miriam klein- the search for charged massive stable particles at dØ: a de/dx study of p20 data

8/3/2019 Miriam Klein- The Search for Charged Massive Stable Particles at D: A dE/dx Study of p20 Data

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The Search for Charged Massive Stable

Particles at D: A dE dx Study of p20 Data

Miriam Klein

May 8, 2009


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Contents

1 Abstract 1

2 Introduction 5

3 Theory 8

3.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . 8

3.2 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 Apparatus 18

4.1 The Tevatron . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.2 The D Detector . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2.1 The Central Tracking System . . . . . . . . . . . . . . 23

4.2.2 The Calorimeter . . . . . . . . . . . . . . . . . . . . . 25

4.2.3 The Muon System . . . . . . . . . . . . . . . . . . . . 27

4.3 Triggering and Reconstruction . . . . . . . . . . . . . . . . . . 284.3.1 Triggering . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.3.2 Reconstruction . . . . . . . . . . . . . . . . . . . . . . 29

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5 Data Cuts and Pre-Analysis 32

5.1 Preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.2 Analysis Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.3 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . 35

5.3.1 Staus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.3.2 Z Boson Decay . . . . . . . . . . . . . . . . . . . . . . 37

5.3.3 W Boson Decay . . . . . . . . . . . . . . . . . . . . . . 37

5.4 Data Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.5 Further Analysis Cuts . . . . . . . . . . . . . . . . . . . . . . 39

6 Results 46

7 Conclusion 56

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AcknowledgmentsFirst, a thank you to my advisor Professor Dave Cutts, for all of his

help with this thesis and his aid with my research this past year. I am very

grateful to his graduate student Yunhe Xie for her extensive programming

and physics knowledge and patience. I would also like to thank Erin Teich

for providing some of the Monte Carlo samples, and the Brown University

HEP faculty.

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Chapter 2

Introduction

This research concerns the search for charged stable massive particles (CM-

SPs) using both run-by-run studies and plots of the energy loss per path

length. CMSPs are dened as particles that escape the D detector prior to

decay (which requires they have a lifetime of at least 100 ns), are electrically

charged, and have a mass of at least 60 GeV. All particles with masses in

the CMSP range that have been observed and veried as of this writing have

lifetimes far too short to escape the detector. CMSPs, however, are a pre-

diction of certain forms of supersymmetry (SUSY) models and the standard

model.

The standard model has been a mainstay of particle physics research since

the middle of the 20th century, and all but one of the non supersymmetricparticles has been detected since its inception. However, while the standard

model predicts the types of particles, it does not offer many explanations

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for mass discrepancies or the relative rarity of certain types of particles.

Supersymmetry was proposed to resolve many of these phenomena. The

basic tenet of SUSY is that each particle has a partner particle with a spin

differing by 12 but which has otherwise the same quantum numbers.

SUSY not only answers many of the questions raised by the Standard

Model, but is also a key component of many modern physics theories, such

as string theory, as well as of other explanations of theories, such as dark

matter (although SUSY is not dependent on these theories or explanations).Showing that one of the predicted SUSY models is true would have astound-

ing implications for physics, opening up a new set of subatomic particles and

providing further evidence for theories in elds beyond high energy physics.

One way of searching for evidence for SUSY is by looking for the nal par-

ticle, known as the LSP (lightest supersymmetric particle) or the end result

of particle decays under a supersymmetric model. CMSPs are not the LSP

because the LSP is predicted by SUSY to be the particle which makes up

dark matter. Dark matter is neutral, so the LSP cannot be a CMSP. CMSPs,

however, may be the NLSP (next lightest supersymmetric particle)which de-

cays into the LSP and if so, would be easier to detect due to their much

greater mass and their charge.

The particles created by accelerator collisions that are studied in this

analysis were all identied as muons by the detector. CMSPs, however, are

much heavier than muons, which have a mass of 105.7 MeV, and because of

this are slower-moving. This in turn means they lose more energy as they

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move through the detector.

CMSPs are thought to be produced in pairs, as are many subatomic

particles. SUSY particles are predicted to carry a quantum number known as

G-parity. G-parity requires that particles be produced in pairs of positive and

negative parity. It also provides the basis for a stable LSP due to quantum

number conservation. Because the D detector has some inefficiencies, and

could fail to detect one of the particles, and because there is still a small

possibility that CMSPs do not come in pairs, this study included single anddouble-muon events.

This paper will rst present a more thorough explanation of the Standard

Model, SUSY, and related theory. It will then give a summary of the workings

of the apparatus: the Tevatron particle collider, the D detector, and some

of the software used in data collection from the detector. After that there

is a section about the analysis, including the preselection of events, the cuts

made in this data, and the Monte Carlo samples used in determining some

of these analysis cuts in order to nd events likely to have a CMSP signal

as opposed to a true muon signal. Finally, we will discuss the results of

the analysis and possible implications and ways to continue the search for

CMSPs.

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Chapter 3

Theory

3.1 The Standard Model

To understand CMSPs it is rst necessary to understand the basics of the

Standard Model of particle physics. The Standard Model is a theory of

the known particles associated with three of the four fundamental forces

(electromagnetic, strong nuclear, and weak nuclear) and their interactions.

All particles outlined in the Standard Model theory, excluding the Higgs

boson, have been observed, and their masses and spin numbers have been as

predicted. In addition, these particles all have a corresponding anti-particle.

