofchargeratioaspossible;however any selectionmay potentiallyhaveadifferentefciencyforpositiveandnegativemuons.Toestimatethe amountofsystematicbiasintroducedbythemuonselection,aso-called N )Tj /T1_1 11.955 Tf 12.44 0 Td [(1testis appliedforeachoftheconsideredrequirements.Thatis,alloftherequirements except fortheoneunderstudyareapplied,andtheratioofefciencies( )ofthenalselection ontheremainingsampleisusedasanestimateforthechargebias: sel = + )Tj /T1_3 11.955 Tf 10.94 9.99 Td ()Tj /T1_1 11.955 Tf 11.95 0 Td (1 (6) The fourselectionrequirementswere:theminimumnumberofDThits,theminimumnumberof z -measuringhitsintheDT(hitsinSuperlayer-2),theminimumnumber ofhitsintheSiliconTrackerouterbarrel,andthemaximumglobal-ttrack 2 .Thesamplewasdividedupintopositiveandnegativemuons,andtherelativeefcienciesofthe N threquirementswerecompared.Theresultingestimateofthechargebiasforeachof theserequirementsareillustratedinFigures 6-3 through 6-6. Animplicitformofselectionarisesfromthesplit-trackrequirement.Recallthat,in Figure 5-2,itwasshownthatrequiringsplit-trackshastheindirecteffectofselectingon smallimpactparameters;andinparticular,thetotaldistancebetweenthePCAandthe centerofthedetector.Figure 6-12 givestherelativeeffectonchargeagainstthethree principleimpactparameters.Sincethesplit-trackefcienciesaresensitiveonlytothe magnitudeoftheimpactparameter(independentofwhichsideofthedetectorthetrack ison),nochargebiasisexpectedtoresultfromthisselection. Overall,selectionisfoundtobeamajorsourceofsystematicuncertaintyinthe analysis(theresultsforeachselectionrequirementaregiveninTables 6-1 and 6-2). Thetwomajorcontributorstothissourceofuncertaintyaretherequirementsonthe numberofhitsintheDTandTOB.Inordertoshowthattheseselectionrequirements 87

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are notpickedatalocal(charge-biasinducing)maxima,therelativeeffectonthecharge ratioisplottedagainstthechoiceofrequirementinFigure 6-13. 6.2.3Mis-Alignment Theprecisealignment[74]ofallthetracking-detectorcomponentsiscrucialfor accuratereconstructionofhighp T muons,whichexperienceonlyslightcurvatures withinthedetector.Inparticular,becausethisanalysisinvolveshitinformationfrom boththemuonspectrometersandthesilicontracker,thereconstructedchargeand momentaofthecosmictracksarehighlysensitivetotherelativealignmentbetween thetrackerandmuonsystems.Inordertoestimatetheeffectofsuchalignments,a comparisonisperformedusingtwoalignmentscenarioswiththeMonteCarlo:onein whichthedetectorhasbeenarrangedinanidealalignment,andoneinwhichithas beenrandomlymisalignedbyrealisticamountsequaltotheuncertaintiesoftherealistic startupalignmentofthedetector(astheyarecurrentlyunderstood). Astudywasconductedinbothscenarios;withthechargeratiomeasuredseparatelyinbothsetsofdetectorconditions.Thedifferenceintheresultingmeasurement isassessedasthechargebiasduetomisalignment,asinEquation 6.Theresultof thisstudyisgiveninFigure 6-7. align = R ideal )Tj /T1_2 11.955 Tf 11.95 0 Td (R startup R ideal (6) A globaldeformationofthedetectorcouldbemissedduringthealignmentprocedures(aso-called 2 -invariantorweakmode[ 75]),andpotentiallyaffectthecharge ratio.Themostproblematicdeformationwouldbeamodewhichcausedaconstant offsetin q = p PCA T ,differentfromzero,affectingthemomentumscaleforcosmicmuonsof oppositechargeinoppositedirections.Atwo-parametertofthesimulated q =p PCA T distributiontothedataisperformedusingmuonsintherange p PCA T > 200GeV =c ,leaving theunknownchargeratioandthe q = p PCA T offsetinthesimulationtovaryfreelyinthet. Anoffsetof0.043 0.022 c /TeVisfound.Themeasuredmuonmomentaarecorrected 88

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f orthisoffsetanditsuncertaintyisincludedasanadditionalsystematicuncertainty on R ,fullycorrelatedbetweenthetwoundergroundmeasurements.Theeffectonthe ratioisapproximately1%and4%,respectively,inthetwohighestmomentumbins;and negliblebelow. 6.2.4Magneticeld ThemagneticeldatCMS[76 ],thoughgenerallyauniform4Twithinthetracker volume,isquitecomplexthroughoutthesolenoidandoutintothereturnyolkandMuon Spectrometers.TheTOSCAeldmapperisusedinCMStoestimatethemagneticeld. Inordertoestimatetheeffectofuncertaintyintheeldmaps,twoseparateconditions werestudied;oneusinganoldermapofthemagneticeld,andonewhichusesthe mapasitiscurrentlyunderstood.Itisassumedthattherelativedifferencebetweenthe twomapsisroughlyequaltothedifferencebetweenthecurrenteldmappingandthe truemagneticeldconditions. Thechargeratiowasmeasuredforasampleofeventsindatawithbotheld conditions,andtherelativedifferenceintheresultwascompared.Theexpression forthebiasintheresultingchargeratioiswritteninEquation 6,andtheresulting uncertaintyisindicatedinFigure 6-8. beld = R current )Tj /T1_1 11.955 Tf 11.95 0 Td (R old R current (6) 6.2.5 MuonRates Somemuons,particularlyforthelowestconsideredmomenta,areabsorbedinthe earthbeforetheycanreachCMS. Apriori,thisisexpectedtobeachargeblindprocess; howeverthereareseveralfactorswhichcaninduceachargebiasinthisprocess.For instance,positivemuonsloseslightlymoreenergy(about0.15%)thandonegative muonsastheytravelthroughmatter[ 26 ];causingaslightchargebias,asindicatedin Figure 6-9. 89

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Although theasymmetricaccessshaftswereremovedasasourceofbiasby applicationoftheparabolicselectionsonbothsidesofthedetector,other(unaccounted for)featuresofthecavernordetectormayinduceachargebias.Inordertocheck,two samplesofMonteCarlo,eachdividedupaccordingtomuoncharge,areexamined.The rstsampleisarepresentationoftheidealmuonuxattheearthsurface(withoutany inuenceduetothelocalgeometryofCMSortheshaftsandcavernsofPoint-5).The secondsampleisrepresentativeoftheportionofthespectrumexpectedtoreachthe trackervolume;andisthussubjecttoalloftheaforementionedcomplications.Theratio ofthetwouxes,representativeoftherelativeacceptanceofCMS,is: = N accepted N ear th (6) ...where N accepted and N earth arethecounts(foreitherpositiveornegativemuons) fromthesub-samplereachingthesilicontrackerofCMS,andthesub-samplerepresentingthetotalspectrumatthesurfaceoftheearth,respectively.Thechargebiasisthen expressedasinEquation 6 rates = + )Tj /T1_4 11.955 Tf 10.93 9.99 Td ()Tj /T1_0 11.955 Tf 11.96 0 Td (1 (6) The resultofthisexerciseisrepresentedinFigure 6-10.Thestatisticaluncertainty, duetothepracticallimitationofniteMonteCarlostatistics(veryfewmuonsatthe surfaceoftheearthactually reach thedetector),isfoundtobesignicantlylargerthan thebiasestimatedtocomefromthissource. 6.2.6MolasseModel Anaccountingofthegeologyofthedetectorsiteinordertounderstandthe materialoverburdenisoneoftherstconsiderationswhichmustbemadeinorder toconvertanymeasurementsofcosmicmuonsincidentuponthedetectorintomeasurementsatthesurfaceoftheearth.Whilenocomprehensivegeologicalsurveywas performedaftertheexcavationoftheshaftsandcavernsforCMS;extensivesurveying 90

