Feasibility Study of a Measurement of P¯P Total Cross-Section At

Feasibility Study√ of a Measurement of pp¯ Total Cross-Section at s =1.96 TeV using the FPD Subdetector of DZero Experiment

by Carolina Garc´ıa

A thesis submitted in partial fulﬁllment of the requirements for the Degree of Master in Sciences - Physics Physics Department Universidad de los Andes

Bogot´a D.C. - Colombia

January 2007

Approved by: PhD., Carlos Avila.´ Dr.rer.nat., Bernardo G´omez. PhD., Carlos Quimbay. i

Abstract

A feasibility study of the total cross-section (σtot) for proton-antiproton collisions at √ center-of-mass energy ( s) of 1.96TeV has been developed. The study consists of changing the position of the FPD subdetector at DZero Experiment and obtaining the total cross-section from the Luminosity Independent Method using MonteCarlo simulations. The elastic events are analyzed separately from the inelastic events. The obtained results show cases with an uncertainty 50% lesser than 2mb, which is the uncertainty reported by real experiments. Hence, we found that the positions 10, 12 and 14σ,whereσ is the beam size, with an emitancia of =10π are optimal

for the σtot measurement using the FPD. Additionally, we estimate an uncertainty of about 1.1mb for the total cross-section measurement when the FPD is located at the positions established in the data-store on February 2006, with a rate of background about 20% for the inelastic events.

Resumen

Se ha realizado un estudio de factibilidad para efectuar la medición de la sección-eficaz √ total (σtot) de las colisiones protón-antiprotón, a energ´ıas de centro-de-masa ( s)de 1.96TeV. El estudio se efectua cambiando la posición del subdetector FPD del exper- imento DCero y obteniendo la sección-eficaz total a partir del Mtodo Independiente de la Luminosidad usando simulaciones de MonteCarlo. Los eventos elásticos son estudiados independientemente de los inelásticos. Los resultados obtenidos muestran casos con una incertidumbre 50% menor a los 2mb reportada por los experimentos reales. Se establece entonces que las posiciones 10, 12 y 14σ, donde σ es el ancho del haz, con una emitancia de =10π son óptimas para la medición de σtot con el FPD. Adicionalmente se estima que con las posiciones establecidas para la toma-de-datos llevada a cabo en febrero de 2006, la medición de la sección-eficaz total que se obtenga con el FPD tendrá una incertidumbre alrededor de 1.1mb con una tasa de background alrededor del 20% para los eventos inelásticos. Acknowledgments

Working in this dissertation and writing this document are a very complete and adorable experience in my life. And, as in the life, the experience and preceded work of others are necessary to achieve that you want (that is close or almost that you desire). Without the help of others (many people out of this paper) I never would have obtained that I started.

First I would like to thank my Advisor professor Carlos Avila, not only for being my advisor and provide me the topic, also for his patience and comprehension of my work. I will always appreciate the opportunity provided by him; although we never found us in a class and he could have said -no- to my interest, he took the risk.

I was fortunate enough to count on Luis Miguel. His constant and important support, in discussing the strategies to obtain results from D0gstart and its physics, is very grateful.

The help of Jorge Molina with the Propagation Function and the email communica- tion is grateful as well.

I am also deeply grateful to Santiago, because of his nice and punctual comments and questions at the end of this process and his ﬁrst explanations when all began.

Many thanks as well to Andres for reading a draft of this document and providing me an unsuspected force to face the ﬁnal steps of this work.

ii iii

The ﬁnancial support, for my Master and this project, from the Physics Department and the Faculty of Sciences at Universidad de los Andes are really appreciated.

It has been a great pleasure and honor to study and work with the scientists listed above and the faculty, staﬀ, and students at the Universidad de los Andes, where I constantly felt inspired by the intelligence and humanity surrounding me.

I would specially like to thank Professor Bernardo Gomez for his always support and provide me the enthusiasm to continue the not easy way that I chose. I owe he more that I could express in a piece of paper. His support made all the diﬀerence in my academic career.

Sources of support, joy, and laughter in my journey at Los Andes, that I would like to thank, are also: Angela, Angelita, Luisilla, CaroV, Magnis, Giova, Diana, Carlitos, Juan Andres, Nicolas and all the people of the FUT 2006.

Last but not least, I am thankful to My Parents. Their sacriﬁces to ensure that I had a good education are appreciated as well as the freedom for choosing my path.

Carolina Garcia Contents

List of Figures vi

List of Tables ix

1 Introduction 2

2 The Total Cross-Section Measurement 6

2.1 The Total Cross-Section (σtot)...... 7

2.2 σtot MeasurementTechniques...... 7 2.2.1 TheLuminosityIndependentMethod(LIM)...... 9 2.3 Physical Quantities Involved in LIM for this Feasibility Study .... 10

3 Accelerator Description 12 3.1TheTevatronatFermilab...... 13 3.2ParticleBeamsandPhaseSpace...... 16 3.2.1 Transversalphasespacedynamics...... 17 3.2.2 Beam Emittance ...... 18 3.2.3 Longitudinalphasespacedynamics...... 19 3.3ParametersfortheTevatron...... 20 3.3.1 LuminosityintheTevatron...... 20

4 Detector Description 23 4.1TheDØDetector...... 24 4.2TheForwardProtonDetector(FPD)atDØ...... 32

iv CONTENTS v

4.2.1 TheRomanpotsoftheFPD...... 33 4.2.2 TheEﬀectiveLengthsofFPD...... 34 4.2.3 TevatronTimingandElasticEventsintheFPD...... 36 4.2.4 High β Store...... 38 4.3TheLuminosityMonitors(LM)atDØ...... 39 4.4CoordinateSystemfortheFPD...... 40

5 Physical Processes Involved in a pp¯ Collision 42 5.1MainDiffractiveProcesses...... 44 5.2Kinematicsoftwo-bodyprocesses...... 47 5.3DifferentialElasticCross-SectionRemark...... 48 5.4Definitionsofusefulvariables...... 49

6 Simulation Description 52 6.1ClassiﬁcationofEventsStrategy...... 52 6.2MonteCarloStudyofElasticEvents...... 54 6.2.1 DistributionoftheTransferredMomentum...... 56 6.2.2 Calculation of the Geometrical Acceptance of the FPD . . . . 59 6.2.3 FiducialCuts...... 62 6.3SimulationStudyofInelasticEvents...... 63 6.3.1 BeamPipeEﬀectViewusingPYTHIAandGEANT4..... 65 6.4TheTotalCross-SectionUncertainty...... 69

7 Inelastic Acceptance Simulation Results 71 7.1 Acceptance of LM for Each Process ...... 72 7.2 Single Diﬀractive FPD Acceptance Changing Positions ...... 74 7.3 Pots located at high β Store...... 77

8 Statistical Errors for σtot,pp¯ Simulation Results 81 8.1TablesofFits...... 81 8.2Tableofeachtermuncertaintycontribution...... 84 8.3Totalcross-sectionuncertaintyresults...... 86 CONTENTS vi

8.4Changingemittance...... 87 8.5 High-β-Storeresults...... 90 √ 9 Systematic Errors for σtot,pp¯ at s =1.96TeV Results 92

10 Background Analysis and Results 95 10.1MultipleInteractions...... 95 10.2HaloBackground...... 97

11 Conclusions 102

Bibliography 105

A The FPD Elastic Dispersion Function 107 A.1 Input parameters ...... 107 A.2Obtainingtheﬁnalpositioninthedetectors...... 109 A.3Theoutputdistribution...... 110

B The FPD Propagator Function 112 B.1 Input Parameters ...... 112 B.2OutputAdjustment...... 113

C Computation Tools 115 C.1NotesofusingDØgstar...... 115 C.1.1CARDFILES...... 117 C.2NotesofusingPOMWIG...... 118 C.3NotesofusingPYTHIA...... 119 C.4NotesofusingGeant4...... 120 List of Figures

1.1 Fit from experimental data of the pp¯ totalcrosssection...... 3

3.1 The Tevatron accelerator chain at Fermilab...... 13 3.2Exampleoflongitudinalalignment...... 19

4.1TheDØDetectorcomponents...... 24 4.2SchematicidentiﬁcationofparticlesintheDØDetector...... 25 4.3SMTdetectorlayout...... 26 4.4CalorimeteratDØDetector...... 28 4.5MuonSystematDØDetector...... 30 4.6TheForwardProtonDetector...... 33 4.7FibersplanesfortheForwardProtonDetector...... 34 4.8TimingintheFPD...... 36 4.9PositionoftheLuminosityMonitors(LM)atDØDetector...... 39 4.10TheLuminosityMonitor...... 40 4.11DØCoordinateSystem...... 41 4.12FPDcoordinatesystem ...... 41

5.1SchematicViewofanElasticprocess...... 44 5.2SchematicViewofSingleDiffractiveSoftProcess...... 45 5.3SchematicViewofSingleDiffractiveHardProcess...... 45 5.4SchematicViewofDouble-DiffractiveProcess...... 46 5.5SchematicViewofDoublePomeronExchangeProcess...... 46

vii LIST OF FIGURES viii

6.1SingleDiffractiveProcessCandidate...... 53 6.2DoublePomeronExchangeProcessCandidate...... 55 6.3Rangeforthefitintheblockfunction...... 56 6.4Distributionsoftheexpectedtransferredmomentum...... 57 6.5 Distributions with =10π changingP1Uposition...... 58 6.6 Schematic View of the FPD Acceptance ...... 60 6.7 Acceptance changing positions for an emittance of =10π ...... 61 6.8 Acceptance changing positions for an emittance of =15π ...... 61 6.9ElasticTrigger(schematic)...... 62 6.10GeometryViewforGeant4SimulationoftheBeamPipe...... 66 6.11SingleDiffractiveSoftEvent...... 66 6.12Inelasticevent...... 66 6.13 Single Diffractive (X+¯p), η Distribution...... 67