All these particles fall into one of two groups: the rst is the bosons, with

integer spin. Bosons are force carriers; interchange of bosons determines thenature of force between objects. The force carrier for the electromagnetic

force is the photon ( ), the carrier for the strong nuclear force is the gluon

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(g), and the carriers for the weak nuclear force are W + , W , and Z bosons.

The second group of particles, the fermions, have half-integer spins and

are the basis for matter. The twelve kinds of fermions can be further broken

up into two more groups. While all fermions interact via the weak nuclear

forces, half also carry a color charge and have strong-force mediated interac-

tions, while the other half do not. Fermions that interact under the strong

force are called quarks, and those that do not are leptons. Additionally, all

quarks have an electronic charge and so can interact via the electromagneticforce, but only three of the six leptons carry a charge. The remaining three,

the electron, muon, and tau neutrinos, only interact via the weak force, and

as such are very difficult to detect. Just as there are six leptons, there are

six types, or avors, of quarks. The upper quarks: the up, charm, and top

quarks each have an electrical charge of +2/3 and the lower quarks: down,

strange, and bottom quarks each have a charge of -1/3. Quarks and leptons

are each grouped into pairs. There are three pairs and we refer to these

pairs as generations. The specic generations are shown in the below gure,

, along with the force carriers.

The below model of elementary particles is arranged not merely by quarks

and leptons, but also by mass. The rst generation is lighter than the second,

which is lighter than the third. Longevity is determined differently. The

electron, for example, is stable and has an innite lifespan. Of the elementary

particles which undergo decay, the longest-lived is the muon, which has a

lifespan on the order of 2 microseconds (10 6 s), which is why muons are one

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of the easier particles to detect.

Because quark interactions are often mediated by the strong force, they

behave according to the theory of Quantum Chromodynamics (QCD). Under

QCD, quarks have a trait other than spin and charge, known as color (no

relation to the conventional, optical denition of color). Quarks can come in

red, blue, or yellow, and anti-quarks come in anti-blue, anti-red, and anti-

yellow. When we include both color and avor, we nd there are eighteen

quarks and eighteen anti-quarks.

It is the quarks and their colors which determine the nature of the sym-

metry associated with QCD. Gluons are made from one quark and one anti-

quark. For any one avor of quark, there are nine possible combinations:

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yy yb yr

by bb br

ry rb rrThese can be further divided into those with differently-colored quarks

and antiquarks (all the combinations in the table excluding the diagonal)

and those pairs along the diagonal. These groups are the explicitly-colored

pairs and the hidden-color pairs, respectively. The hidden-color pairs have

an equivalence such that there are effectively two different kinds of hidden-

color pairs, making eight gluons in all. The three colors give QCD group

symmetry of special unitary group 3, which is written as SU(3) and means

that it is the group of 3 3 unitary matrices, each with a real ( 1) deter-

minant. Because of the eight gluons, the SU(3) group in QCD has eight

generators, all of which are linearly independent of each other. Another ele-

ment of supersymmetric theory is that the fundamental forces, at the early

stages of the universe, were unied. Forces are often described in terms of

their elds, so this theory is called Unied Field Theory. The so-called The-

ory of Everything, the unication of all force elds, predicts that gravity split

off rst; however, physicists have not yet been able to prove the existence

of the predicted gravitational force carriers, the gravitons. Grand Unied

theory concerns the remaining three fundamental forces. The strong force,

mediated by gluons, was the second force to specialize. The electromagneticand weak nuclear forces can be united in the electroweak force. This uni-

cation requires that two new quantum numbers, the weak isospin and weak

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hypercharge, be included. The weak isospin is ( I 3 weak ) and has SU(2) group

supersymmetry. The weak hypercharge, Y weak , has U(1). The weak and

electromagnetic currents each couple to a combination or component of one

of these quantum numbers. Together, electroweak theory has SU(2) U(1)

symmetry, and by combining these further with the SU(3) group symmetry

from the strong force, we nd that the Standard Model has group symmetry

of SU(3) SU(2) U(1).

This creates a problem: gluons and photons, the carriers that mediate thestrong and electromagnetic forces respectively, are both massless, but the W

and Z bosons are not. To reconcile the transformations provided for by the

Standard Model, we must introduce several further concepts. These will be

explained in more detail in the following section; the ultimate conclusion is

that in order to give the W and Z bosons mass, there must exist a new parti-

cle, called the Higgs particle or more specically, the Higgs boson, a particle

with zero spin and a minimum mass of 114 GeV, which is its own antipar-

ticle. The Higgs boson has not yet been detected and has been nicknamed

the God Particle, referring to its central but as of yet unconrmed place in

Unied Field Theory. Physicists hope that when the Large Hadron Collider

(LHC) becomes fully operational it will be able to detect the particle. The

Tevatron may also be capable of Higgs Boson detection.