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w asdonebothpriortotheconstructionoftheringintheearly1980'sfortheconstruction ofLHC'spredecessor(LEP),andinthemid1990'sforthetwomainexcavationsneeded fortheLHC(thatis,theCMSandATLAScavernsatPoint5andPoint1,respectively). ThemolasseaboveCMSisknowntobecomposedofmorethan70mofmoraines androckleftbehindduringglacialadvancesandretreatsduringtheAlpineRissand W urmeras[77 ].Themoraineitselfisacomplexarrayofstratawiththinlayers(nominally50cm)ofsilt,sand,gravel;alongwithlayersofsandstoneupto5mthick.Within themoraine,therearealsotwoaquiferlevelseachestimatedtovaryfrom10mto 22mthickovertheregion[ 78 79 ]. Inordertoestimatethemolassemodelsystematic,two additional propagationsof themuonswereperformed;onethroughanextraamountofmaterialoverburden(equal tothemolasseuncertainty),andonethroughcorrespondinglylessmaterial.Dividedby materialtype,thereareroughly50mofmorainesand22mofsandstone,witharelative uncertaintyonthedensityofeachcomponentof 5%.Thisuncertaintycorresponds toatotalof3mofrock(or,equivalently,about5mmoraines).Theresultingcharge biasisexpressedinEquation 6,withthecorrespondinguncertaintyindicatedin Figure 6-11 rock = R +3 mrock )Tj /T1_1 11.955 Tf 11.95 0 Td (R )Tj /T1_0 7.97 Tf (3mrock R (6) 6.2.7 ResolutionEstimates InSection 5.4,itwasshownthatthetwolegsofthesplitmuontrackwerefound tohaveapersistentcorrelationwithintherealisticMonteCarlosample,duetosome aspectoftheunderlyingtrackreconstruction.Suchacorrelationwouldcausethe prescribeddetectorresolutionestimator, d C ,tounderestimatetheactualresolution byapredictableamount;howeverthecorrelationitselfcannotbederivedfromthe data.Acorrection,giveninEquation 5,wasconstructedbycomparingtheresolution estimatorwiththetrueresolution.Inordertoaccountforthefactthatthecorrectionitself 91

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is notdata-driven,anadditionalsystematicuncertaintyequaltohalfofthecorrectionis assumed. Apossibleexplanationfortheobservedcorrelationsisrelatedtothealignment, sincerelativeoffsetswithinthedetectormayresultinshiftingthetwo(nearby)measurementssimilarly.WhiletheMonteCarloapproximatesmis-alignmentsbyrandomly shiftinggroupsofdetectorelementsaroundaccordingtotheestimatedpositionaluncertainties,thedataisaligneddifferently(usingindividualtracks).Notethatdespite thisobviousdifferenceasimilarcorrelativeeffectislikelytoappear,sincesomeofthe same tracksusedtomeasurethechargeratioarealsousedtoperformthealignments ofthesilicontrackerandmuonsystems[ 80 81 ],andfurthermore,fromwhichtheMonte Carloalignmentuncertaintyhasbeenapproximated. 6.3OtherSourcesofError 6.3.1AtmosphericConditions ThelocalelevationwhereCMSisinstalledisapproximately500mabovesea-level. Inordertoexploretheeffectsofatmosphericconditionsonmeasurementsinvolving cosmicmuons;publicweather,solar,andgeomagneticdatafromtherunperiodwas usedtoestimateandsimulatetheatmosphericdensity,fromgroundleveltohigh altitudes.Noextremeatmosphericconditionswereobservedduringthecourseofthe experiment,andtherelativevariationofatmosphericdensitywithrespecttothemean sea-level,aswellastheoffsetbetweenmeansea-levelandtheactualelevationofthe earthsurfacenearCMS,areextremelysmallandhavebeenneglected.Detailsofthis studyarepresentedinAppendix B. 6.3.2UnfoldingProcedure Inordertocheckwhethertheunfoldingprocedureitselfinducesachargebiasin thenalresult,anestimatorisconstructedusinganensembleoftoyMonteCarloexperiments.Foreachexperiment,anumberofpositiveandnegativemuonsatthesurface 92

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of theearthisconstructedfromaPoissondistribution,usingthemigrationmatrixestimatedfromdatatodeterminetherelativenumbers.Thecurvatureofeachtoymuonis randomlyassignedaccordingtothe q = p distributionindata,andsmearedaccordingto theenergylossresolution.Twomeasurementsoftheresultingcurvaturearerandomly extractedfromtheactualmigrationmatrix(tosimulatethesplittrackmeasurements) andareusedtoconstructanewmigrationmatrixfortheexperiment.Finally,thetoy sampleisunfoldedusingthenewmigrationmatrixtogenerateameasuredcurvature distribution,whichisthencomparedwiththeinputcurvatures.Thetoyexperimentwas repeated500times;theresultingpullsdistributionsaresummarizedinFigure 6-15. Theresultingbiasisnegligible,asthemeanvaluesforallbinsarealmostzeroandthe widthsareveryclosetoone. 6.4Summary Thestatisticaluncertaintyisapproximately1%forallbinsexceptthehighestmomenta;whereithasamaximumofover3%and6%forthetotalmomentumandvertical momentumformulations,respectively.Thesystematicuncertaintyisunder1%inmost bins,exceptforthelowestmomentumbin(duetoincreaseduncertaintyinthedetector acceptance)andthehighesttwomomentumbins(duetotheincreasedsensitivityto magneticeldandalignmenteffects).Themaximumsystematicuncertaintyinanybin isunder5%.Itisfoundthatselectionisanimportantsourceofsystematicuncertatiny forallmomentumbins.Thesystematicuncertaintyduetoselectionrequirementsare giveninTables 6-1 and 6-2,forthetotalandverticalmomenta,respectively.Thenal systematicuncertainties,includingalleffects,aresummarizedinTable 6-3. 93

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Figure 6-1.Chargeratiopullsdistributionsfor500experiments.(Left)Pullsmeans. (Right)Pullswidths.(Top)In p bins.(Bottom)In p cos z bins. 94

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Figure 6-2.Chargebiasduetothehardwaretrigger( )=R Figure 6-3.Chargebias( )= R fromselectionon20ormoreDriftTubehits. 95