6.14 Single Diﬀractive (X+¯p), pt Distribution...... 67

6.15 Single Diﬀractive (p+X), pt Distribution...... 67 6.16 Single Diﬀractive (p+X), η Distribution...... 67

6.17 All QCD processes, Pt Distribution...... 67 6.18 All QCD processes, η Distribution ...... 67 6.19SingleDiﬀractive(p+X)...... 67 6.20 Single Diﬀractive (X+¯p) ...... 68 6.21MSEL=2Inelasticprocess...... 68

7.1DistributionsmeasuredbyLuminosityMonitorSouth...... 73

8.1 Fit example for AD-PU detectors with =10π changing positions. . . 82 8.2 Fit example for AD-PU detectors at 12σ with =10π...... 83 8.3 Fit example for AD-PU detectors at 14σ with =10π...... 84

B.1 Enter parameters for the Propagator Function ...... 113

C.1ThedataﬂowfortheD0gstar...... 116 C.2TheLuminosityMonitorgeometryatDØgstar...... 118 LIST OF FIGURES ix

C.3 Pythia Processes for MSEL=2 with 10000 events ...... 121 List of Tables

2.1PythiaCross-SectionsValues...... 8

3.1 Operation performance of the Tevatron for Run I and goals for Run II 22

4.1 Input event rates at diﬀerent levels of trigger ...... 31 4.2 FPD detectors parameters for =10π ...... 35 4.3 FPD detectors parameters for =15π ...... 37

6.1 Common area region for AD-PU and =10π ...... 63 6.2 Common area region for AD-PU and =15π ...... 64 6.3 LM acceptance using a tube of beryllium ...... 69

7.1 Acceptance of the Luminosity Monitors for 10000 events ...... 74 7.2 FPD acceptance at 10σ,with =10π ...... 75 7.3 FPD acceptance summary, with =10π ...... 76 7.4 FPD acceptance at 10σ,with =15π ...... 77 7.5 FPD acceptance summary, with =15π ...... 78 7.6 FPD acceptance for High β run usingPOMWIG...... 79 7.7 FPD acceptance for High β run usingPYTHIA...... 80

8.1 Fit table at 10σ with =10π ...... 82 8.2 Fit table at 12σ with =10π ...... 85 8.3 Fit table at 14σ with =10π ...... 85 8.4 Each term uncertainty contribution with =10π ...... 86 8.5 The total cross-section uncertainty with =10π ...... 87

x LIST OF TABLES 1

8.6 Fit table at 10σ with =15π...... 88 8.7 Fit table at 12σ with =15π ...... 88 8.8 Fit table at 14σ with =15π ...... 89 8.9 Each term uncertainty with =15π ...... 89 8.10 The total cross-section uncertainty with =15π ...... 90 8.11 High β run uncertainty contribution of each variable with =10π .. 91 8.12 High β run results with =10π ...... 91

9.1 New σtot from position uncertainty with =10π ...... 93

9.2 New σtot from eﬀective length uncertainty with =10π ...... 94

9.3 New σtot from sistematic uncertainty for the High-β-Store positions . 94

10.1 High β run Tevatron parameters for FPD roman pots atp ¯ side.... 96 10.2PythiaCross-SectionsValues...... 97

11.1 Summary of the Total Cross-Section for diﬀerent positions of the FPD 104 11.2 Total Cross-Section Uncertainty for the FPD located at the High-β-Store positions104

A.1 P1U fits with =10π at 10σ ...... 110 A.2 Roman Pot fits with =10π at 10σ ...... 111 A.3 P1U and A1D fits with =10π changingpositions...... 111

B.1 Tevatron latticep ¯ side...... 114 Chapter 1

Introduction

The total cross section for proton-antiproton collisions (σtot,pp¯) has been measured by √ several experiments at diﬀerent center-of-mass energy ( s), but just few measurements in the high energy scale are diﬀerent from cosmic ray data1. This is because √ there is only information available from the Tevatron at Fermilab ( s=2 TeV) and √ the proton synchrotron, SPS at CERN ( s=0.4TeV).

√ In Fermilab, three measurements at s =1.8TeVofthep¯p total cross section have been reported. In 1992, E710 experiment measured σtot,pp¯ =(72.8±3.1)mb [1]. Then, in 1994 CDF experiment measured σtot,pp¯ =(80.03±2.24)mb [2]. And ﬁnally in 1999,

E811 experiment measured σtot,pp¯ =(71.71 ± 2.02)mb [3]. Results from E811 and E710 are similar and both their measurements diﬀer in more than three standard deviations when compared to the CDF measurement.

The discrepancy between these measurements has a negative impact when one wants

to do extrapolations at higher energies, for example to predict the value of σtot at the energy of the LHC accelerator, or when one wants to use σtot to normalize information of cross sections measured at the Tevatron.

1cosmic rays in the earth atmosphere are radiation composed of approximately 87% protons, 12% alpha particles and other heavier atomic nuclei

2 CHAPTER 1. INTRODUCTION 3

Figure 1.1: Fit from experimental data of the pp¯ total cross section.

We can see a higher uncertainty of the prediction of (σtot,pp¯) at LHC energy scale [4]. Plot taken from [5]

Figure 1.1 shows a ﬁt of experimental data, including data from cosmic ray experiments, to establish the behavior of σtot with the rise of energy, and also to extrapolate at LHC energy. Until now the question has been whether σtot increases as log s or as log2 s. In the Tevatron collider the results of the experimental groups E710 and E811 seem to favor a log s increase, while CDF data favors log2 s [4].

Then, it becomes necessary to study the possibility of making a new measurement at Fermilab that could solve the discrepancy. This document presents the study of √ the feasibility to get a new measurement of the p¯p total cross section at s =1.96 TeV using the subdetector Forward Proton Detector (FPD) of the DZero experiment.

The study in this dissertation consists of changing the positions of the FPD roman pots, accorded with the emittance of the beam, in order to simulate the corresponding total cross-section measurement with its uncertainty. An injection optics is required CHAPTER 1. INTRODUCTION 4

and used in our study; this implies a low luminosity, which allows a FPD position closer to the beam line.

The structure of this dissertation is as follows.

In chapter 2 we present the total cross-section (σtot) deﬁnition and the measurement techniques developed for pp¯ colliders focusing on the luminosity independent method which is the technique used in our study.

In chapter 3, basic concepts of accelerator physics are introduced, with an emphasis in the Tevatron description. The components and the physical advantages of the detectors at DZero (DØ) Experiment that we use for our feasibility study are described in chapter 4. These detectors are the Forward Proton Detector (FPD) and the Lu- minosity Monitors.

An overview of the physical processes involved in the pp¯ collisions are explained in chapter 5, including an introduction of the elastic and single scattering processes, as well as the deﬁnition of Mandelstam variables and other useful kinematics variables.

The simulation description for our study of the σtot uncertainty is discussed in chapter 6. The results of the detectors acceptance, according with the simulation of pp¯ √ collisions at s =1.96 TeV, for the diﬀerent types of QCD processes are presented in chapter 7.

The results of σtot uncertainty study presented in this document, are divided according to the source of the uncertainty involved. Uncertainty results from the statistical errors are reported in chapter 8; uncertainty results from systematic errors are reported in chapter 9.

√ An analysis of the background present in the pp¯ collisions at s =1.96 TeV (Tevatron CHAPTER 1. INTRODUCTION 5 center-of-mass energy) is discussed in chapter 10. The conclusions of this feasibility study are present in chapter 11.

In addition, a brief introduction to the software used in this total cross-section uncertainty study (the ELASTIC DISPERSION SOFTWARE, PROPAGATOR FUNCTION, PYTHIA, POMWIG, and DØ GEANT Simulation of the Total Apparatus Response (DØgstart)), are discussed in appendices A, B and C. They also reported details of the simulation parameters. A CD is available with this document, where the code of main programs and results are presented. Chapter 2

The Total Cross-Section Measurement

Although the diﬀerent high energy experiments around the world are interested in diﬀerent processes, they must share the same normalization constant if they belong to the same collider. This normalization constant could be the luminosity of the ac-

celerator or the total cross-section σtot. Therefore, providing a correct measurement of σtot, with low uncertainty, is a basic goal in the frontier of experimental physics.

Furthermore, the total cross-section also gives how many collisions will take place when the bunches cross inside the collider. Then, in order to have the most complete detection system to be able to sustain the collision, it is necessary to measure σtot or to extrapolate the current data to the energy required.

An actual example is the experiment TOTEM at the Large Hadron Collider (LHC) √ that is expected to run in 2008 with a center-of-mass energy of s =14TeV. The experiment TOTEM has the aim to measure the total cross-section and study the √ diﬀractive processes that appear in the proton-proton collision at s =14TeV [5].

6 CHAPTER 2. THE TOTAL CROSS-SECTION MEASUREMENT 7

2.1 The Total Cross-Section (σtot)

The total cross-section σtot is the eﬀective area over which one incident particle inter- acts with one target particle [6]. The most important feature is that this quantity is independent of the initial wave functions that represent the particles in the collision.

This collision is know as a scattering event. σtot has the dimensions of an area and √ its basic unit in high-energy physics is 1 barn=10−24cm2.At s =1.8TeV,thep¯p total cross section on the order of 102mb [3] (1mb =10−3barns).

The probability of interaction between the incident particle and the target per unit flux is also known as the total cross-section. The interaction can produce different outcomes; there are elastic processes (el), single diffractive (sd), double diffractive (dd), and non-diffractive (nd) processes (refer to chapter 5 for processes definitions). The three last processes are known as inelastic events, where there is always creation of particles. In p¯p collision there are two kinds of single diffractive process, one when the proton fragments and the other when the antiproton fragments. We can take into account the contributions of each physical process separately, hence σtot,pp¯ becomes:

σtot,pp¯ = σel + σine = σel + σsdp + σsdp¯ + σdd + σnd (2.1)

Using the MonteCarlo generator of collisions PYTHIA C.3, we obtain the values of √ each term of eq.2.1 in the table 2.1 for a pp¯ collision at s =1.96 TeV. Notice that the total cross-section values are actually the sum of the others.

2.2 σtot Measurement Techniques

Due to the development in higher energy experiments a lot of techniques for the total cross-section measurement have appeared over the decades. We will bring up only three of them which are most used in pp¯ colliders.