Like the Higgs Boson, CMSPs are also massive compared to other parti-

cles, and therefore share some of the same challenges in detection apply such

as the necessity of a collider capable of reaching very high energies. In addi-

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tion to the requirement that CMSPs have a mass of at least 60 GeV (although

many are predicted to be much more massive), charged stable massive parti-

cles, as their name suggests, all carry an electronic charge and can escape the

D detector before they decay. The long life time is what is meant by sta-

ble; it does not refer to particles that due to quantum number conservation

do not decay at all, and so some physicists refer to CMSP as charged massive

long-lived particles instead, to denote the difference. There are several means

of detecting these particles. The greater mass means a longer time-of-ight,and the charge means that energy loss is very likely through interactions

with other charged particles such as electrons. However, the greater mass

and consequently lower speed mean that despite this energy loss, CMSPs will

still have a greater energy than faster particles. Their large mass also means

that their collisions are elastic, so CMSP collisions do not create showers of

hadrons and deposit all of their energy in the calorimeter, unlike all other

particles with the exception of muons and neutrinos.

3.2 Supersymmetry

Why must supersymmetry (SUSY) exist in the rst place? Inclusion of the

Higgs Boson in order to reconcile the group symmetry gives rise to what is

known as the hierarchy problem. The experimental and theoretical values of the Hamiltonian equation for different particles, especially as-of-yet undiscov-

ered massive particles, when the Higgs boson is included, vary considerably

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and so the correction term must be very large due to quantum effects. The

Hamiltonian in this case is complex, but has the scalar vector potential:

V = m 2H |H | 2 + |H | 4 ,

where m H is related to the Higgs mass, H has a nonzero expectation value,

and is a coupling constant for the Higgs eld. More generally, supersym-

metry attempts to explain in terms of mass and energy why we have not

yet found the particle which mediates gravity and reconcile various incon-

sistencies in experimental data versus theoretical predictions of elementary

particles. At this time, concerns about a large correction term may seem

absurdthe Higgs boson has not even been detected, let alone its mass de-

termined. However, attempts to nd the Higgs may result in discoveries of

new particles and once the Higgs mass has been measured, physicists want

a theory that will be consistent with the new data, regardless. Should a

new massive particle which couples to the Higgs eld be discovered, it alone

would require an even greater correction term of unacceptable magnitude. It

is possible to assume that the Higgs boson does not exist, or that if it does,

no massive particles couple to the Higgs eld, but this leaves us back with

the unication of gravity problem and is not a safe assumption. SUSY allows

the Standard Model, including the Higgs, and without any ne-tuning of the

Lagrangian required.

A dening requirement of supersymmetry is that each particle has a su-

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perpartner, a corresponding particle with a spin one-half apart; that is, each

boson is paired with a fermion. The supersymmetric particles are called

sparticles. The supersymmetric partners of fermions are similarly named:

selectron, stau, sneutrino, and so on; the partners of bosons acquire an ino

suffix (zino, wino, higgsino, etc.) All quantum numbers other than the afore-

mentioned spin, such as color, charge, and isospin, are identical for particles

and their sparticles. SUSYs introduction of the superpartner groups, known

as supermultiplets, cancels the Higgs mass normalization, as shown in thebelow Feynman diagram.

While this explains the hierarchy problem and offers some possible an-swer regarding the huge differences in particle size for different force carriers,

SUSY comes with its own questions. If a massless particle, such as the pho-

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ton, has a counterpart which differs only in spin, why has this other massless

particle never been detected? It is well within the range of our current de-

tectors. The lack of sparticles indicates that while the symmetry did exist in

earlier stages of the universe, it has since been broken (become asymmetric)

and the sparticles now have masses on the TeV scale at least.

There are several ways in which SUSY may have been broken, but the

most relevant to this paper is gauge-mediated supersymmetry breaking (GMSB).

GMSB results from normal gauge interactions and works with the introduc-tion of a new chiral supermultiplet in addition to those predicted by the

Standard Model and SUSY: the messengers. Messengers can couple to ei-

ther the SUSY particles or to whatever caused the breaking of SUSY. In

GMSB, the lightest supersymmetric particle (often abbreviated LSP) is the

gravitino, the superpartner of the undiscovered and likely very massive gravi-

ton. The gravitino has a predicted mass in the 1 keV range, far below the

energies reached by modern colliders. This gravitino would be produced by

a series of particle decays: rst, a superpartner pair would be created. Each

particle of this pair would decay one of the next lightest supersymmetric par-

ticles (NLSP), which may be either a neutralino or a slepton. If they decay

into a neutralino, the neutralino will then further decay into a gravitino and

a photon, and the gravitino could be detected indirectly as an event with

the appropriate amount of missing energy. The predicted detector signature

would therefore need to have two photons and a large value for the missing

energy, corresponding to the multiple decays and their byproducts. Should

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the pair of particles decay into sleptons, they would decay into the lightest

slepton, as marked by the term NLSP(next lightest supersymmetric parti-

cle, ie: the particle that decays into the LSP). This slepton is the stau, the

superpartner of the tau particle. The stability of the gravitino means that

the NLSP is also most likely fairly stable, even in the case of staus, which

decay into gravitinos very gradually. This means that a CMSP may very well

exist: stability is accounted for; the superpartners, according to GMSB, are

massive; and the charges of a particle and its superpartner are still predictedto be equal, so it would be charged.