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Figure 6-4.Chargebias( ) = R fromselectiononthreeormore z measuringshits (DriftTubeSuperlayer-2). Figure 6-5.Chargebias( )= R fromselectiononveormoreoutertrackerbarrel hits. 96

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Figure 6-6.Chargebias( )= R fromselectiononthemaximum 2 Figure 6-7.Chargebias( )= R fromalignmentuncertainty. 97

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Figure 6-8.Chargebias( )= R frommagneticelduncertainty. Figure 6-9.Chargebias( )= R fromasymmetricenergylossbetweenpositiveand negativemuonsastheytravelthroughmatter. 98

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Figure 6-10.Chargebias( )=R frommuonrateuncertainty. Figure 6-11.Chargebias( )=R duetomolasseuncertainty. 99

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Figure 6-12.Left:distributionsof + and )Tj /T1_0 11.955 Tf 7.09 -4.34 Td [(,withthesecondnormalizedtotherst(fora bettershapecomparison)vs.variousimpactparameterquantities.Right: ratioofthenormalizeddistributions. 100

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Figure 6-13.Left:distributionsof + and )Tj /T1_0 11.955 Tf 7.09 -4.34 Td [(,withthesecondnormalizedtotherst(fora bettershapecomparison)vs.differentchoicesforselectionrequirements. Right:ratioofthenormalizeddistributions. 101

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Figure 6-14.Left:distributionsof + and )Tj /T1_0 11.955 Tf 7.09 -4.34 Td [(,withthesecondnormalizedtotherst(fora bettershapecomparison)vs.variablesrelevanttothepaththemuonstake throughtheearthtoreachCMS.Right:ratioofthenormalizeddistributions. 102

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Figure 6-15.Chargeratiopullsdistributionsfor500experiments.(Left)Pullsmeans. (Right)Pullswidths.(Top)In p bins.(Bottom)In p cos z bins. 103

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T able6-1.Selectionrelativebiasesin p bins DT =R (%) p range(GeV/c) R stat. q 2 + 2 = 30 -50 1.2682 1.15 2.56 -1.28 2.22 -0.58 50 -70 1.3020 1.22 0.45 -0.42 0.17 -2.51 70 -100 1.2745 0.87 0.18 -0.13 0.12 -1.04 100 -200 1.2798 0.83 0.23 -0.20 0.12 -1.73 200 -400 1.2945 1.60 0.27 0.16 0.22 0.74 400 1 1.3493 3.53 0.62 -0.40 0.47 -0.85 SL2 =R (%) p range(GeV/c) R stat. q 2 + 2 = 30 -50 1.2682 1.15 1.12 -0.01 1.12 -0.01 50 -70 1.3020 1.22 0.14 -0.11 0.09 -1.34 70 -100 1.2745 0.87 0.18 -0.17 0.07 -2.44 100 -200 1.2798 0.83 0.16 -0.14 0.07 -1.95 200 -400 1.2945 1.60 0.16 0.05 0.15 0.36 400 1 1.3493 3.53 0.44 0.29 0.33 0.87 T OB =R (%) p range(GeV/c) R stat. q 2 + 2 = 30 -50 1.2682 1.15 1.75 0.89 1.51 0.59 50 -70 1.3020 1.22 0.13 0.11 0.07 1.55 70 -100 1.2745 0.87 0.06 0.04 0.04 0.99 100 -200 1.2798 0.83 0.12 -0.12 0.04 -2.88 200 -400 1.2945 1.60 0.17 -0.15 0.08 -1.89 400 1 1.3493 3.53 0.59 -0.55 0.21 -2.61 2 =R (%) p range(GeV/c) R stat. q 2 + 2 = 30 -50 1.2682 1.15 0.88 0.30 0.83 0.36 50 -70 1.3020 1.22 0.13 -0.11 0.07 -1.71 70 -100 1.2745 0.87 0.07 -0.05 0.06 -0.84 100 -200 1.2798 0.83 0.11 0.08 0.07 1.03 200 -400 1.2945 1.60 0.58 -0.55 0.19 -2.91 400 1 1.3493 3.53 0.91 -0.75 0.52 -1.45 104

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T able6-2.Selectionrelativebiasesin p cos z bins DT =R (%) p cos z range(GeV/c) R stat. q 2 + 2 = 30 -50 1.2653 1.11 0.78 0.42 0.66 0.65 50 -70 1.2795 0.85 0.85 -0.84 0.11 -7.59 70 -100 1.2815 0.89 0.49 0.47 0.13 3.78 100 -200 1.2913 1.04 0.16 0.02 0.15 0.14 200 -400 1.3359 2.52 0.84 0.76 0.35 2.18 400 1 1.4395 6.39 1.22 -0.88 0.85 -1.03 SL2 =R (%) p cos z range(GeV/c) R stat. q 2 + 2 = 30 -50 1.2653 1.11 0.35 -0.05 0.35 -0.14 50 -70 1.2795 0.85 0.13 -0.12 0.06 -2.05 70 -100 1.2815 0.89 0.21 -0.20 0.07 -2.67 100 -200 1.2913 1.04 0.11 -0.04 0.10 -0.37 200 -400 1.3359 2.52 0.26 0.10 0.24 0.42 400 1 1.4395 6.39 0.83 0.60 0.57 1.04 T OB =R (%) p cos z range(GeV/c) R stat. q 2 + 2 = 30 -50 1.2653 1.11 1.30 -1.17 0.56 -2.08 50 -70 1.2795 0.85 0.11 -0.10 0.04 -2.31 70 -100 1.2815 0.89 0.05 0.04 0.04 0.96 100 -200 1.2913 1.04 0.10 0.08 0.05 1.82 200 -400 1.3359 2.52 0.11 -0.01 0.11 -0.07 400 1 1.4395 6.39 0.24 0.07 0.23 0.32 2 =R (%) p cos z range(GeV/c) R stat. q 2 + 2 = 30 -50 1.2653 1.11 0.31 -0.14 0.28 -0.51 50 -70 1.2795 0.85 0.09 -0.08 0.05 -1.72 70 -100 1.2815 0.89 0.09 0.05 0.07 0.78 100 -200 1.2913 1.04 0.22 -0.19 0.12 -1.55 200 -400 1.3359 2.52 0.94 -0.87 0.36 -2.40 400 1 1.4395 6.39 1.87 -1.53 1.09 -1.40 105