Luminosity dependent method CHAPTER 2. THE TOTAL CROSS-SECTION MEASUREMENT 8

Physical Process Cross Section [mb] Total 73.9765863 Elastic 15.0208516 Single diffractive X+¯p 6.236495 Single diffractive p+X 6.236495 Double diffractive 7.45168221 Inelastic, non-diffractive 39.0310625

Table 2.1: Pythia Cross-Sections Values

This is the most direct method for the total cross-section measurement. It depends on the total number of collisions Ntot and the integrated luminosity L. In the collider t L the integrated luminosity is obtained during a period of data t by L = 0 dt,where L is the instantaneous luminosity. The total number of events in the collision is expressed in terms of the number of elastic collisions Nel and the number of inelastic collisions Nine as Ntot = Nel + Nine. The total cross-section is measured from the basic deﬁnition of luminosity as:

N N + N σ = tot = el ine (2.2) tot L L The precision of this method is limited by the systematic error of the luminosity (about 6% to 7%). In section 3.3.1 we discuss the luminosity of the Tevatron collider.

From the measurement of elastic scattering

This method is based on the Optical Theorem to measure σtot from the elastic cross- section σel. The optical theorem is a statement of the conservation of probability in 2 a scattering event, and relates a cross section (|fk(θ)| ) to an amplitude (Im fk(θ)) in a particular direction (with the forward direction as θ =0)[7]

4π σ = Im f (θ) (2.3) tot k k where k is the relative momentum of the incident particles. Choosing Im fk(θ)as CHAPTER 2. THE TOTAL CROSS-SECTION MEASUREMENT 9

the imaginary part of the elastic cross-section amplitude, and k =1/(c)(where is the Planck constant and c is the light speed):

dσel | |2 2 2 with dt = fk(θ) =(Re fk(θ)) +(Im fk(θ)) , equation (2.3) becomes: 2 2 22 2 dσel − (Re fk(θ)) σtot =16π c 1 (2.4) dt σel(θ)

( ) and with ρ = Re fk θ Im fk(θ) dσ 1 σ2 =16π22c2 el (2.5) tot dt 1+ρ2

The measurement of the elastic cross section, in the colliders, is usually performed in the transferred four-momentum region 0.01 ≤|t| < 0.1(GeV2) in order to get, by suitable extrapolation, the number of elastic events per unit interval of t at t =0. From experiments, the relation is an exponential function of t (as discussed in section

6.2) [1] dσ dσ el = el exp (bt) (2.6) dt dt t=0 Recall the luminosity deﬁnition L = N/σ and expressing it only for the elastic part: dN dσ el = L el (2.7) dt t=0 dt t=0 Finally, the total cross-section is obtained from (2.5) with (2.7): 2 2 2 1 16π c dNel σtot = 2 (2.8) L 1+ρ dt t=0 This method requires again the knowledge of the luminosity, hence there is a scale

−1/2 error about 3.5% mainly because the relation σtot ≈ L .

2.2.1 The Luminosity Independent Method (LIM)

The Luminosity Independent Method (LIM) for the total cross-section measurement is the technique used by the experiments E710, CDF and E811 for the measurement CHAPTER 2. THE TOTAL CROSS-SECTION MEASUREMENT 10

of σtot in the Tevatron [1],[2],[3].

The total cross-section is obtained by joining the results of the above techniques. Taking the ratio of (2.8) to (2.2):

2 2 16π c (dNel/dt)t=0 σtot = 2 (2.9) 1+ρ Nel + Ninel 2 2 Recalling that: 16π c are the known common constants, Nel is the number of elas-

tic events, (dNel/dt)t=0 is the extrapolation of σel to a transferred four-momentum

of t =0,Nine is the number of inelastic collisions and ρ is the ratio of the real to ( ) imaginary part of the forward scattering amplitude Re fk θ . Im fk(θ)

Because this technique is luminosity independent, the precision of σtot measured is better than the other techniques.

2.3 Physical Quantities Involved in LIM for this Feasibility Study

The technique used in this feasibility study is the luminosity independent method (LIM) discussed in the above section. Changing the location of the FPD detectors an

analysis of the σtot measurement is presented in this dissertation, according with the

number of inelastic collisions Nine, the number of elastic collisions Nel and extrapolation of σel to t = 0, obtained.

The value of ρ in LIM, eq 2.9, is ﬁxed to 0.15 according with experimental data [3]. MonteCarlo studies are developed for elastic and inelastic events separately, as explained in section 6.2. The number of inelastic events is measured directly by taking into account the acceptance of each inelastic process, while the number of elastic events is measured from the expected distribution of the transferred four-momentum generated only by elastic processes. CHAPTER 2. THE TOTAL CROSS-SECTION MEASUREMENT 11

From experiments, the relation between the elastic cross-section σel and the transferred four-momentum t is known. The distribution is an exponential function: dσ dσ el = el exp(bt) (2.10) dt dt t=0 then, the ﬁt in the elastic distribution of the transferred four-momentum expressed 2 2 dNel −Bt 16π c as dt = A exp , with the constant C = 1+ρ2 , in the eq 2.9, gives that the luminosity independent method looks like:

A σtot = C A (2.11) B + Ninel where Ninel is expressed as Ninel = Nsd +Nnd +Ndpe with Nsd as the number of events

for single diﬀractive sd processes, Nnd is the number of non-diﬀractive nd processes

and Ndpe is the number of events for double pomeron exchange dpe processes. Refer to more details on inelastic processes in chapter 5. Chapter 3

Accelerator Description

The experiment with alpha particles by Rutherford began the demonstration of scattering techniques in nuclear physics. This famous experiment shows, because of the angular distribution of scattered alpha particles from an atomic target, that atoms have small nuclei at their center where the mass is concentrated. Further studies established that these nuclei are made of protons and neutrons.

Higher energy experiments, many decades later, showed that protons and neutrons themselves contain small hard constituents, the quarks. In fact, the rise in energy in scattering experiments also allowed discovering new particles.

In order to reach higher energies and open a deeper understanding in particle and nuclear physics, particle colliders were developed. The reason is that the relative momentum k of the particles must be higher to produce a small space resolution. The space resolution is limited by the wavelength of their relative motion λ =2π/k.For √ a scattered particle 1 and a target particle 2, k ∼ 2E1M2 while for colliding beams √ k ∼ 4E1E2 [8].

The high energy collider considered in the feasibility study presented in this document that is explained in the ﬁrst section of this chapter, is the Tevatron at the Fermi Na- tional Accelerator Laboratory (Fermilab) located in (Batavia-Illinois) United States

12 CHAPTER 3. ACCELERATOR DESCRIPTION 13

of America. Then in sec 3.2 we discuss concepts of beam optics like the transport matrix and beam emittance. At the end are presented the parameters of the Tevatron.

3.1 The Tevatron at Fermilab

Figure 3.1: The Tevatron accelerator chain at Fermilab. It is possible to see the points where DØ and CDF experiments are located.

Since 1988 and until the LHC begin to run in 2007, the Tevatron at Fermilab is the highest energy particle collider in operation of the world. It was the ﬁrst superconducting synchrotron constructed. From 1992 to 1996 data collection took place in the called Run I. Since 2001 to 2009 takes place the so called Run II.

The Tevatron is a complex chain of increasing energy accelerators, that accelerates protons and antiprotons (to almost 1000 GeV each) to two collisions points the DØ and CDF. A schematic view of the Tevatron is shown in ﬁg 3.1, their components are explained as follows [9]: CHAPTER 3. ACCELERATOR DESCRIPTION 14

COCKCROFT-WALTON This is the pre-accelerator that creates H- ions and accelerate them to a kinetic energy of 750 KeV. The process begins with hydrogen gas released into a magnetron surface plasma source. The electron is removed from the hydrogen atom with an electric ﬁeld, produced between the anode and cathode of magnetron. The free protons are able to be attached to the cathode surface or to capture two electrons, this latter form the H- ions. Outside the magnetron, the H- ions are guided using a magnetic ﬁeld and an accelerated from 18 KeV to 750 KeV.

LINAC This is a linear accelerator of about 152 m long where the H− ions reach a kinetic energy of 400 MeV and are converted in a stream of protons. The acceleration is done by a set of oscillating electric ﬁelds and the H− ions get stripped of their two electrons when the passed through a carbon foil.

BOOSTER This is a fast-cycling circumference ring of about 478 m circumference. where the proton beam reaches an energy of about 8 GeV and after about 20000 revolutions 5 to 7 bunches are produced, each containing about 5-6x1010 protons. The synchrotron constraints the protons to a closed circular orbit, using a series of bending magnets and quadrupole focusing ﬁelds, and accelerates them with a set of radio frequency cavities (RF) that steadily increases their energy. The magnetic ﬁeld strength and the RF frequency increase in a synchronous manner as the particles energy rise.

MAIN INJECTOR It has two functions: To coalesce the proton bunches into a single high-intensity bunch of about 5x1012 protons with an energy of 150 GeV and to extract proton bunches at 120 GeV for the antiproton facility. The Main Injector is another synchrotron ring of about 3 Km of circumference and it works with a current of about 9.375 Amperes. CHAPTER 3. ACCELERATOR DESCRIPTION 15

TARGET HALL AND ANTIPROTON SOURCE The 120 GeV proton bunches delivered by the Main Injector are used to produce antiprotons. The proton beam is directed to impact on an external nickel/cooper target disk of 10 cm in diameter and 24cm thick. Lithium collector lens focus the secondary particles, like the antiprotons, produced after the impact. For a million of protons sent only eight antiprotons are produced, this is a disadvantage that becomes the main limiting factor for the Tevatron: the intensity of the antiproton beam.

Since the antiprotons are produced in a large range of momentum and angles, they are derived to a Debuncher that reduce the momentum spread of the antiprotons and also restrict their transverse oscillations. The Debuncher is a ring of about 518m of circumference.

When a coherent beam of 8 GeV antiprotons is achieved, the antiprotons pass to the Accumulator where they are arranged into bunches. The Accumulator is a ring that cool the antiprotons, using RF and stochastic cooling techniques, with a rate up to 10x1012 antiprotons per hour.