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Chapter 4

Apparatus

4.1 The Tevatron

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The Tevatron is a circular particle accelerator at the Fermi National Acceler-

ator Laboratory (Fermilab) in Batavia, Illinois. At this time, it is the highest

energy particle collider in the world. The Large Hadron Collider, or LHC, is

a new collider at CERN in Geneva, Switzerland. Once it is turned on at the

end of 2009, the LHC will replace the Tevatron as the most powerful collider,

although the Tevatron will remain in operation until at least 2010, until the

LHC and its detectors are fully running. The Tevatron derives its name from

its proton accelerators, which accelerate proton and anti-proton beams to anenergy of approximately 1 TeV (Teraelectron volt).

There are several accelerators that bring the beams to their full speed.

First, a preaccelerator ionizes hydrogen gas to create H- ions, which are made

of a single proton and two electrons. The Cockcroft-Walton accelerator then

uses a positive voltage to accelerate these ions to energies of 750 keV. The

ions go down a transfer line (named the 750 keV line for obvious reasons),

also considered part of the preaccelerator, to the LINAC. The LINAC, or

linear accelerator, is actually made of a two separate linear accelerators: a

drift tube, which starts with the lower energy ions, and a side-coupled cavity

which accelerates the particles that have gone through the drift tube to an

energy of 400 MeV. The ions then pass through a carbon foil layer which

strips off the electrons, leaving only the proton to go ahead.

The protons enter the Booster, a synchotron, or circular acceleratorthe

rst of several in the Tevatron. The Booster uses a series of magnets spaced

around a circle of radius 75 m to collect the protons into a beam and then

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accelerates this beam to 8 GeV, into the Main injector. The Main Injector

is also a synchotron with a circumference approximately seven times longer

than that of the Booster. The Main Injector rst accelerates the proton

beam to 120 GeV. If the beam is to be used in antiproton stacking, the Main

Injector does not accelerate it any further; if it is to be injected through the

Tevatron, it is accelerated up to 150 GeV. The antiprotons mentioned come

from the Antiproton source, a series of three parts: the 120 GeV proton

beam is shot at a nickel target. For every 105

106

protons that strike thetarget, approximately one antiproton is obtained. These are focused through

a lens made of lithium and selected for energies of approximately 8 GeV

before they are collected in the Debuncher. The Debuncher, as its name

indicates, decelerates the faster antiprotons so that the particles are closer

in momentum, and spreads out the particles linearly so that they are not

all bunched together. The antiprotons are released in groups, or pulses, and

stored in the Accumulator, where the range of momenta is further decreased,

and accumulated until there is a sufficient number to create an antiproton

beam, which then moves on to the Recycler, a storage ring that also saves up

antiprotons until needed, at which point they go through the Main Injector

again to be accelerated to 150 GeV.

In the meantime, the 150 GeV beam, proton or antiproton is injected to

the Tevatron, a synchotron nearly 4 miles in circumference. Each beam is

accelerated with RF carriers from 150 GeV to 980 GeV; the energy of the

collision is therefore 1.96 TeV. The proton and anti-proton bunches move in

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opposite directions around the ring so that they may collide, with the D

and CDF detectors at two of the major points of collision. The beams are

steered around the rings through the Tevatron by cryogenically cooled su-

perconducting magnets. Another set of magnets serves to focus the beams,

narrow their cross-sectional area, and steer them through the center of the

appropriate detector to maximize the rate of collision. The proton and an-

tiproton beams are equal in mass and opposite in charge, so they reach the

exact same energies while traveling in opposite directions around the ring.The Tevatron, during a run, has ppcollisions every 396 ns.

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The above gure shows a schematic of the Tevatron apparatus.

4.2 The D Detector

The D detector is one of the two main detectors along the Tevatron ring,

and has three main parts: a central tracking system, a liquid argon and

uranium calorimeter, and a muon system. The central muon tracking sys-

tem and a forward muon system comprise the total muon system. The D

detector uses a right-handed coordinate system in which the z-axis is along

the line of the proton beam. The y-axis points up, and the x-axis points

out from the center. However, for most purposes it makes more sense to use

cylindrical coordinates. In addition, instead of the polar angle it is often

more helpful to refer to the , when referring to the direction of the particle

relative to the z-axis. This term is called the pseudorapidity and is equal to

= ln tan2

The pseudorapidity is an approximation of the actual rapidity, which takes

into account relativistic particles. The actual rapidity is also Lorenz invariant

and is given by the equation

y = 12

ln E + pLE pL

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4.2.1 The Central Tracking SystemThe D detector central tracking system measures interactions with || < 1

and consists of two trackers: the silicon microstrip tracker (SMT) and the

central ber tracker (CFT). Both are surrounded by a solenoid. In order for

detectors to be nearly perpendicular to the surfaces for all values of , the

SMT is surrounded by six barrels in four layers, which measure the r

coordinate for lower absolute values of

. The term forward is used to referto the areas of the detector where the pseudorapidity is large 1 < || < 4;

|| > 4 is too close to the beam line for the detector to measure. Distributed

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between the barrels are sixteen disks which also surround the track. The

front disks measure both the r and r z coordinates for higher values

of . The SMT uses both single- and double-sided silicon sensors for muon

detection. The SMT displays a signal to noise ratio of between 12:1 and 18:1,

depending on several factors including time since the previous shutdown and

charge-up time.