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T able6-3.Totalsystematicuncertainty =R (%) p range(GeV/c) R stat. syst. selection alignment B eld tr igger r ates roc k resolution 30 -50 1.268 1.15 2.13 1.59 0.10 0.20 0.47 1.30 0.26 0.04 50 -70 1.302 1.22 0.63 0.45 0.01 0.01 0.25 0.10 0.35 0.07 70 -100 1.274 0.87 0.74 0.14 0.10 0.01 0.10 0.10 0.70 0.03 100 -200 1.280 0.83 0.33 0.25 0.08 0.16 0.01 0.10 0.04 0.08 200 -400 1.295 1.60 1.25 0.59 0.22 0.44 0.14 0.10 0.84 0.48 400 1 1.349 3.53 3.48 1.01 0.99 2.55 0.59 0.10 1.21 1.33 =R (%) p cos z range(GeV/c) R stat. syst. selection alignment B eld tr igger r ates roc k resolution 30 -50 1.265 1.11 1.96 1.25 0.00 0.10 0.46 1.39 0.36 0.05 50 -70 1.280 0.85 1.00 0.85 0.10 0.07 0.09 0.03 0.51 0.07 70 -100 1.281 0.89 0.73 0.48 0.43 0.13 0.12 0.03 0.27 0.10 100 -200 1.291 1.04 0.60 0.19 0.18 0.18 0.02 0.03 0.49 0.13 200 -400 1.336 2.52 1.90 1.16 0.93 0.67 0.09 0.03 0.47 0.86 400 1 1.440 6.39 4.68 1.76 0.58 2.39 0.44 0.03 0.44 3.52 106

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CHAPTER 7 RESULTOFGLOBALMUONANALYSIS Themainfocusofthisdissertationisthemeasureofchargeratioincosmicmuons usingglobalmuontracks.Theresultsofthisanalysis,obtainedusingthemethodology ofChapter 5 andwiththecalculationofsystematicuncertaintyasinChapter 6,are presentedhere.Thesystematicuncertainties,brokendownaccordingtotheirsource, arepresentedinFigure 7-1.Thetotalerrorfromallsources,statisticalandsystematic, areprovidedinFigure 7-2.Thestatisticalandsystematicuncertaintiesarefoundto beofroughlyequalimportance;combiningforatotaluncertaintyof2%inthelowest momentumbin,5%inthehighestbin,withaminimumofabout1%inbetween.The unfoldedratiosofpositivetonegativemuonsissummarizedinTable 7-1,andillustrated inFigure 7-3.Itisobservedthatthechargeratioisapproximately1.27(aspredicted)at lowmomenta;andincreasingathighmomentauptoabout1.4above600GeV/c. Becausethenalmeasurementofchargeratioisbasedonthecombinedresultsof allthreeanalyses(theearthsurfaceanalysis,thisanalysis,plustheotherunderground analysis);theprecisetssuchastheresultforthefractionofpionsandkaonsproducingmuonsfromthisoneanalysisarenotshownhere.Instead,theymaybefoundasa tforallCMSdatainthenextchapter. 107

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Figure 7-1.Individualsystematicuncertaintiesforglobalmuonanalysis Figure 7-2.(Blueopensquares)Measuredchargeratiorelativestatisticaluncertainties. (Blacksolidcircles)Unfoldedchargeratiorelativestatisticaluncertainties. (Redlines)Unfoldedchargeratiorelativesystematicuncertainties.Left: presentedin p bins.Right:in p cos z bins. 108

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Figure 7-3.(Blueopensquares)Measuredchargeratio.(Blacksolidcircles)Unfolded chargeratio,statisticalerroronly.(Redlines)Statisticalandsystematic errors.Left:In p bins.Right:in p cos z bins. Table7-1.Unfoldedchargeratioasafunctionof p and p cos z withallcorrections applied,alongwiththestatisticalandsystematicuncertainties. p r ange(GeV/c) a verage(GeV/c) R stat syst 30 -50 39 1.268 0.031 0.015 0.027 50 -70 62 1.302 0.018 0.016 0.008 70 -100 84 1.274 0.015 0.011 0.009 100 -200 135 1.280 0.011 0.011 0.004 200 -400 263 1.295 0.026 0.021 0.016 400 1 640 1.349 0.067 0.048 0.047 p cos z r ange(GeV/c) a verage(GeV/c) R stat syst 30 -50 39 1.265 0.029 0.014 0.025 50 -70 62 1.280 0.017 0.011 0.013 70 -100 82 1.281 0.015 0.011 0.009 100 -200 131 1.291 0.016 0.013 0.008 200 -400 259 1.336 0.042 0.034 0.025 400 1 613 1.440 0.114 0.092 0.067 109

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CHAPTER 8 COMBINEDRESULTOFCHARGERATIOMEASUREMENT 8.1SystematicUncertainties Systematicuncertaintiesarisefromreconstructionandinstrumentaleffectsthat canaffectdifferentlythedetectionefciencyandmomentummeasurementof + and )Tj /T1_0 11.955 Tf 7.08 -4.34 Td [(.Theyareevaluatedasafunctionofthemuonmomentumestimatedonthe earthsurface.ThesystematicuncertaintiesoftheglobalmuonCRAFTanalysiswere describedinChapter 6.Thestand-alonemuonanalysisbasedonthesamedatasethadshared,orsimilarlyestimated,errors;withafewdifferences, eg.,toproduce anadditionalcorrectionforchargemis-assignment.TheMTCCuncertaintieswere largelybasedonthelimiteddetectorresolution,giventhefactthatitwasonlypartially instrumented,anddidnotrequiremanysophisticatederrorassessmentssincethedata wascollectedontheearthsurface. Withineachanalysis,severalofthesystematicuncertaintiesareassumedtobe correlatedbetweenmomentumbinsincludingthetriggerefciency, 1 chargemisassignment,andasymmetriesinthedetectoracceptance.Intheglobalandstand-alone muonanalyses,systematicuncertaintiesfrommaterialdensities,eventselection, alignment,andmagneticeld,aretreatedasuncorrelatedbetweenmomentumbins; howevercorrelatedbetweenthetwoanalyses. Forthe2008CRAFT(underground)analyses,themagneticeldisknownwith highprecisionintheregioninsidethesuperconductingsolenoid,howeverwithless precisioninthesteelreturnyoke[ 76].Systematiceffectsonthechargeratioduetothe uncertaintyonthemagneticeldarelessthan1%.Apossiblebiasinthepositiveand negativemuonrates,duetoasymmetriesindetectoracceptanceanduncertaintiesin 1 The triggerefciencyturn-onoccursaroundafewGeV/cjustenoughtopenetrateafewlayersofthesteelyokeandmuchbelowthe10GeV/cthresholdusedinthe analyses. 110