RECYCLER This is a permanent magnet storage ring that accumulates and re-cools the dilute antiprotons to 8 GeV of energy. When antiprotons reach energy of 8 GeV they are transferred to the Main Injector where their energy is boosted to 150GeV.

TEVATRON This is the synchrotron ring where the proton-antiproton collisions take place. The Tevatron circumference is about 6 Km and has superconductive magnets to produce ﬁelds of 4 Tesla. In this tunnel the proton and antiproton beams delivered by the Main Injector reach an energy of 0.98 TeV each. Once this energy is reached, the beams are squeezed to small transverse dimensions at two diﬀerent locations of the ring named BØ (where the CDF particle detector is located) and DØ (where the CHAPTER 3. ACCELERATOR DESCRIPTION 16

DØ particle detector, discussed in next chapter, is located). The ﬁnal beams in the Tevatron, as mentioned before, are not continuous, they are conformed by bunches (groups of particles) moving in opposite directions inside the ring, therefore they have a certain time structure (discussing in 3.3).

3.2 Particle Beams and Phase Space

The particles in accelerators rings or linacs are bent and accelerated according to a beam transport system. This system is called Lattice and it is composed of arrays of magnets and radiofrequency (RF) cavities.

The magnets are divided in to quadrupoles and dipoles in order to keep the particles inside the accelerator. The quadrupoles have the function of focusing the particles while the dipole magnets deﬂect them.

The radio frequency cavities have the function of accelerating the particles using RF ﬁelds from electromagnetic waves.

Then, the particles equations of motion are like the equations of particles moving in an electromagnetic ﬁeld governed by the Maxwell equations. The solution of the diﬀerential equations, from a point (u0,u0) of the phase space to another (u,u ), is expressed as: u(s) C(s) S(s) u0 = (3.1) u (s) C (s) S (s) u0 where u stands for x,y or z, u = du/ds with s being a free parameter in the phase space and the Matrix: C(s) S(s) M = (3.2) C(s) S(s) is called the Transport matrix, if we calculate the principal solutions for individual magnets only. Since the motion of the particle is in three dimensions we have a 6x6 CHAPTER 3. ACCELERATOR DESCRIPTION 17

matrix. The matrix is written as the product of ordered individual matrices, each one representing a physical term in the lattice i.e. a dipole, with the rightest matrix as the ﬁrst that the particle meets.

In order to understand the dynamics of the bunches, it is usually expressing the motion in the transverse and longitudinal plane, separately.

3.2.1 Transversal phase space dynamics

In the case of periodic systems, for the transverse plane, the equation of motion is called Hill’s equation: u + K(s) · u =0 (3.3)

where u stands for x or y and K(s) is a function that depends on the distribution of the focusing along the beam line. The ansatz obtained is similar to the solution of a harmonic oscillator equation [10]: √ u(s)= β(s)cos[ψ(s) − ψ0] (3.4)

the terms and ψ0 are integration constants. is the beam emittance and it is discussed in the next section. The phase ψ(s)andβ(s) are called betatron functions or lattice functions. In sec. 4.2 we present the betatron functions of the Tevatron in the region where the FPD subdetector of DØ experiment is located.

The betatron functions are very useful to expresses the beam dynamics. It can be

shown that the general transport matrix, from a point s0 to any point s, is [10]:

β(s) (cos[ψ(s)] + α0 sin[ψ(s)]) β(s)β0 sin[ψ(s)] M = β0 √α0−α(s) − 1+√α(s) α0 β0 − cos[ψ(s)] sin[ψ(s)] ( ) (cos[ψ(s)] α(s)sin[ψ(s)]) β(s) β0 β(s) β0 β s (3.5)

From the interaction point s0 to any point s1, only for a 2D transportation we have: y(s1) y(s0) = M01 (3.6) y (s1) y (s0) CHAPTER 3. ACCELERATOR DESCRIPTION 18

Solving y(s1)=y1 from eq. 3.6 using eq. 3.5, we obtain:

Y 01 y1 = m01 y0 + L θ eff y β1 m01 = (cos φ + α0 sin φ) β0 Y 01 Leff = β1β0 sin φ (3.7)

where y0 is the beam oﬀset in the y direction at the interaction point and θy is the Y 01 angle in the vertical plane of the scattered particle. Leff is called the eﬀective length from the interaction point at DØ to the point y1.

Another variable that is related to the beta functions β is the beam transverse size σ. It is obtained for each axis as: β σ2 = − (3.8) 2πln(1 − F ) where is the beam emittance (discussed in the next section) and F is the fraction of particles that are contained inside the envelope β.

3.2.2 Beam Emittance

The region in the phase space (plane uu) which is occupied by the particles in a beam is the beam emittance [10]. Therefore there is an emittance in x and an emittance in y. The usual unit of is π and corresponds with the constant of motion given by eq. 3.4, that is the called Courant-Snyder invariant:

γu2 +2αuu + βu2 = (3.9) this expression relates the emittance with the betatron functions and corresponds to an equation of an ellipse of area π. According to the Liouville’s theorem, any particle starting with a trajectory inside the ellipse of parameters β, α and γ will stay on it, although the betatron functions change in each point.

In the accelerator the beam emittance is a measure of the ”transverse or longitudinal temperature” and depends on the characteristics of the beam and other eﬀects. For CHAPTER 3. ACCELERATOR DESCRIPTION 19

the Tevatron the emittance of antiproton beam is 15π while for the proton beam is 20π. We present more characteristics for the Tevatron in sec.3.3.

3.2.3 Longitudinal phase space dynamics

For systematic acceleration the phase of the RF fields in each of the accelerating sections must reach specific values at the moment the particles arrive. If the phase at the fields in each of N accelerating section is adjusted to be the same at the time of the arrival of the particles, the total acceleration is N times the acceleration in each individual section. This adjustment is the synchronicity condition.

The lowest frequency of the electromagnetic ﬁeld that satisﬁes the synchronicity condition is [10]: 2π w1 = (3.10) ∆T where ∆T is the time that need the particles to travel the distance between successive accelerating sections.

Figure 3.2: Example of longitudinal alignment.

Figure 3.2(taken from [11]) presents an example of the synchronicity condition in the Tevatron (discussed in debunching of the Antiproton source in the above section). In CHAPTER 3. ACCELERATOR DESCRIPTION 20

each cycle, the particles that arrive ﬁrst to the cavity are accelerated less than the others, the opposite occurs if the particle arrives late (it receives more energy). After many turns, all particles are aligned with almost the same energy.

In the phase space diagram are stable and unstable regions deﬁned by the separatrices given from the trajectories with an ideal momentum. The stable regions are called buckets.

3.3 Parameters for the Tevatron

TheTevatronatFermilabhastwomainruns.TheRunIwhichfinishedwiththeTop Quark discovery and the Run II that is still active and it is expected to finish in 2009. Run I data taking occurred during four years (since 1992). The collider was turned off until 2001 in order to achieve a higher luminosity (refer to the following sec. 3.3.1) and to increase its center of mass energy. The Tevatron parameters for the different runs of the DØ Experiment (discussed in chap. 4) is presented in table 3.1 taken from [11].

A basic upgrade in Run II is the Main Injector. This new ring is located outside of the enclosure of the Tevatron ring not in the same tunnel as in run I. the new Main injector reduces halos and backgrounds seen in the colliding detectors during Run I and it is capable of delivering up to 3 times as many protons as the Main Ring of Run I.

3.3.1 Luminosity in the Tevatron

Luminosity L is the number of particles passing down the line of collision per unit time, per unit area. For a synchrotron collider L depends on several parameters,

among them we have the number of bunches Nb andinthecaseofTevatronthe

number of protons and antiprotons per bunch (Np and Np¯), as [11]:

L 3γf0NBNpNpF = ∗ (3.11) β (p + p¯) CHAPTER 3. ACCELERATOR DESCRIPTION 21

∗ with γ = E/m as the relativistic energy factor, f0 is the revolution frequency, β is the beta function at the low beta focus, F is the form factor that describes the reduction in the luminosity when the bunch length is comparable to the beta function. p and

p¯ are the emittance of the beam, according to the case. L has units of cm−2s−1 and is a measure of sensitivity and gives directly the number of events per second for a cross section of 1cm2. For this, assuming a given cross-section one can estimate the number of reactions per seconds by

N N /s R = events = σ flux = σ L (3.12) s F

In colliding beam storage rings it is desirable to provide a very low value of the betatron function at the beam collision point to maximize the luminosity. For our study of the total cross-section measurement it is required a low luminosity operation because we are interested mostly in soft hadronic processes (discussed in sec.5) and we need to locate the FPD roman pots as close as possible to the beam center. Therefore, we use a high beta lattice for our simulations. CHAPTER 3. ACCELERATOR DESCRIPTION 22

RUN Ib (1993-95) Run IIa Run IIa Run IIb (6x6) (36x36) (140x103) (140x103)

Protons/bunch 2.3x1011 2.7x1011 2.7x1011 2.7x1011 Antiprotons/bunch 5.5x1010 3.0x1010 4.0x1010 1.0x1010 Total Antiprotons 3.3x1011 1.1x1012 4.2x1012 1.1x1013 Pbar Production Rate 6.0x1010 1.0x1011 2.1x1011 5.2x1011 hr−1 Proton emittance 23π 20π 20π 20π mm-mrad Antiproton emittance 13π 15π 15π 15π mm-mrad β∗ 35 35 35 35 cm Energy 900 1000 1000 1000 GeV Antiproton Bunches 6 36 103 103 Bunch length (rms) 0.60 0.37 0.37 0.37 m Crossing Angle 0 0 136 136 µrad Typical Luminosity 0.16x1031 0.86x1032 2.1x1032 5.2x1032 cm−2sec−1 Integrated Luminosity† 3.2 17.3 42 105 pb−1/week Bunch Spacing ∼3500 396 132 132 nsec Interactions/crossing 2.5 2.3 1.9 4.8

Table 3.1: Operation performance of the Tevatron for Run I and goals for Run II † The typical luminosity at the beginning of a store has traditionally translated to integrated luminosity with a 33% duty factor. Operation with antiproton recycling may be somewhat diﬀerent. Chapter 4

Detector Description

The DZero (DØ) Experiment is installed at the Fermilab Tevatron collider, as mentioned in chapter 3. The DØ Experiment studies include both known and new physics from the proton-antiproton collisions at center-of-mass energy of 1.96 TeV. The Ex- periment studies in detail the high-mass states, high Pt phenomena, B physics, the top quark and the W and Z bosons. In the new physics the studies include the search of the Higgs boson and new phenomena beyond the Standard Model such as searches for supersymmetry and extra dimensions. All this is done using the DØ Detector.