The CFT consists of eight concentric supporting barrels which hold the

many scintillating bers. Each barrel has two doublets (two-layered systems)of bers. The rst doublet is parallel to the z-axis and therefore the proton

beam. The second doublets alternate between 3 in relation to the z-axis,

with the innermost barrels angled doublet at +3 . When charged particles

pass these layers of bers, they excite electrons in the bers, which transmit

a light signal down through a waveguide ber to the visible light photon

counters (VLPC). The forward muon system covers the region 1 < || < 2,

but the drift tube tracking and detectors work in approximately the same

manner as in the central tracking system.

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4.2.2 The Calorimeter

The calorimeter provides the primary measurement of the energy of electrons,

photons, and jets. A solenoid, added to the detector between Run I and Run

II, provides a momentum measurement but at high energies the calorimeter

is more accurate. The calorimeter is in fact three smaller separate uranium

and liquid argon calorimeters, one of which is central (CC) and the other

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two of which are the end calorimeters, and an intercryostat detector. The

CC spans the region of approximately ( || 1). The end calorimeters, ECN

(end calorimeter north) and ECS (south) cover the remaining range, up to

(|| 4).

In order to more effectivelydetect different types of particles, the calorime-

ters are constructed in four layers. The acceleration (scattering) of elec-

tromagnetic particles produces brehmmstrahlung radiation, the emission of

photons. These photons then create electron-positron pairs, which furtherradiate photons. These interactions continue until all the nal products have

energies below a threshold of approximately 10 MeV and can therefore be

measured by summing all of the ionization energies. The electromagnetic

sections of the calorimeters are made of 3-4 mm plates of depleted uranium

with liquid argon between the plates and the interactions are measured by the

ionization deposited in the liquid argon and collected by cells of multilayered

circuit boards which can detect the electromagnetic charges of the ions. The

other type of particle the calorimeter can measure is the hadron. Hadrons

are particles made of quarks bound together by the strong force, and there-

fore behave rather differently than electromagnetic particles. Like electrons

and photons, hadrons lose energy by producing secondary particles which in

turn make additional particles, until the original energy is collected into a

shower of particles which are measured by their ionization energies generated

in the liquid argon. Through interactions with atomic nuclei, hadrons can

also create emissions of particles such as pions, which then decay into muons;

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but these particles travel much further into the calorimeter. The hadronic

sections of the calorimeter are split into two levels in order to cover a wide

range of particle energies. The ne hadronic sections are made of a uranium

niobium alloy and are 6 mm thick, and the coarse hadronic sections are much

thicker, at 46.5 mm. In the CC, this layer is made of copper, and in ECN

and ECS it is made of stainless steel. The signal detectors here are also

high-voltage electrodes, collecting ions generated in the liquid argon between

the plates, by the secondary particles in the shower.

4.2.3 The Muon System

The muon system is made of three layers, called A, B, and C. The A-layer is

surrounded by a 1.8 Tesla (T) toroid and is the innermost layer; the B and C

layers both reside outside the toroid. All the muon system layers include drift

tubes and scintillator counters. The drift tubes are used to track muons, and

the scintillator counters measure the time and position of a muon moving

through the detector. This information can be used to determine the speed

of the detected particle. The drift tubes contain gas and a positively charged

wire, so when a charged particle enters, it ionizes the gas and the released

electrons move towards the wire. This interaction further ionizes the gas and

therefore amplies the signal. Muons not only can penetrate deep into the

calorimeter, but also carry a charge. The lack of brehmmstrahlung radiation

makes it difficult to measure their energy in the calorimeter, which is why a

special muon system was created.

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4.3 Triggering and Reconstruction

4.3.1 Triggering

Even considering the time it takes between bunches of injected proton or an-

tiproton beams, as well as shutdowns, the high luminosity of the D detector

means that data collected in Tevatron runs amount to over one million Ter-

abytes per year (each event is about 1 MB). This does not even include every

run; only about 100 events can be written every second, but approximately2.5 million collisions occur every second. Therefore, something must be done

to determine which events should be written and which should be discarded.

Many events are in fact nothing more than particle scattering with no new

particles created from the collision, and are therefore unimportant from a

modern particle physics perspective; these scatterings have been thoroughly

studied over the past few decades. In order to select events, the detector

includes a triggering system. The triggering system does record some events

that do not t the specied criteria as its rst few runs, as a test, but these

make up only a small fraction of the saved data. There are three levels to

the trigger system, named L1, L2, and L3. The rst level (L1) is hardware

based and accepts events at a rate of approximately 2 kHz. L2 includes

hardware parts and simple microprocessors corresponding to each section of

the detector, and has an accept rate of 1Hz. L3 is a more advanced farm of

microprocessors, consisting of hundreds of separate, rack-mounted high end

PCs which reduce the accept rate to 10 Hz, and sends events which pass

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the nal selection to systems which buffer the events and rewrite them to

an offline location to be written. Writing the events also includes some re-

constructed information so that the data will be more easily accessible for

physical analysis.

4.3.2 Reconstruction

After passing through several systems for data acquisition and storage, the

remaining events that have passed through L3 are reconstructed using the

DRECO program. Raw information, either from the detector or from a

Monte Carlo (MC) simulation, is input into DRECO. DRECO, in turn,

outputs each event with all the reconstructed data associated with it. The

process of reconstruction takes several steps. First, detector unpackers orga-

nize and decode the raw information, which may also involve calibration of

the data based on factors specic to each run. This information can be used

to locate the general regions in which hits or showers occurred. Next, data

from the tracking system, along with SMT and CFT hits, are used to recon-

struct the full track of a particle from this system and the nal scintillator

hits.