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the materialdensitiesusedinthematerialmap(knownwithin5%),yieldsanegligible uncertaintyonthechargeratioexceptforinthelowestmomentumbin.Additionalbiases duetoselectionareexpected,howeverpredictedtobesmall(below1%).Thehardware triggerhasaslightasymmetrywithregardstoitsefciencyonpositiveandnegative muons,againlessthan1%,andwhichiscorrelatedbetweenthetwounderground analyses.Theeffectofsuchtriggerbiashasbeenestimatedusinginformationfrom eachhalfofthedetector,usingaso-calledtag-and-probetechniquetotestforthe presenceofatriggerinonesidegivenatriggerintheoppositesideofthedetector.In the2006MTCC(surface)analysis,systematicuncertaintiesarisemainlyfromthenite precisionofthedetectoralignmentparameters[ 82],fromthecorrectionofthecharge mis-assignmentprobability,andfromtheslightlylargeruncertainty, 5%,inthescaleof themagneticeldinthesteelreturnyoke. Intheglobalmuonanalysis,theeffectofchargemis-assignmentissmall(dueto theaccuratemomentumresolutionwithinthesilicontracker),andrangesfromlessthan 0.01%at10GeV/ctoabout1%at500GeV/c.Thesemis-assignmentsareautomatically correctedforintheunfoldingprocedure,usingadata-drivenestimationofthedetector resolution.Intheundergroundstand-alonemuonanalysis,chargemis-assignment isestimatedandcorrectedforusingtheMonteCarlosimulation,withanadditional uncertaintyduetothedifferenceofmomentumresolutionbetweentheMonteCarlo andthedata.Possibleeffectsfrompotentialresidualmis-alignmentthatcouldleadto momentummigrationsandincorrectchargeassignmentswereevaluatedbystudying variousrealisticmis-alignmentscenariosindataandsimulation.Onlythetwohighest momentumbinsarepotentiallyaffectedbysuchamis-alignment,yieldingabiasinthe chargeratioaround1%inthetwohighestmomentumbinsfortheglobal-muonanalysis. Forthestandalone-muonanalysis,theeffectinthechargeratioislessthan1%upto 400GeV/c,and4%inthehighestmomentumbin.Thealignmentuncertaintiesassumed intheseanalysesarewellconrmedbythelatestresultsfromLHCcollisions[ 83 ]. 111

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8.2 MeasurementoftheCosmicMuonChargeRatio Theresultsfromthe2006(earthsurface)dataarepresentedinFigure 8-1,both uncorrectedandafterappliedcorrectionsforenergylossinthedetectorandtherate ofchargemis-assignment.ResultsfromthetwoCRAFTanalysisarepresented,as observedwithinthedetectoratthePCAandasafunctionoftransversemomentum, inFigure 8-2;andasafunctionofmomentumattheearthsurface,beforeandafter corrections,inFigure 8-3. ThetotalsystematicuncertaintiesinthethreeanalysesaresummarizedinTable 81,asafunctionof p and p cos z attheEarth'ssurface.Thenalresultsofallthree analysesareshowninFigure 8-4 asafunctionofthemuonmomentum.Intheregion wheretheresultsoverlap,agreementbetweenthemisgood;sotheindividualanalyses arecombinedbyconstructingacovariancematrixoftheresultsandusingstandard multi-variateanalysistechniques[ 84, 85].TheresultingdatapointsaregiveninTable 82 asafunctionof p and p cos z .TheyareshowninFigure 8-4 (a)asafunctionof p andinFigure 8-4 (b)asafunctionof p cos z 8.2.1MeasuredChargeRatioBelow100GeV/c Intheregion p < 100GeV/c,thereisameasurementofsix p binsfromtheMTCC analysisandthree p binsfromtheCRAFTanalyses.Themeasuredchargeratiointhis rangeistreatedasaconstant,withthesetwelvedatapointscombiningtoformasingle measurementofthechargeratiousingthesameprescriptionforcorrelationsbetween theanalysesasintheprevioussection.Theresultingmeasurementisfoundtobe: R =1.2766 0.0032(stat.) 0.0032(syst.), 2 ndf = 7.3 = 11 Thisresultisingoodagreementwithpreviousmeasurements[8789 ]and representsasignicantimprovementinprecision.Fortheverticalcomponent, p cos z < 100GeV/c,theprocedureisrepeated;withtheresult: 112

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R = 1.2772 0.0032(stat.) 0.0036(syst.), 2 ndf = 15.3 = 11 ...wheretheslightlylarger 2 isindicativethatthetislessconsistentwiththe aconstantchargeratiohypothesis.Intheplotsfor p cos z ,thechargeratioisseen tobeginrisingbefore100GeV/c.Restrictingthetto70GeV/corlessyieldsabetter (moreconstant)result: R =1.2728 0.0039(stat.) 0.0040(syst.), 2 ndf = 4.0 = 8 8.2.2ChargeRatioBetween5GeV/cand1TeV/c Consideringthefull p cos z rangemeasured,aslopedriseinthechargeratio isseen,asshowninFig. 8-4.Comparingtopreviousmeasurementsinthesame momentumranges,theCMSresultsagreewellwherethereisoverlap:withthe L3+Cmeasurement[ 87]below400GeV/c,andwiththeUTAH[86 ],MINOS[ 93 ]and OPERA[ 24 ]measurementsabove400GeV/c.Additionalmeasurementsfromother experiments[ 23 8792]arenotshownintheplot,howeveraresimilarlyconsistentwith theresult. InEquation 1,theparameterizedexpression[25 ]forthechargeratiowasgiven. AtperformedtothecombinedCMSchargeratiomeasurement,intheentire p cos z region,andwithaxedrelativeamountofkaonproduction,yields f =0.553 0.005, and f K =0.66 0.06,witha 2 = ndf =7.8=7.Figure 8-4 illustratesthettoCMSdata, togetherwithatperformedonpreviousmeasurementsfromL3+CandMINOS[ 26]. Thevalueof f isconsistentwiththepredictionof R =1.27forpions[27]citedin Chapter 1 ;asthisresultgives R =1.24 0.03.Thevalueof f K yields R K =2.0 0.5 theresultindicatesthatthechargeratioincosmickaonsisindeedhigherthaninpions. 113

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Figure 8-1.Resultsfrom2006MTCCanalysis.Left:uncorrectedchargeratioasa functionofmomentum.Right:chargeratiowithcorrectionsforenergyloss withinCMSandforchargemis-assignmentasafunctionofmomentum. Figure 8-2.Resultof2008CRAFTanalyses.Cosmicmuonchargeratio,uncorrected andmeasuredatthePCAasafunctionoftransversemomentum.Solid circles:globalmuonanalysis.Redopencircles:stand-alonemuonanalysis. Onlystatisticalerrorsdisplayed. 114