In this chapter a description of the DØ Detector is presented, focusing on the detectors used in the feasibility study presented in this dissertation: The Forward Proton Detector (FPD) and the Luminosity Monitors (LM). The reasons for choosing these detectors are also explained.

The information in this chapter was obtained from theses [12], [9], from the proposal of the FPD subdetector [13] and the website of the DØ Experiment (http://www- d0.fnal.gov/index.html, where information are on the write-ups, design reports and publications of the individual subsystems can be found).

23 CHAPTER 4. DETECTOR DESCRIPTION 24

Figure 4.1: The DØ Detector components.

4.1 The DØ Detector

The DØ Detector is designed and constructed to allows an optimize measurement of final states that contain photons, electrons, muons, jets, missing transverse momentum, lower Pt and B physics. It is a nearly-hermetic particle detector that covers almost all angles of the collisions in an assemble of about 13mx12mx20m (high,wide,long) and weighs approximately 5500 tons. Its platform is mounted on mechanical rollers that allow the detector to move from installation stage to the collision hall where operation and data acquisition takes place. A side view of the DØ detector is presented in figure 4.1(Taken from [14]), and a brief review of their components is explained next and an schematic view of the particle identification is presented in fig 4.2 (Taken from [12]).

TRACKING SYSTEM CHAPTER 4. DETECTOR DESCRIPTION 25

Figure 4.2: Schematic identiﬁcation of particles in the DØ Detector.

The main goal of the Tracker System is an eﬃcient measure of the tracks and vertices from the collision. The high radiation levels in the Tevatron do not allow the detector to be located suﬃciently close to the interaction region for an accurate vertex resolution. For this two systems were developed: the Superconducting Silicon Microstrip Tracker SMT and the Central Fiber Tracker CFT. Additional components, the preshowers detectors and the solenoid magnet, are included to improve the accuracy.

The SMT provides the most accurate measurements when the tracks are in the longitudinal direction (normal incident to the detector plane). As the component closest to the Tevatron beam pipe it also reconstructs secondary vertex of relatively long- lived decaying particles (like partons composed of b and c quarks). The SMT has an hybrid design composed of barrel detectors (measuring in the plane rφ and disk detectors (measuring in planes rz and rφ). The use of the silicon (semiconductor) oﬀers the advantages: low ionization energy, for a good detectable signal; long mean free path and high mobility for fast and good charge collection eﬃciency, low atomic number for prevent multiple scattering, and CHAPTER 4. DETECTOR DESCRIPTION 26

provide a well developed technology. The SMT has six 12.4cm long barrel detectors that achieve a total of about 60cm long. Every detector barrel contained eight layers of rectangular silicon microstrip detectors called ladders. The ladders allow the determination of the third coordinate and consist of double-sided silicon with: axial strips on one side and strips with a small stereo (solid) angle on the other side of the sensor. Figure 4.3(taken from [9]) shows the layout of the SMT detector: layers 1,2,5 and 6 are innermost barrels with a stereo-angle of 90◦ and at radius of 2.7cm; layers 3,4,7 and 8 with a stereo-angle of 2◦; the outermost barrels not provide information of the angle and are single sided, their layers are 1,2,5 and 6 and at radius of 9.7cm. F-disks are the disks between the barrel sections with an stereo angle of 35◦ while the H-disks are located further away on each side of the interaction point an covers an stereo angle of 15◦ .Theread- out of the SMT include 793,000 channels compare with the 55,000 of the Calorimeter.

Figure 4.3: SMT detector layout.

The CFT has two purposes. It surrounds the MST to covers a region of |η| < 2so the combination improve the overall tracking quality. And it provides a fast track trigger (level 1) within the range |η| < 1.6. CHAPTER 4. DETECTOR DESCRIPTION 27

It consists of 32 concentric barrel-shaped layers of scintillating fibers to a total of about 76,800 scintillating fibers. The 32 layers are arranged in 16 doublet layers, which are then grouped together in eight superlayers (cylinders made of carbon fiber), located at radius from 19.5cm to 51.4cm. An offset, of a half fiber diameter, between the two layer that composed the double layer, improves the coverage (cosmic ray muons has a hit position resolution of about 100µm). The two double layer that composed the superlayer are located in a way that the inner doublet layer is oriented at alternating 3◦ stereo angle. Every fiber is 0.35µm in diameter and its inner polystyrene core is surrounded by two layers of cladding (acrylic and fluoroacrylic), each is 15µm thick. The fiber scintillates around the green visible spectrum, with a peak emission wavelength near 530nm. The fibers are mated to 7-11m long waveguides by plastic, diamond-finish optical connectors. Each waveguide conduct the scintillation light to a visible Light Photon Counter (VLPC) that has a high gain (50,000 electrons per converted photon) and a 80% of quantum efficiency for visible light. A VLPC is a variant of the solid-state photomultiplier, based on silicon diodes with an operating temperature around 10K.

The preshower detectors were designed to aid electron and photon identification and triggering; as well as the increase of the electromagnetic resolution (lost with the addition of the solenoid). They lay just beyond the tracking system and are divide in the central preshower CPS and Forward Preshower FPS, both with a technology similar as the CFT. The CPS covers a region of |η| < 1.2 and the FPS covers 1.4 < |η| < 2.5. The fibers of these detector are wavelength shifting fibers (WLS) with a triangular cross-section of 7mm base.

A superconducting solenoid (magnet) surrounds the central tracking system for a better measurement of the charged particles momentum. It produces a mean ﬁeld strength of 2 Tesla with a stored energy of 5MJ. The solenoid is a two layer coil arranged in 2.8m long and 60cm of radius. 36 three-dimensional magnetic ﬁeld sensors CHAPTER 4. DETECTOR DESCRIPTION 28

monitored the ﬁeld produced.

CALORIMETERS The calorimeter of DØ are divide in three modules: the Central Calorimeter CC covering |η| < 1, and two End Calorimeter EC, one at the north and one south, that cover the region 1 < |η| < 4. They are liquid argon calorimeters and provide energy measurements for electrons, photon and jets. The liquid argon as the active material of the calorimeter oﬀers a uniform gain and highly ﬂexible in segmenting the calorimeter volume into readout cells. In a general calorimeter a particle, after interacting with the detector material, loses practically all its energy in ionization, excitation or heat. When these processes oc- cur, cascades of interaction occurs, called showers. Part of the loss energy is released in a recordable signal (scintillating light or ionization). Figure 4.4 (taken from [9]) shows a schematic view of the calorimeters CC and

Figure 4.4: Calorimeter at DØ Detector.

CE. Each one is composed of an electromagnetic (EM), a ﬁne hadronic (FH) and a coarse hadronic (CH) section, in order to measure the longitudinal shower shape to distinguish between electrons and hadrons. A read-out cell is the smallest unit of the calorimeter volume, with a typical transverse CHAPTER 4. DETECTOR DESCRIPTION 29

sizes of ∆η =0.1and∆φ =2π/64 ≈ 0.1 except for the third layer in the EM section where the cells cover (0.05,0.05) in (η,φ). The set of cells, each one from diﬀerent layer, that are aligned along the outward direction1 is called Tower, and it organized the cells in a pseudo-projective geometry (a straight line can be drawn through the interaction point and the cells of one tower, but that the side of the cells are not aligned toward the interaction point).

MUON SYSTEM The muon system is located at the out layer of the DØ Detector because the muons typically do not lose much energy initiated electromagnetic showers (via bremsstrahlung) at Tevatron energies. Only the ionization of the detector media brings information about its passage. Then, the muon system is composed of Drift chambers and, since they have a bad timing system, scintillation counters. A layout of the total system is presented in ﬁgure 4.5 (taken from [12]) and its purpose is the identiﬁcation of muons and an independents measurement of their momentum.

The central system is composed of the WAMUS drift chambers, the Cosmic cap, the bottom and the A-φ scintillation counters; the forward muon system consists of the FAMUS drift chambers and the pixel scintillation counters. A magnet is included to enable a momentum measurement of the muons. The total muon system is divide in three sublayers called A (the inner),B and C. The WAMUS (Wide Angle MUon Spectrometer) are composed of proportional drift tube chambers (PDT) covering the |η| < 1 region; each chamber are composed of about 24 aluminum tubes of 10.1cm diameter and 5.5cm high; the gas inside is a

mixture of 80% Ar, 10% CH4 and 10% CF4 allows a maximum drift time of 500ns. The A-φ scintillation counters covers the A-layer of the PDT with a timing resolution of about 4ns, while the bottom and Cosmic Caps counters are located outside

1The outward direction is approximately the direction of the shower development inside the calorimeter CHAPTER 4. DETECTOR DESCRIPTION 30

Figure 4.5: Muon System at DØ Detector. the B and C-layer, respectively. The Cosmic Caps timing resolution is about 5ns but can be improved to 2.5ns with oﬀ-line corrections.

The FAMUS (Forward Angle MUon Spectrometer) are composed of Iarocci mini Drift Tubes (MDT) covering the 1 < |η| < 2 region; The Iarocci drift-cells have an efficiency close to 100% but it is reduce in 6%, because the 0.6mm space separation between two cells (each cell is 9.4mm wide). The efficiency for finding two hits on a muon track in one layer of the MDT detector, including the effects of the supported wires, edges, voltage, gas and connectors, is about 90%. The momentum resolution of the total forward system is about 20% for low momentum muons.