Vertexing is the third step: the program nds primary vertices, or points

at which proton-antiproton interactions likely occurred. Vertex information

is necessary to reconstruct certain physical. kinematic quantities such as the

transverse energy of a particle. Next, secondary vertices are also predicted;

these points are more important in reconstructing the decay of short-lived

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particles. DRECO is not fully feed-forward and once these vertices are

calculated, they run through multiple algorithms along with information from

the previous steps in order to predict the type of physics object the event

contains. While there are many types of physics objects, we will talk about

muon reconstruction here as it is the most relevant. Muon reconstruction has

three parts. First, the program locates the hits. By using the tracking system

drift tubes and the scintillators, the muon trajectory can be calculated. The

second step is segment nding, which works by a process known as a linkedlist. Hits within a maximum distance of each other, in this case 20 cm, are

matched together if they are not in the same plane or the same drift-tube

wire hit. This match is called a link. If two links also match in the same way,

they are linked together until the link segments are all put together to make

a straight line. Judgment of which links should be put together is based

on chi-squared values and the scintillator hits themselves. In the nal step,

track tting, segments from the different muon system layers are then put

together to create local tracks, although this requires some attention paid to

layer-specic quantities. Finally, the reconstructed local track is matched to

one of the tracks found in the central tracking system (that is, the CFT and

SMT) to create a global track. This process includes consideration of the

solenoid and toroid magnets and their elds, energy loss in various parts of

the detector, and multiple scattering.

Once all of this information has been reconstructed, it must be com-

pared with the ever-present background signals in order to distinguish events

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from regular noise. This comparison is made with MC simulations of back-

ground and of signals. The PYTHIA event generator is the one used for

these events and for the majority of events at D. PYTHIA is based

on the Python programming language and is widely used in simulation of

high-energy physics events, including those at D. The model approxi-

mates the Tevatrons proton-antiproton collisions, including both the current

model of particle physics and quantum effects. PYTHIA simulations are sent

to DGSTAR(D0 GEANT Simulation of the Total Apparatus Response.GEANT is a program developed at CERN and stands for GEometry ANd

Tracking), a program which simulates the D0 detectors response to the par-

ticles generated by PYTHIA. DGSTAR then determines the trajectories of

the simulated particles as well as many trajectory-dependent variables: hits

and their location, particle interactions, and energy loss during those events.

DSIM approximates the digitization of the real events, complete with any

detector program glitches so as to make the simulation as close to reality as

possible. The DSIM output then goes to DRECO to reconstruct the MC

data in the same manner as the raw data is reconstructed.

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Chapter 5

Data Cuts and Pre-Analysis

5.1 Preselection

In order to reduce the reconstructed data to a more manageable level, pres-

election cuts were implemented. This meant that only events that contained

certain characteristics were written to a subset of les which would be pro-

cessed and analyzed, as the other events, while important from a physical

standpoint, were not important to the goals of this analysis. Most of the

preselection consisted of cuts: rejecting certain sections of the data which

could be unreliable or unhelpful in the research. Cosmic rays, for example,

are a source of muons that can penetrate the detector. The detector is en-

closed, which can cut down on some of the background radiation, but theenclosure is meant more to prevent high levels of radiation from escaping

and, like the calorimeter, provides an appropriate shield against particles

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with the exception of neutrinos and muons, which are rarely produced in the

Tevatron. There is a certain part of the detector known as the bottom hole

and detection in this area is unreliable, so muon events in that area were

rejected. Also, in order to eliminate possible cosmic rays, muons had to be

at least .02 cm from the beams in events for which there had been SMT hits.

This minimum distance is called the distance of closest approach (DCA). For

tracks in which there were no SMT hits, the DCA had to be less than .2 cm

to pass the preselection. The SMT is used because it is closest to the line of the proton or antiproton beams, so hits detected in the SMT give the highest

accuracy in determining the position of an event.

There are also other criteria imposed, more concerned with creating a

data set that would include only relevant events. Muons had to have a pT

(transverse momentum) of at least 20 GeV, and each event had to have at

least one good muon. The one muon and two muon events were each se-

lected to have the correct number of good muons, and further cuts specic

to the type of event will be discussed later. Some of the other cuts had to do

with the effects of the data reconstruction; muons were analyzed in relation

to the primary vertex (ie, the reconstructed position of the collision) in order

to match it to a central track, but if there was no sufficiently close vertex,

they were still included in the preselected data. Finally, the muons had to

have segments for both the A and the BC layers of the track; these types

of muons are called Medium Nseg 3 muons, or muons of medium quality

(having a certain number of hits and other characteristics) and segments for

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all three layers, with BC included together.

In addition, several minor preselection processors were included in the

conguration le. The rst eliminated any duplicate events which could

potentially skew the data. While it was unlikely any events were duplicated,

the amount of reconstruction, preprocessing, and transfer of the raw data

can lead to multiple copies of a single le as it is preferable to losing the only

copy of a le.

The data also passed through a data quality processor which eliminatedany bad runs; that is, runs during which there was excessive noise, a partial

shutdown or malfunction of some part of the detector. It also excluded

special runs during which the specications of the detector, for some reason

or another, were deliberately different than they are normally. Such runs are

useful in some types of analysis, but not in a general survey such as this one.