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Figure 8-3.Resultof2008CRAFTanalyses.Cosmicmuonchargeratio,extrapolatedto theearthsurface,asafunctionofthemuonmomentumattheearthsurface. Left:globalmuonanalysis.Right:stand-alonemuonanalysis.Opensquares indicatetheuncorrected,pre-unfoldedratio,andclosedcirclesarethe unfoldedratiowithstatisticalerroronly.Thelinesdenotestatisticaland systematicuncertaintiesaddedinquadrature. Table8-1.Chargeratio R andrelativestatistical(stat.)andsystematic(syst.) uncertaintiesinbinsof p (GeV/c),forsurfacedataandfrombothanalysesof undergrounddata.Therelativeuncertaintiesareexpressedin%. p 2006 surface 2008 global-muon 2008 standalone-muon range R stat. syst. R stat. syst. R stat. syst. 5 10 1.249 2.31.3 )Tj 1 0 0 1 72 720 Tm 254.998 -506.26 Td [()-2195()]TJ ET q 1 0 0 1 72 720 cm 0.398 w q 1 0 0 1 313.46 -510.59 cm 0 0 m 0 14.44 l S Q Q BT /T1_2 11.955 Tf 401.74 213.74 Td ()Tj 1 0 0 1 72 720 Tm 367.948 -506.26 Td [()-3080()]TJ /T1_0 11.955 Tf -334.888 -14.45 Td [(1020 1.279 0.51.5 )Tj 1 0 0 1 72 720 Tm 254.998 -520.71 Td [()-2195()]TJ ET q 1 0 0 1 72 720 cm 0.398 w q 1 0 0 1 313.46 -525.04 cm 0 0 m 0 14.45 l S Q Q BT /T1_2 11.955 Tf 401.74 199.29 Td ()Tj 1 0 0 1 72 720 Tm 367.948 -520.71 Td [()-3080()]TJ /T1_0 11.955 Tf -334.888 -14.44 Td [(2030 1.276 0.72.1 )Tj 1 0 0 1 72 720 Tm 254.998 -535.15 Td [()-2195()]TJ ET q 1 0 0 1 72 720 cm 0.398 w q 1 0 0 1 313.46 -539.49 cm 0 0 m 0 14.45 l S Q Q BT /T1_2 11.955 Tf 401.74 184.85 Td ()Tj 1 0 0 1 72 720 Tm 367.948 -535.15 Td [()-3080()]TJ /T1_0 11.955 Tf -334.888 -14.45 Td [(3050 1.279 0.92.6 1.268 1.22.1 1.287 0.51.5 5070 1.285 1.63.4 1.302 1.20.6 1.274 0.50.8 70100 1.223 2.15.1 1.274 0.90.7 1.272 0.40.9 100200 1.287 2.48.9 1.280 0.80.3 1.298 0.30.6 200400 )Tj 1 0 0 1 72 720 Tm 142.048 -607.38 Td [()-2195()]TJ ET q 1 0 0 1 72 720 cm 0.398 w q 1 0 0 1 200.51 -611.71 cm 0 0 m 0 14.44 l S Q Q BT /T1_0 11.955 Tf 278.48 112.62 Td (1.295 1.61.3 1.305 0.81.4 > 400 )Tj 1 0 0 1 72 720 Tm 142.048 -621.83 Td [()-2195()]TJ ET q 1 0 0 1 72 720 cm 0.398 w q 1 0 0 1 200.51 -626.16 cm 0 0 m 0 14.45 l S Q Q BT /T1_0 11.955 Tf 278.48 98.17 Td (1.349 3.53.5 1.350 2.26.0 115

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Figure 8-4.Combinedresultofchargeratiofromallanalyses.Left:thethreeCMS results,andtheircombination,asafunctionofthemuonmomentum.Data pointsareplacedatthebinaverage,withthepointsfromthestand-alone andglobalmuonanalysesoffsethorizontallyby 10%forclarity.Right:The nalCMSresult,asafunctionoftheverticalcomponentofthemuon momentum,togetherwithsomepreviousmeasurementsandatofthe pion-kaonmodeltotheCMSdata. Table8-2.Themuonchargeratio R fromthecombinationofallthreeCMSanalyses,as afunctionof p and p cos z ,inGeV/c,togetherwiththecombinedstatistical andsystematicrelativeuncertainty,in% p r ange hp i R uncertainty p cos z r ange hp cos z i R uncertainty 5 107.01.2502.45 2.5 105.31.2740.99 102013.71.2770.85 10 2013.61.2511.26 203024.21.2761.34 20 3024.11.2621.88 305037.81.2791.10 30 5037.71.2921.27 507058.51.2750.54 50 7058.41.2670.71 7010082.51.2750.68 70 10082.41.2890.70 100200134.01.2920.52 100 200133.11.2920.72 200400265.81.3081.29 200 400264.01.3301.99 > 400698.01.3213.98 > 400654.0 1.3786.04 116

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CHAPTER 9 CONCLUSIONS CosmicmuonshaveprovidedtheCompactMuonSolenoidwithawealthofuseful data,whichhasbeenpreviouslyusedforcommissioningthedetector[ 94 103],but hasnowbeenutilizedtoproducetherstmeasurementofphysicsinvolvingmuonsat thecompletedCMSdetector.Theratioofpositivetonegativecosmicmuonuxeshas beenmeasured,andfromthismeasurement;anew,precisionestimateontherelative fractionsofmuonproducingpionandkaondecayshasbeenobtained[ 104, 105].The nalresultforthemeasurementofthecosmicmuonchargeratiofromCMSbeing combinedfromthreeseparateanalysesisfoundtobeinagreementwithprevious measurements,butwithahigherprecisionuptoamuonmomentaof500GeV/c. Thisdissertationdetailedoneofthreeanalysesperformedaspartofthecharge ratiomeasurement.Theanalysiswasconductedon2008(underground)data,including informationfrombothsilicontrackingandmuonspectrometers.Inthisanalysis,datadriventechniqueswereusedtoestimatethedetectorresolution;thevalidityofwhich hasbeenconrmedusingnumerousMonteCarlotests,bothidealizedandrealistic. Energylossintheearthwasestimatedusingananalyticalextrapolator(withadditional effectsduetostragglingenergylossesaccountedfor)inordertoconvertmeasured particlecurvatureswithinCMStomeasurementsatthesurfaceoftheearth,anda matrixunfoldingtechniquewasusedtoconvertthemeasuredparticlecountsintoan estimateofthetrueparticlecounts. 117

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APPENDIX A TESTSOFTHEDATA-DRIVENRESOLUTION A.1RandomNumberTests A.1.1UncorrelatedMeasurements InSection 5.4,thedata-drivenestimationofdetectorresolutionisdened.Inorder totestthevalidityofsuchanestimatoringeneral;apairofrandomnumbers, C 1 and C 2 (meanttobesuggestiveofthetwoindependentmeasuresoftrackcurvature),are generatedaccordingtosomeresolutionfunctioneitherGaussian,exponential,ora superposition.Aswiththeactualmeasuresofcurvatureforthedata,thehalf-sumgives thebestapproximationofthetruevalue;howeverinthiscase,thedistributionofthehalfsumiscenteredonzerobyconstruction,suchthatthehalf-sumis(also,byconstruction) equaltotheresolutionfunction.Ifthehalf-differenceisidenticaltothehalf-sumwithin thelimitsofstatisticaluncertainty,itisthereforeavaliddescriptionoftheinputresolution function. Figure A-1 showstheagreementbetweenthetworesolutionsifbothofthemeasurementsareGaussianfunctionsofthesamewidth.InFigure A-2,botharegenerated accordingtothesameexponentialprobabilitydistribution.Inbothcases,thedistributionsofthehalfsumandhalfdifferenceagreewell.Althoughthereisnoreasonto expecttheresolutionshouldbedifferentbetweenthetopandbottomtracks,thetestwas alsoexpandedtotheunlikelyscenarioinwhichthetwomeasurementsaredominated bydifferentresolutioneffects.InFigure A-3,oneofthemeasurementshasexponential smearingandtheotherhasGaussian,whileinFigure A-4,bothmeasurementsare havethesameGaussianorexponentialtypeofresolution,butoneofthemeasurements issmearedafactorofthreetimesmorethanother.Inallcasesthereisquitegood agreementbetweenthehalf-sumandhalf-differencedistributions,indicatingthatthe half-differencerepresentstheresolutionwell. 118