The Solid-iron Magnet produced a toroidal ﬁeld of 1.8 Tesla, with a current of 1250 A. The central toroid magnet is 109cm thickness and 1973tons weight. The forward toroid core is made of steel pieces weld in a single plate. CHAPTER 4. DETECTOR DESCRIPTION 31

DATA ACQUISITION SYSTEM Just few events in a million are interesting for the studies of new physics at the Tevatron. Having a beam crossing every 396ns exceeds the rate at which the event processing can be recorded hence a system that discard the non-interesting event is required. This type of selection according to a speciﬁed pattern is called triggering and in the DØ Detector the trigger is divide in three levels: L1, L2 and L3, in order of increasing sophisticated selection and decreasing output rate, as present in table 4.1. After a decision is made, the events is sent to the Data Acquisition System (DAQ) and moved to storage tapes.

Trigger Level Event Rate Decision time per event L1 2.5 MHz 4.2µs L2 6KHz 100µs L3 1KHz 150ms

Table 4.1: Input event rates at diﬀerent levels of trigger

The levels L1 and L2 use hardware devices called Field Programmable Gate Arrays (FPGA) to make decisions very quickly, and the L3 uses software ﬁltering algorithms running on a set of high performance processors.

The trigger in L1 is based on the information obtained from the CFT, preshower detectors, calorimeter and muon counters. In L2 a correlation of the information taking by L1 is made. Then a compilation of the correlations between the detectors is made in order to form measurable physical quantities. This data is digitalized and loaded onto the so called single board computers (SBC). In L3 a partial reconstruction of the event is obtained using algorithms implemented under a LINUX environment with high-performance. CHAPTER 4. DETECTOR DESCRIPTION 32

The data taking, at the DØ Detector, from the creation of the proton and antiproton beams, the collisions each 395ns, to a low luminosity or any disadvantage that prevents to continue, is recorded in the so called store. The duration of the store depends on the luminosity and the beam conditions, and takes maximum 2 days (with 2nights).Commonly,thedataisdivide each 0-4 hours in a unit called run that has fews to one million events.

Remmark

The feasibility study presented in this document is based on the use of the For- ward Proton Detector (FPD) and the Luminosity Monitors (LM) that belong to the DØ Experiment. We also could have included in this study the central detector to reconstruct vertices and tracks. But since we just want the number of events that hit the detector as it is discussed in sec.2.3, this can be done with the luminosity monitors, which have high acceptance. The use of the central detector will allow reduction of backgrounds when counting inelastic events.

4.2 The Forward Proton Detector (FPD) at DØ

The Forward Proton Detector (FPD) at DØ Experiment is a subdetector installed for Run II of the Tevatron (discussed in chap.3). The addition of this detector, at the higher energy of the Tevatron, facilitates studies of the structure of the pomeron and its dependence on diffractive mass and momentum transfer, determination of the quark and gluon content of the pomeron, search for diffractive production of heavy objects such as W bosons, and studies of hard double pomeron exchange as well as soft diffractive processes such as elastic scattering and single diffractive [13].

The main measurement of the FPD is the tracking of the scattered protons or an- CHAPTER 4. DETECTOR DESCRIPTION 33

tiprotons. This allows us to calculate the momentum and scattering angle of each particle. The points of the track are measured from a series of devices shown in ﬁg- ure 4.6(taken from FPD lectures): There are low beta quadrupole magnets Q,dipole magnets D and electrostatic separators S that bend the particles. A and P are roman pots explained in the next section.

Figure 4.6: The Forward Proton Detector.

4.2.1 The Roman pots of the FPD

The Roman Pots are stainless steel pots that are used as containers of a scintillating ﬁber detector. The importance of this pots design is that let us locate the detectors as close as possible to the beam line, so they can track scattered particles at very small angles which are not detected by the DØ central detector. In total the FPD has 18 remotely controlled roman pots, located at 6 diﬀerent positions.

The six locations correspond to 2 stations in the proton side after the collision (P1 and P2) and 4 stations in the antiproton side (A1, A2, D1 and D2), they are shown in ﬁg 4.6 with their corresponding z distance from the interaction point.

Two stations make up 4 spectrometers and 1 spectrometer is composed of 2 roman pots. For example, the 4 spectrometers of the proton side (after the collision) are composed of the roman pots P1U-P2U, P1D-P2D, P1I-P2I and P1O-P2O. The let- ters U and D means up and down from the beam line while I and O means in and CHAPTER 4. DETECTOR DESCRIPTION 34

out from the center of the Tevatron ring.

Figure 4.7: Fibers planes for the Forward Proton Detector.

Each scintillating fiber detector that is inside of each roman pot consists of six scintillating fiber planes as shown in fig 4.7 (taken from FPD lectures). The triggering is made with one scintillation block that is part of the detector. Two planes have fibers oriented at 45 degrees (U,U’), others two planes have fibers at 90 degrees (X,X’), fibers in the remaining two planes are at 135 degrees (V,V’)[15]. The configuration of fiber planes gives a resolution of 80µm in the hit coordinate. The area of each detector is 2cmx2cm.

4.2.2 The Eﬀective Lengths of FPD

The general solution of the beam dynamics in terms of the betatron functions (sec 3.2) are used to determinate the beam lattice parameters at every pot location of the

FPD. The parameter values of eq. 3.7, from the interaction point s0 to any vertical pot s1 of the FPD roman pots, with a beam emittance of 10π and 15π, are presented in tables 4.2 and 4.3 respectively.

The eﬀective length measured for each roman pot remain the same when the beam emittance increases (discussed in sec.3.2.2), while the beam size increases, as reported in tables 4.2 and 4.3. The ﬁrst one is because Tevatron lattice does not change (the CHAPTER 4. DETECTOR DESCRIPTION 35

LEFFX(m) LEFFY(m) m01x m01y σx(mm) σy(mm) tminx tminy pot 11.086 4.931 -3.217 -5.505 0.383 0.226 0.0733 0.1292 D2I 11.658 5.338 -3.179 -5.346 0.399 0.227 0.0720 0.1111 D1I 17.642 9.601 -2.773 -1.577 0.579 0.301 0.0663 0.0605 A2U 17.642 9.601 -2.773 -1.577 0.579 0.301 0.0663 0.0605 A2D 17.678 9.625 -2.779 -1.580 0.580 0.302 0.0663 0.0605 A2I 17.678 9.625 -2.779 -1.580 0.580 0.302 0.0663 0.0605 A2O 20.010 11.294 -2.591 0.096 0.654 0.352 0.0656 0.0598 A1U 20.010 11.294 -2.591 0.096 0.654 0.352 0.0656 0.0598 A1D 19.973 11.265 -2.586 0.096 0.652 0.351 0.0656 0.0598 A1I 19.973 11.265 -2.586 0.096 0.652 0.351 0.0656 0.0598 A1O 11.297 20.014 0.398 0.010 0.372 0.624 0.0667 0.0598 P1U 11.297 20.014 0.398 0.010 0.372 0.624 0.0667 0.0598 P1D 11.266 19.976 0.397 0.010 0.371 0.623 0.0667 0.0598 P1I 11.266 19.976 0.397 0.010 0.371 0.623 0.0667 0.0598 P1O 9.594 17.646 -0.493 -0.253 0.312 0.550 0.0649 0.0598 P2U 9.594 17.646 -0.493 -0.253 0.312 0.550 0.0649 0.0598 P2D 9.620 17.684 -0.457 -0.254 0.313 0.551 0.0650 0.0598 P2I 9.620 17.684 -0.457 -0.254 0.313 0.551 0.0650 0.0598 P2O

Table 4.2: FPD detectors parameters for =10π CHAPTER 4. DETECTOR DESCRIPTION 36

magnets and their position are preserved ). The parameters reported in the tables correspond as follows for each axis (x or y). LEFF is the eﬀective length measure on

the detector, m01 is m01 related with the betatron functions discussed in sec 3.7, σ is the beam size (eq.3.8), and tmin is the momentum transferred for each axis.

The transferred four-momentum t is calculated from the eﬀective length (Leff ) in any position (x,y), as: x2 y2 t = 2 + 2 (4.1) Leffx Leffy where x,y are the coordinates of the hit, from the center of the beam, at a speciﬁc detector location.

4.2.3 Tevatron Timing and Elastic Events in the FPD

Figure 4.8: Timing in the FPD. CHAPTER 4. DETECTOR DESCRIPTION 37

LEFFX(m) LEFFY(m) m01x m01y σx(mm) σy(mm) tminx tminy pot 11.086 4.931 -3.217 -5.505 0.469 0.277 0.1100 0.1939 D2I 11.658 5.338 -3.179 -5.346 0.489 0.278 0.1081 0.1667 D1I 17.642 9.601 -2.773 -1.577 0.710 0.369 0.0994 0.0908 A2U 17.642 9.601 -2.773 -1.577 0.710 0.369 0.0994 0.0908 A2D 17.678 9.625 -2.779 -1.580 0.711 0.370 0.0994 0.0908 A2I 17.678 9.625 -2.779 -1.580 0.711 0.370 0.0994 0.0908 A2O 20.010 11.294 -2.591 0.096 0.800 0.432 0.0983 0.0898 A1U 20.010 11.294 -2.591 0.096 0.800 0.432 0.0983 0.0898 A1D 19.973 11.265 -2.586 0.096 0.799 0.430 0.0983 0.0898 A1I 19.973 11.265 -2.586 0.096 0.799 0.430 0.0983 0.0898 A1O 11.297 20.014 0.398 0.010 0.456 0.765 0.1000 0.0897 P1U 11.297 20.014 0.398 0.010 0.456 0.765 0.1000 0.0897 P1D 11.266 19.976 0.397 0.010 0.454 0.763 0.1000 0.0897 P1I 11.266 19.976 0.397 0.010 0.454 0.763 0.1000 0.0897 P1O 9.594 17.646 -0.493 -0.253 0.382 0.674 0.0974 0.0896 P2U 9.594 17.646 -0.493 -0.253 0.382 0.674 0.0974 0.0896 P2D 9.620 17.684 -0.457 -0.254 0.383 0.675 0.0974 0.0896 P2I 9.620 17.684 -0.457 -0.254 0.383 0.675 0.0974 0.0896 P2O

Table 4.3: FPD detectors parameters for =15π CHAPTER 4. DETECTOR DESCRIPTION 38

For a normal run operation the beams of the protons and antiprotons in the Tevatron are grouped in three superbunches each, separated 2.6µs. Inside each superbunch there are 12 bunches separated by 396ns. The first bunches of the superbunch that collide are defining the start time (clock with t=0). When the second bunches are approaching to the collision point, they cross the detector (quadrupole Q2 station fig 4.8 taken from [16]) in the so called early time, after the collision the particles cross again the detectors but now they are in time.