Finally, partial detector reads (events in which, for some reason, not all

the information was read out from the reconstructed le) were eliminated in

the preselection.

5.2 Analysis Cuts

Once the events have been preselected, the analysis can begin. However, it

can be helpful to look at different parts of the data, depending on what weare searching for. In this case, we are looking for CMSPs. As we have said

before, the energy loss of CMSPs over a certain distance should be greater

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than that of faster moving particles, due to the lower velocity. The value

dE/dx, energy loss per unit length, is inversely proportional to the square

of the velocity. However, CMSPs do not lose as much energy than some

smaller particles, as CMSPs do not have inelastic interactions that produce

showers of secondary particles. CMSPs must be distinguished from meson-

decay events which can also produce muons. To do so, isolation cuts were

applied. In one, the total transverse energy across all tracks inside a cone of

radius 0.5 around the muon in the event had to be less than 2.5 GeV, wherethe radius is dened as

R = ( )2 + ( )2

The other cut was a halo cut: the sum transverse energy in the calorimeter

cells in the ring of radius 0.1 < R < 0.4 around the muon track must also be

less than 2.5 GeV.

When looking at the single muon events, muons had to pass both of these

selection cuts. When looking at double muon events, each muon had to pass

at least one of these cuts or one muon had to pass both.

5.3 Monte Carlo Simulations

Signal samples for staus (stable scalar tau particles), W-produced muon

events, and for Z-produced muon events were created using PYTHIA, as

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discussed above. All data was saved in Common Analysis Format (CAF)

trees. CAF is based in ROOT, an object-oriented framework for physical and

statistical analysis. These CAF trees include the trigger and reconstructed

object information that is used in the analysis of high-energy physics events.

5.3.1 Staus

The stau events for p20 data lacked correctly simulated dE/dx information,

so p17 stau simulations had to be used. The stau events were produced at

mass points of 60, 80, 100, 150, 200, and 250 GeV and reconstructed in the

same manner as the actual detector data. The masses given are all within

the predicted stau mass range of 60 GeV to 300 GeV and should therefore all

show some deviation from muon events. While staus are generally thought

to be produced in pairs, this does not eliminate staus as a potential particle

match. The detector is not perfectly efficient and therefore may miss some

particles, or one of the staus produced may not penetrate the detector suffi-

ciently to be written to the eventual reconstructed data. Also, while it is less

likely, it is still possible that the prediction that staus are created in pairs

is false. The stau events were split into two-muon and one-muon events, de-

pending on whether the staus, as the new particle signal simulation sample,

were to be compared with two-muon events (Z decay) or single muon events

(W decay). The data itself was selected to have both single and double muon

events, and was later divided into the two categories. The tables on page 45

shows the distribution of single and double muon events for the various data

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and MC samples.

5.3.2 Z Boson Decay

The Z boson (mass 91 GeV) can decay in several different ways. One of

the possible branches in the Z particle life time is Z + . The detec-

tor signature for this type of decay is distinctive, showing two high-energy

isolated muons. The Z-produced muon event MC exists for comparison pur-

poses. Staus are also predicted to be pair-produced, but would differ from

known Z decay events resulting in two muons, as the stau particles are far

more massive that the muon, whose mass is approximately 0.1 GeV. There-

fore, data which matches stau patterns and not Z-produced muon patterns

may in fact be CMSPs instead of muons. The Z + events were created

using the p20 MC production parameters.

5.3.3 W Boson Decay

The W boson can also decay in several different ways, either into an up and

a down quark, or into a neutrino and a lepton, in our case a muon. The W

lifetime is very short, so detectors usually detect the products; however, neu-

trinos are very difficult to detect because they are chargeless, so the detector

signature is a single isolated high-energy muon and missing energy (of the

neutrino). The W + events are used as comparison to single-muon

events in the data; if a single muon event is inconsistent with both Z and

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W decay, it is possible that the signal is from a CMSP. The W events used

here are from the p17 MC production parameters for the same reason that

we used p17 staus.

5.4 Data Sample

The data sample used for this research was from the p20 data set, where

p20 refers to the release of the software packages used for reconstruction and

analysis. This corresponds to dates after June of 2008, well into Run II,

which began in March 2001. Integrated luminosity for the runs analyzed was

approximately 3 fb, as shown in the below graph.

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All data in the graphs have also passed through the preselection criteria

and one of the two isolation cuts, or both, as discussed in the sections on

preselection and Monte Carlo samples. As a cross check, the data sample with

transverse momentum under a cut of 50 GeV was run against the Z

events, if it had two muons, or the W events, if it had one. This

momentum is too low for most stau events, and so the data should appear

to have a distribution much like the background MC, as shown here.

5.5 Further Analysis Cuts

Following the processing of the Monte Carlo simulations through the halo

and cone cuts, the MC samples were compared. The kinematics of standard

muon events (the Z boson decay sample) differ from those of possible CMSP

events (the stau samples). As said before, CMSPs are much heavier and have

both a greater ionization energy loss and a lower velocity. The transverse

momentum graph for muons, given by

pT = p sin

displays a much narrower peak at lower momentum values; in contrast, for

CMSPs with large enough mass, the lower velocity is counteracted by the

much greater mass in momentum calculations. Staus, for example, display a

much wider peak, with a much greater proportion of high-momentum events.