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A.1.2 SelectiononIndependentMeasures Atemptationinthisanalysisistoonlyaccepteventsinwhichthetopandbottom legagreeaboutthechargeofthemuon.Tosimulatehowthisaffectstheresult,the distributionsofthehalf-sumandhalf-differencearecomparedifeventsareaccepted accordingtowhetherthetwomeasurementsagreeonthesignofthemeasurement. TheoutcomeisshowninFigure A-5,thetwodistributionsdisagree.Intheweakercase, selectionmaybeappliedsuchthatthedifferencebetweenthemeasuresiscutoffat certainvalue,byselectingoneventswithcurvatureswhichdifferbynomorethanaset amount.TheresultisdisplayedinFigure A-6.Again,itisclearthatthehalf-differenceis apoorestimatorofthetrueresolution. Fromthesetests,itisclearthattherelativeorabsoluteagreementsbetweenthe measurementsmust not beusedasaselectionvariableifthehalf-differenceisto beusedtoestimateresolutioneffects.Suchselectionresultsinsculptingthehalfdifference,whichdoeslittlemorethanhidetheactualdetectorresolution. A.2ComparisonwiththeRealisticMonteCarlo TheresolutionestimatorinMonteCarloiscomparedwiththedatainFigure A-7, showingthattheactualdetectorperformancewasrelativelyworsethanthesimulation predicts.TheresultsaresummarizedinFigure A-8. InSection 5.4,itwassuggestedthatthehalf-differencebetweenthetwomeasurementswasunderestimatingthetrueresolution;andinFigure 5-12,theamountof thenecessarycorrectiontoconvertthehalf-differenceintoamoreaccurateresolution estimatorwasdened.Figure A-9 givestheactualcorrelationbetweenthetopandbottommeasuresofcurvatureintheMonteCarlo,andshowsthatthetwomeasurements are correlatedwitheachother.Thecorrelationisfoundtobenearlynegligibleforlow momentumtracks,butincreasessignicantlywithmomentum.AssumingGaussianerror distributions,theunder-estimationfactors(printedoutinTable A.2)canbepredictedvia 119

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an analyticalformula.Assumingthatthewidthsofthetopandbottommeasurementsof curvaturearethesame( T = B = )then: a = 1 2 ; 1 = 2 = C + = a C 1 + aC 2 C )Tj /T1_0 11.955 Tf 17.05 -4.94 Td (= aC 1 )Tj /T1_2 11.955 Tf 11.95 0 Td [(aC 2 (A) + = a 2 2 + a 2 2 +2 a 2 COV 1,2 )Tj /T1_0 11.955 Tf 17.05 -4.94 Td (= a 2 2 + a 2 2 )Tj /T1_0 11.955 Tf 11.96 0 Td (2 a 2 COV 1,2 )Tj ET q 1 0 0 1 72 720 cm 0.478 w q 1 0 0 1 147.15 -361.61 cm 0 0 m 14.17 0 l S Q Q BT /T1_1 11.955 Tf 220.12 347.2 Td ( + = s 2 )Tj /T1_2 11.955 Tf 11.96 0 Td (CO V 1,2 2 + CO V 1,2 )Tj ET q 1 0 0 1 72 720 cm 0.478 w q 1 0 0 1 147.15 -401.62 cm 0 0 m 14.17 0 l S Q Q BT /T1_1 11.955 Tf 220.12 307.19 Td ( + = s 1 )Tj /T1_1 11.955 Tf 11.95 0 Td ( 1,2 1 + 1,2 Theamountofcorrectionrequiredmaybepredictedbythestrengthofthecovariancebetweenthetwomeasurements.InTable A.2,thepredictedratiosarecompared withthosepreviouslyobserved.Ingeneral,thepredictedvalueisfoundtoliesomewhatbetweenthevaluefromtheGaussiantandtheRMS;andfurthermore,thatthe predictionagreeswiththevalueobtainedfromtheRMStobetterthan10%. 120

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Figure A-1.Comparisonofthehalf-sumandhalf-differencedistributionsforGaussian smearingwiththesameresolutionfortopandbottom.Intheleftpanel,in linearscale;intherightpanel,logarithmicscale. Figure A-2.Comparisonofthehalf-sumandhalf-differencedistributionsforexponential smearingwiththesameresolutionfortopandbottom.Intheleftpanel,in linearscale;intherightpanel,logarithmicscale. 121

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Figure A-3.Comparisonofthehalf-sumandhalf-differencedistributionsfora combinationofGaussianandexponentialsmearing.Intheleftpanel,in linearscale;intherightpanel,logarithmicscale. TableA-1.Thecorrectionstotheresolution, (d C ) = (deltaC )andcorrespondingRMS ratioscomparedwiththeanalyticalprediction. p PCA T r ange(GeV/c) ( d C ) = ( C ) r ms ( d C ) = rms ( C ) 1,2 [%] predicted ratio 10 -20 0.97 0.97 2.75 0.973 20 -30 0.91 0.93 8.35 0.920 30 -50 0.82 0.89 14.9 0.861 50 -100 0.72 0.82 24.3 0.780 100 -300 0.64 0.83 27.1 0.757 300 1 0.59 0.88 19.2 0.823 122

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Figure A-4.Comparisonofthehalf-sumandhalf-differencedistributionsfordifferent resolutionsbetweentopandbottom.Inthetopleftpanel,Gaussian smearingwheretheresolutionofonelegisthreetimesworsethanthe other.Inthetoprightpanel,thesamedistributioninlogarithmicscale.Inthe bottomleftpanel,exponentialsmearingwherethelifetimeforonelegis threetimeslargerthantheother.Intherightpanel,thesamedistributionin logarithmicscale. 123

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Figure A-5.Testsoftheresolutionfunctionbehaviorwhenpickingeventsinsucha fashionastosculptthehalf-differencedistributionbyselectingonevents whichagreeoncurvature.Eventswerepickedsuchthatthecurvature betweenthetopandbottomlegagree. 124

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Figure A-6.Testsoftheresolutionfunctionbehaviorwhenpickingeventsinsucha fashionastosculptthehalf-differencedistributionbyselectingonevents whichtendtoagreeoncurvature.Eventswerepickedsuchthatthe curvaturedifferenceislessthantwobetweenthetopandbottomleg. 125

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Figure A-7.Data(blacksolidcircles)andMonteCarlo(redopencircles)momentum resolutionatthePCAin p PCA T bins. 126

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Figure A-8.Data(blacksolidcircles)andMonteCarlo(redopencircles).Left:mean valueofGaussiants(momentumscale).Right:widthofts(momentum resolution). 127

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Figure A-9.Correlationbetweentopandbottomindividualtrueresolutions,inbinsof truetransversemomentumatthePCA. 128