The time of ﬂight for the particles from the center of DØ an the quadrupole castle Q1 is 77ns while it is 103 ns for Q2. So to have a coincidence implies a delayed of 26 ns between the signals of Q1 and Q2. The DØ master clock announces when both bunches crosses to each other in the interaction point and the FPD system begin analysis with the crossing of the second bunch of the superbunch.

When there is a early time the ﬂag halo bit is set to 1 and this set can later be used in the analysis to reject most of the halo-halo background that produce early timing in the detectors that are passed by before the particle bunch reaches the interaction point.

4.2.4 High β Store

On February 17th-18th 2006 a special run at the Tevatron took place, in order to locate the FPD Roman Pots as close as possible to the beam line. The data was stored in the so called Store 4647. The special Tevatron conditions were:

1. Injection tune with β∗D0=1.6m

2. One proton bunch colliding on one antiproton bunch

3. electrostatic separators were turned oﬀ

4. Scraping in vertical and horizontal planes (using collimators)

The last 2 items were performed to reduce the emittance of the beams. CHAPTER 4. DETECTOR DESCRIPTION 39 4.3 The Luminosity Monitors (LM) at DØ

The main goal for the Luminosity Monitors(LM) at DØ is to measure the Tevatron luminosity. The detector was designed to provide a precise measurement of the rate for non-diﬀractive inelastic collisions that is used to calculate the Tevatron luminosity. Figure 4.9 presents the position of the LM inside the DØ Detector that covers a region of 2.7 < |η| < 4.4 (refer sec.4.4 for η deﬁnition).

Figure 4.9: Position of the Luminosity Monitors (LM) at DØ Detector.

The LM consists of plastic scintillation detectors with fine-mesh photomultiplier as it is shown in figure 4.10. There are 24 identical 5/8” thick photomultipliers wedges, in each one side of the pp¯ collision, that composed one of the two luminosity counters at DØ. The photomultipliers operated with high gain in the magnetic field of ±1TeV while maintaining the desirable low noise. The time of flight resolution achieved for this system is about 200ps. [17].

For the feasibility study presented in this document, we required that a considerable number of luminosity monitor cells were on. This clears part of the possible back- CHAPTER 4. DETECTOR DESCRIPTION 40

Figure 4.10: The Luminosity Monitor. Figures taken from [18]. ground events, for example when a cosmic ray could turn on a cell. This number of turned on cells are called multiplicity on the LM. Also we expect to have energy deposited in the calorimeter of DØ detector if the signals of the LM correspond to an inelastic event.

4.4 Coordinate System for the FPD

The DØ Detector uses a standard right-handed coordinate system. The coordinate system origin is located at the collision point. The direction of the +x axis is a vector pointing radially outwards from the center of the Tevatron ring, the +y axis direction is vertically upwards and the +z axis direction is along the proton direction, as they are presented in ﬁgure 4.11 (taken from [9]). Since some of the detectors have a cylin- drical symmetry it is also convenient to use a combination of spherical coordinates (z ,φ ,θ) along with the Cartesian ones. The angles φ and θ are the azimuthal and polar angles, respectively, with θ=0 along the proton beam direction.

In the FPD, each roman pot has its own coordinate system that corresponds with the usual 2D Cartesian plane. Figure 4.12, taken from [19], presents the origin and direction of each axis for each roman pot. CHAPTER 4. DETECTOR DESCRIPTION 41

Figure 4.11: DØ Coordinate System.

Figure 4.12: FPD coordinate system Chapter 5

Physical Processes Involved in a pp¯ Collision

The proton (p) is a hadron composed of three quarks: two u and one d,asweknow. Hence in a proton-antiproton collision the physical processes involved are mainly the hadronic processes, those have a space resolution of approximately 1fm, which is the size of a hadron. The hadronic processes are divided in soft processes and hard processes according to the energy scale obtained.

The soft processes can be identified by the small momentum transfer squared of the particles (t ∼ 0.1GeV2), contrary of what characterizes a hard process where jets of 2 t>1GeV (as large-pT jet and heavy particles) are presented in the final state. And example of hadronic soft process is elastic diffraction and an example of hard process is the deep inelastic scattering.

The processes can be identiﬁed by channels depending on the resulting particles. The typical processes studied at the DØ Experiment using PYTHIA (refer appendix C) are listed bellow [20]:

42 CHAPTER 5. PHYSICAL PROCESSES INVOLVED IN A P P¯ COLLISION 43

1 pp¯ −→ PYTHIA default minimum bias 2 pp¯ −→ ccbar 3 pp¯ −→ b bbar 4 pp¯ −→ ttbar 5 pp¯ −→ prompt-photon 6 pp¯ −→ h0 7 pp¯ −→ Z0 8 pp¯ −→ W+- 9 pp¯ −→ Z0 + JET 10 pp¯ −→ W+- + JET 11 pp¯ −→ h0 Z0 12 pp¯ −→ h0 W+- 13 pp¯ −→ CMSrecommendedmin.bias

From a theoretical point of view the particle physics processes those involved by the strong interaction are explained by the Quantum Chromodynamics (QCD) theory. Two diﬀerent approaches were developed for the hadronic processes: The perturbative QCD and non-perturbative QCD. Although soft and hard processes have a non-perturbative origin, the hard process is explained by QCD perturbative because of the high value of the transferred momentum [21]. The soft processes are described by the Regge Theory, which is an approach adopted since 1960-70 decade. The Regge theory established that soft hadronic phenomena at high energies are universally dom- inated by the exchange of an enigmatic object, the pomeron1.

In the following section the diﬀractive processes are explained in detail, those are well detected by the Forward Proton Detector (FPD) at DØ Experiment. All processes out of this discussion are the non-diﬀractive processes.

1Perturvative interactions are implemented by PYTHIA while the Regge theory is implemented by POMWIG. Refer to sec. 7.3 for this discution CHAPTER 5. PHYSICAL PROCESSES INVOLVED IN A P P¯ COLLISION 44 5.1 Main Diﬀractive Processes

The diﬀractive processes are deﬁned as a reaction in which no quantum numbers are exchanged between the colliding particles. It is almost always characterized by a large rapidity gap 2.

For our feasibility study we simulated all QCD processes using PYTHIA (with option MSEL=2) and POMWIG (refer appendix C) for single diffractive process. We specially take the elastics and single diffractive process separately of the others inelastic events, because with the FPD we are able to detect particles with low momentum √ transfer (θ ∼ t) as presented in sec.4.2.1. We next discuss the main diffractive process.

Elastic Diﬀraction

p +¯p −→ p¯ + p (5.1)

When the particles after the collision are the same as the incident particles the process is called elastic scattering. The energy of each particle before and after remains the same. An schematic view for pp¯ elastic scattering is shown in fig 5.1 (This figure and all the schematic view in this section are taken from [13]). This process has a clear rapidity gap as presented in right side of the figure.

Figure 5.1: Schematic View of an Elastic process.

Single Difracctive

2A rapidity gap can be understand as an angle separation space CHAPTER 5. PHYSICAL PROCESSES INVOLVED IN A P P¯ COLLISION 45

p +¯p −→ p + X or p +¯p −→ p¯ + X (5.2)

p +¯p −→ p + jj or p +¯p −→ p¯ + jj (5.3)

Figure 5.2: Schematic View of Single Diﬀractive Soft Process.

A single diffractive process corresponds to one in which one of the incidents particles comes out intact after the collision while the other is divided in a bunch of particles that preserve its quantum numbers. It is possible to have a single diffractive soft (fig 5.2 taken from [13]) and a single diffractive hard process (fig 5.3 taken from [13]); we can identify the hard one by the outcome of jets (denoted by jj) , or by boson W/Z production, or hard quarks of high energy photons produced.

Additionally, in a pp¯ collision we recognize two possible single diffractive soft processes and also two hard: one where the p was the particle diffracted called single diffractive p¯ process, and the other where the diffracted particle was thep ¯ called single diffractive p process.

Double Difracctive

Figure 5.3: Schematic View of Single Diﬀractive Hard Process. CHAPTER 5. PHYSICAL PROCESSES INVOLVED IN A P P¯ COLLISION 46

p +¯p −→ jj + X (5.4)

As its name tell us, a double diffractive process is in which both incidents particles finished in two particle bunches with the same initial quantum numbers of each particles and separated by a rapidity gap as in figure 5.4.

Figure 5.4: Schematic View of Double-Diﬀractive Process.

Double Pomeron Exchange

p +¯p −→ p +¯p + jj + X (5.5)

A Double Pomeron Exchange process can be identify when the initial particles loose a 10% of their initial momentum but remain intact at the end of the collision, and there are rapidity gaps in both sides of the interaction point. An schematic view is presented in ﬁgure 5.5.