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The following plots show the pT and dE dx of both the single and double muon

events after processing but prior to any other analysis cuts.

Graph 2: 1D plot of pT for single muon events.

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Graph 3: 1D plot of dE dx for single muon events.

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Graph 4: 1D plot of pT for double muon events.

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Graph 5: 1D plot of dE dx for double muon events.

To separate as many muon (background) events from stau (signal) events,

a hyperbolic cut along a two-dimensional plot of the dE dx vs the transverse

momentum was applied. The cut was placed at an optimal position that

retained as many stau events as possible while at the same time maximizing

the ratio of signal to background plus signal, S S + B . The below graph shows

this cut with the Z + background sample.

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Graph 2: Graph of dE dx vs pT for Z + events with the hyperbolic cut

overlaid

For double muon events, the hyperbolic curve which optimized the stau

data and minimized the fraction of background events for all of the mass

points had the equation y = 1x +50 + .06. The parameters of the curve (of

formula y = 1x + a + b were varied with a step size of 5 for parameter a and of

.005 for b.

This was obviously less than ideal and a smaller step size over a greater

range would provide a better curve, but the hyperbola given gave S S + B equal

to at least 98% in all cases, as shown in the below table:

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Table of Double Muon Events

Stau Mass (GeV) Signal to Signal + Background60 .9820

80 .9908

100 .9921

150 .9942

200 .9944

250 .9945The same hyperbola was used for the single muon selection, with the

exception of the 60 GeV mass point, which was optimized by y = 1x +50 + .055.

The below table shows the signal to signal plus background ratio for the

optimal cut.

Table of Single Muon Events

Stau Mass (GeV) Signal to Signal + Background

60 .9914

80 .9952

100 .9962

150 .9976

200 .9952

250 .9977

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Chapter 6

Results

The most striking nding in the data before any cuts were made was a sharp

drop in the mean value of dE dx at run 240665, found in a run-by-run study

intended to search for any dependence of dE/dx on run number. Runs before

this one have a very consistent dE dx of .08848, and runs after are also consistent,

but with a mean dE dx of .07452.

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Graph 1: Mean value of the dE dx vs the run number

The shift in mean dE dx was corrected for in the nal data. As the plot of the

mean dE/dx showed that aside from the drop, the data was very consistent,

the correction was made by simply adding a constant value to the dE dx of any

runs after 240665. This value was .01396, the difference between the mean

of the runs before run 240665 and the mean of the runs after.

The below graphs show the results of the hyperbolic cut on the data for

the muon pair sample, the single muon sample, and the different cut for the

60 GeV single muon sample.

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Graph 3: Graph of dE dx vs pT for single muon events with the hyperbolic

cut overlaid.

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Graph 4: Graph of dE dx for single muon events passing the hyperbolic cut.

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Graph 5: Graph of dE dx vs pT for single muon events with the hyperbolic

cut for 60 GeV overlaid.

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Graph 6: Graph of dE dx vs pT for single muon events passing the hyperbolic

cut for 60 GeV.

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Graph 7: Graph of dE dx vs pT for double muon events with the hyperbolic

cut overlaid.

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Graph 8: Graph of dE dx vs pT for double muon events passing the hyperbolic

cut.

The below table shows the number of events in a sample of data or MC

which passed the analysis cuts and single or double muon requirement nd

the number of which passed the hyperbolic cut for each muon requirement,

as well as the initial sample size that passed the preselection.

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Table of Stau Samples

Stau Mass (GeV) 60 80 100 150 200 25

Initial Sample Size 100000 100000 100000 100000 50000 100

After Single Muon Selection 33561 35253 34697 37380 18367 37

After Double Muon Selection 66746 62574 74314 66153 34559 678

Hyperbolic Cut for Single Muons 11125 17371 21682 33990 17253 36

Hyperbolic Cut for Double Muons 6377 12661 14795 20055 20686 211

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Table of Data and MC Background Samples

Sample Type W Z Data

Initial Sample Size 513500 51155 5999509

After Single Muon Selection 69220 - 1852694

After Double Muon Selection - 21605 209963

Hyperbolic Cut for Single Muons 83 - 16676

Hyperbolic Cut for Single Muons, 60 GeV cut - - 19492

Hyperbolic Cut for Double Muons - 117 2562

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Chapter 7

Conclusion

The dE dx run study and post-hyperbolic cut data both will contribute to the

search for CMSPs in Run II p20 data; while similar analysis has been carried

out, it has not been conducted with a data set of this size. The cut was not

very specic, and in further studies the parameters could be varied along a

wider range with a smaller step size in order to truly optimize the position

of the cuts and the amount of possible CMSP data passing the cut. An

Articial Neural Network or similar system which could make an even more

tted boundary between background and signal events would be ideal, and

given more time could provide a much more accurate and precise selection.

Finally, the dE/dx information and other variables would be best studied

if the MC sample was from the same version as the data; that is, from p20.In particular, a supersymmetric particle other than the stau, such as the

chargino, could be implemented in further studies to expand the range of

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types of CMSPs.

The study demonstrates the value of using a muon candidates dE dx in

the silicon detector to distinguish actual muons from potential CMSPs. An

earlier study used the time-of-ight to separate the events, and using both

variables together in an analysis will be a powerful tool for a possible discov-

ery.

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