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APPENDIX B ATMOSPHERICDEPTH B.1Introduction TheCMSexperimentislocatedat46 18 0 34northlatitude,6 4 0 37eastlongitude;whereground-levelisroughly505mabovesea-level.Theatmosphericconditions duringCRAFT08weremeasuredusingmeteorologicaldatareportedbytheGeneva CointrinInternationalAirport[ 106],approximately5milesaway,andsimulatedtohigh altitudesusingtheNRLMSISE-00(USNavalResearchLaboratory,MassSpectrometer andIncoherentScatterRadar,Extended)model[ 107]. B.2MeasuredAtmosphericPressure Publishedweatherdataiscalibratedaccordingtothestationelevation;suchthatthe reportedpressuresareactuallyextrapolationstosea-level, P msl ;ratherthantheactual P station 1 Inordertoconvertthereportedvaluestomeaningfulatmosphericdensities, thedatamustberecalibratedtotheappropriatealtitudeinthiscase;fromsea-level,to thestationelevation(430m)andnally,totheelevationabovePoint-5(505m).These conversionsareperformedbyapplyingtheidealgasrelation,Equation B P = P 0 e )Tj /T1_3 5.978 Tf 5.75 0 Td (h M g R T (B) Here h isthealtitudinaldifferencebetween P and P 0 M isthemolecularweight ofthegas, g isaccelerationduetogravity, T istemperatureinKelvin,and R isthe gasconstant.TheInternationalStandardAtmosphere(ISA)wasusedforthisstudy: g =9.807, M =28.964 g = mol ,and R =8.3145 J =K mol 1 This issothatisobarpressurecontourmapsarenotundulyinuencedbytopography;butcomplicatesanyapplicationofthedatainthiscontext. 129

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B.3 EffectiveElevation Theeffectiveelevation,intermsofatmosphericdepth,isquiteuidwithtime.Itmay becomputedbysolvingEquation B for h ,usingthestandardatmosphericpressure (101.325kPafortheISA)asitsreferencepressure.Theresultingelevationasafunction oftimeispresentedinFigure B-3. B.4AtmosphericDensity Thelocalairdensity,neargroundlevel,maybemeasured[ 108]from: = (P d M d + P v M v ) R T (B) ..where P d and P v arethepartialpressuresofdryairandwatervapor, T isthe temperatureinKelvin, R istheuniversalgasconstant,and M d and M v arethemolecular weightsofdryairandwatervapor,respectively.Thepartialpressureofwatervaporwas computedusingtheLowe[ 109]approximation(whichdependsonlyonthemeasured dewpointtemperature). 2 B.5NRLMSISE-00AtmosphericSimulation NRLMSISE-00istypicallyusedforatmosphericsimulationsinrocketryandsatellite applications,butsuitstherequirementsofthisstudywell.Themodelwasusedto simulatetheatmosphericdensitiesaboveCMSasafunctionofbothtimeandaltitude, usingthemaindriversoftheupperatmospheresolarultra-violetradiation[ 110 ]and geomagneticheating[ 111]asinputs.Lowaltitudemeteoroligicaleffectsareaccounted forindirectlybysimulatingfromtheeffective,atmosphericaltitude(computedpreviously) ratherthanthetrueelevation. Theairdensityatgroundlevel,computedfromtheweatherstationdatausing Equation B,andsimulateddirectlyinNRLMSISE-00,isillustratedinFigure B-2. 2 The polynomialapproximationintroducesanegligibleerrorthousandthsofapercentpresumedmuchsmallerthanthemeasurementaccuracy. 130

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The high altitude uncertaintiesontheNRLMSISE-00modelhavebeensolved elsewhereusingloworbitalsatellitedata[ 112],andhasbeenfoundtovaryfrom1015%uptoaround200km,risingtoamaximumof30%ataltitudesnear600km.By comparisonwithmeasuredvalues(aftercorrectingforelevation)anerrorofatmost2% isobservedatgroundlevel. Theresulting,altitudedependent,simulationsofatmosphericdensityareindicated inFigure B-1.Alsoindicatedinthegurearethetotal(altitudedependent)variations intheresultingdensities(overthedurationoftheexperiment),andthetheoretical uncertainty.Nearlyalloftheintegratedatmosphericmassisintherst30kmabove groundlevel,wherethetotalerrorandtime-dependentvariationsarequitesmall. B.6Summary Theeffectiveelevation,consideringthemassofairaboveCMSasafunctionoftime duringthe2008CRAFTexerciseisgiveninFigure B-3 .Giventhattheearthmaterial isatleast1500timesmoredensethanair,the500melevationofthesurfaceatCMS isequivalenttonomorethan30cmofmoraine.Includingatmosphericeffects,the effectivealtitudeduringCRAFTvariedfromjustbelow300mtomorethan600m;or between24cmand36cmofmoraineequivalent.Giventhatmaterialuncertaintyabove CMSisalready5mofmoraines,noadditionaluncertaintyisexpectedfromthesmall variationsintheatmosphere. 131

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Figure B-1.AirdensitiesasafunctionofaltitudeduringCRAFT08usingNRLMSISE-00. Figure B-2.Airdensitiesatgroundlevel:measuredfromGenevaInternationalAirport dataandsimulatedusingNRLMSISE-00. 132

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Figure B-3.TheeffectiveelevationofgroundlevelaboveCMSduringthetimeofthe experiment,usingdatapublishedbytheGenevaAirport. 133

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BIOGRAPHICAL SKETCH MichaelSchmittisafthgenerationFloridian,borninHollywoodFlorida.From ayoungageMichaelwaseagertodiscovertheworkingsoftheworldaroundhim. Hegraduatedfromhighschoolin1999andpostgraduationbeganpursuinghigher educationatPalmBeachCommunityCollege.DuringhisenrollmentatPalmBeach CommunityCollege,hereceivedacademicrecognitionmanytimes.Amongthese includethePresident'sHonorCerticateandanhonorforAcademicExcellencein mathematics. MichaelbeganhisundergraduateworkattheUniversityofFloridainAugustof2001 andsoughthandsonexperienceasaDemonstrationLaboratoryAssistant.In2002,he tookonadditionalresponsibilitiesasanUndergraduateResearchAssistantworkingon theColliderDetectoratFermilab,basednearChicago.HereceivedhisBachelor'sof Sciencedegree(withamajorofPhysics)withhighesthonorsin2003,andwasgranted anAlumniFellowshippositionwiththeUniverityofFlorida. Overthepastsevenyears,Michaelhasbeenateachingassistant,aresearch assistantontwomajorparticlephysicscollaborations,andawonderfulhusband.Heis anincrediblydiverseandknowledgeableindividual,whoislookingforwardtoafuture wherehecancontinuetolearn,develop,andovercomenewchallenges. 144

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Photog raphoftheauthorstandinginfrontofthe z -minusend-capoftheCMSdetector (ataheightofthreetofourstories)takenonSeptember20th,2006.Atthistime,CMS wasinthemidstofacosmic-shutdown;MTCC(Phase-I)endedinAugust,butwould resumeinOctober(Phase-II).OnNovember2nd,veweeksafterthisphotographwas taken,themachinebeganitspiecemealdescent100mintotheearth;aprocesswhich wouldtakefourteenmonthstocomplete.Anotherninemonthswouldpassbeforethe dataonwhichthisthesiswasbasedcouldbecollected. ThankstoDr.ArnoHeisterfor takingthisphotograph. 145


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