Figure 5.5: Schematic View of Double Pomeron Exchange Process. CHAPTER 5. PHYSICAL PROCESSES INVOLVED IN A P P¯ COLLISION 47 5.2 Kinematics of two-body processes

The process 1+2−→ 3 + 4 (5.6) is described by using the Mandelstam Variables (s, t, u) that are three Lorentz invariant kinematical variables, with the same value in any inertial system. The sum of the three Mandelstam variables obey:

4 2 s + t + u = mi (5.7) i=1 and are deﬁned as

2 2 s =(p1 + p2) =(p3 + p4)

2 2 t =(p1 − p3) =(p2 − p4)

2 2 u =(p1 − p4) =(p2 − p3)

The process of eq. 5.6 is called the s-channel process where s denotes the center of mass energy squared and t is the squared transferred momentum. The corresponding analogous processes are:

1+3¯ −→ 2+4¯ (t − channel) (5.8)

1+4¯ −→ 2+3¯ (u − channel) (5.9)

(5.10)

For example, in an elastic scattering like pp¯ → pp¯, the Mandelstam variables are deﬁned as [6]:

2 2 s =(pp,in + pp,in¯ ) =(pp,out + pp,out¯ )

2 2 t =(pp,in − pp,out) =(pp,in¯ − pp,out¯ ) (5.11)

2 2 u =(pp,in − pp,out¯ ) =(pp,in¯ − pp,out) CHAPTER 5. PHYSICAL PROCESSES INVOLVED IN A P P¯ COLLISION 48

Because the momentum cannot be measured directly, the experimentally available parameters used at colliders are energies and scattering angles (θ). The Mandelstam variables in the center of mass frame become:

2 2 s =4(pp,in + mp,in¯ )=2mp(mp + E) t = −2p2(1 − cos θ) (5.12)

u = −2p2(1 + cos θ) where p is the momentum of the incident particle respect to the center of mass frame and E is the energy respect to the laboratory frame. At very high energies, scattering angles are small, so an approximation of (5.12) is expressed as:

s ≈ 4p2

t ≈ −p2θ2 (5.13)

In the case of inelastic events the Mandelstam variables are similar to (5.11) but taking into account the new particle. For example in the production of a jet, Mandelstam variables look like [22]:

2 s =(pp,in + pp,in¯ )

2 t =(pp,in − pjet,out) (5.14)

2 u =(pp,in¯ − pjet,out)

5.3 Diﬀerential Elastic Cross-Section Remark

The diﬀerential cross-section for the elastic scattering depends on the energy and the square of the transferred four-momentum t or any other angular variable. The region with |t| < 0.001 (GeV/c)2 is called Coulomb region, with 0.001 < |t| < 0.01 (GeV/c)2 is called Coulomb-Nuclear region, the next is called Nuclear Diﬀraction region with 0.01 < |t| < 0.5(GeV/c)2 and the large angle region involved |t| > 0.5(GeV/c)2. CHAPTER 5. PHYSICAL PROCESSES INVOLVED IN A P P¯ COLLISION 49

In proton-antiproton collisions each region is governed by a diﬀerent function. The main functions are: √ 2 παc Coulomb = G2(t)expiαφ (5.15) |t| (1 + ρ2)0.5σ Nuclear = tot expbt/2 (5.16) (16π)0.5c where G(t) is the proton form factor

−2 |t| G(t) ≈ 1+ (5.17) 0.71

φ is the phase of Coulomb amplitude relative to nuclear: 0.08 φ ≈ ln − 0.577 (5.18) |t| and α is the ﬁne structure constant

1 α ≈ (5.19) 137

The Coulomb function is obtained from the Rutherford scattering and corresponds to the electromagnetic interaction, while the nuclear function is obtained from experimental methods based on hadronic interactions. The diﬀerential cross-section is calculated as the norm of the sum of each contribution[23]:

dσ 4π(c)2α2 α(ρ − αφ)σ (1 + ρ2)σ2 = G4(t)+ tot G2(t)expbt/2 + tot expbt (5.20) d|t| |t|2 |t| 16π(c)2

For the study presented in this document the third term is the dominant and from it the total cross-section σtot is calculated, as discussed in chap.2.

5.4 Deﬁnitions of useful variables

The physical variables used in the analysis of scattering processes in high energy experiments are: the transverse momentum, Feynman’s variable, pseudorapidity and the fractional momentum loss. Their deﬁnitions are present as follows. CHAPTER 5. PHYSICAL PROCESSES INVOLVED IN A P P¯ COLLISION 50

Transverse Momentum Pt

pt = pSin(θ) (5.21) 2 2 2 −1 where p = px + py + pz and θ is the usual polar angle θ = Cos (pz/p)measure from the beam line.

Transverse Energy Et

Et = ESin(θ) (5.22) where E is the energy of the particle and θ is the usual polar angle.

Feynman variable xF

|pf | xF = (5.23) pi where pf is the ﬁnal momentum of the intact particle after the scattering and pi is its initial momentum. In high energy hadron scattering the Feynman variable is used to calculate the momentum transferred as: P 2 t − t (5.24) xF Fractional momentum loss ξ For an intact particle the fractional momentum loss is:

pi −|pf | ξ =1− xF = (5.25) pi where pf is its ﬁnal momentum and pi is the initial. Otherwise, the fractional momentum loss can be reconstructed using

1 i ξ ≈ √ Ei expη (5.26) s T i

i i where the sum is over particles in the ﬁnal state, and ET and η are the transverse energy and pseudorapidity of the ith particle. This approximation assumes that the energy of the incoming particle is large. CHAPTER 5. PHYSICAL PROCESSES INVOLVED IN A P P¯ COLLISION 51

Pseudorapidity η and Pseudorapidity gap

1 E+Pz The deﬁnition of rapidity y = 2 ln E−Pz , for the case p>>mis expressed as:

1 Cos2(θ/2) + m2/4p2 + .... y = ln ∼−ln(tan(θ/2)) (5.27) 2 sin2(θ/2) + m2/4p2 + .... and in this case the rapidity is renamed as pseudorapidity η:

η = − ln(tan(θ/2)) (5.28)

From the above deﬁnitions the next identities can be obtained [22]:

sinh η =cotθ (5.29) 1 cosh η = (5.30) sin θ tanh η =cosθ (5.31)

Regions of high η, close to the outgoing beam particle are referred to as forward while the region |η|∼0 is referred to as central.

The pseudorapidity gap for a scattering process is characterized by:

−∆η 1 − xF exp (5.32) Chapter 6

Simulation Description

In this dissertation, the study of the total cross-section is developed in two separated parts according with the measurement involved, and consists of the determination of the eﬀect that produce the change in the location of the FPD Roman Pots. One part is implemented for the study of the elastic collisions and the other for the study of the inelastic collisions. MonteCarlo simulations are used in both parts of this study.

√ Proton-antiproton collisions at a center-of-mass energy of s =1.96 TeV are generated using PYTHIA (a standard generator of particle collisions in high energy physics discussed in appendix C.3). The events produced are classiﬁed according with the physical process simulated in each collision, as it is explained in the ﬁrst section of this chapter. In the following two sections the study of the elastic and inelastic collisions are described in order to establish the total cross-section uncertainty discussed in the last section of this chapter.

6.1 Classiﬁcation of Events Strategy

All QCD processes are simulated using PYTHIA, a standard generator of particles collision at high energy physics (discussed in appendix C.3), for proton-antiproton √ collisions at center-of-mass energy of s =1.96TeV, hence the classiﬁcation of relevant processes is established before starting the simulation description of the study

52 CHAPTER 6. SIMULATION DESCRIPTION 53

Figure 6.1: Single Diﬀractive Process Candidate There are hits in the LM-south and FPDp ¯ side. of the total cross-section measurement.

First, the resulting events that have an intact antiproton (¯p) and/or proton (p)are identify. Intact means that the particle is one of the initial collision particles. An intact particle has mainly two physical characteristics 1:

Pseudorapidity |η| > 7.5 (6.1)

Energy E>90% of pbeam = 980GeV (6.2)

The classification strategy for our study is as follows: An event with intact particles on both sides of the interaction point and those particles with energy of 980GeV each is elastic. An event with intact particles in both sides and any of those particles with energy different from 980GeV is DPE (Double Pomeron Exchange).Asingle diffractive p process is when there is only one intact particle that is the proton; analogy if the intact particle is an antiproton the process is single diffractive p¯.Anevent without intact particles is non-diffractive (Although a double diffractive process does not have intact particles also, it is more probable to have non-diffractive processes than double diffractive processes).

The triggering of the above classiﬁcation is established since we are interested in the

1Conditions 6.1 and 6.2 are required because it is possible to have a particle with |η| > 7.5from a secondary or much higher order vertex. CHAPTER 6. SIMULATION DESCRIPTION 54

measurement of the events after the reconstruction. The measurements, in this dissertation, is doing using the FPD detector and Luminosity Monitors (LM) of the DØ Experiment, as discussed in chapter 4. Each kind of process in a proton-antiproton collision implies a diﬀerent triggering in the following way:

1. A single diﬀractive p process has at least, a hit in the LM north2 and a hit in one FPD spectrometers of the opposite side (p side).

2. A single diﬀractivep ¯ process has at least, a hit in the LM south and a hit in one spectrometer of the FPD on thep ¯ side. An example of this case is presented in ﬁgure 6.1(taken from [13]).

3. An elastic process has hits in both sides of the FPD detector (no hits in LM).

4. A double pomeron exchange process has hits in both sides of the FPD detector. An example of this trigger is presented in ﬁgure 6.2(taken from [13]).

5. A non-diﬀractive process has at least hits in both LM.

The number of hits in each detector is used to obtain the acceptance of the detector to a certain process. Since the processes single diﬀractive p andp ¯ are symmetric, the calculations can be simpliﬁed by taking into account the detectors acceptance only in one of the two sides of the collision. The FPD acceptance obtained, in our study, corresponds to thep ¯ side where there are more roman pots of the FPD detector.

6.2 MonteCarlo Study of Elastic Events

When an elastic event is produced in the Tevatron the best way to detect the intact particles is by the FPD subdetector, because of the small angles obtained in this scattering process (discussed in sec.4.2). For this, the simulation of elastic events is specially developed for the FPD roman pots.

2As mentioned in chapter 4 the outgoingp ¯ after the collision takes the north side of DØ detector CHAPTER 6. SIMULATION DESCRIPTION 55

Figure 6.2: Double Pomeron Exchange Process Candidate. There is not hit in the LM and there are hits in both sides of the FPD.

The total cross-section measurement, eq 2.11, is obtained from the MonteCarlo of Elastic Events according with the luminosity independent method. The exponential

dNel −Bt ﬁt on the distribution of the transferred momentum dt = A exp as well as the number of inelastic events area used in the total cross-section measurement. For this, eq 2.11 joins the all simulations described in this chapter and changing the position of the FPD roman pots brings a study of the total cross-section uncertainty.

This section explains the main steps to reach the corrected exponent or slope (in a logarithm axis) label B and extrapolation point label A, of the exponential ﬁt for the distribution of the transferred momentum, with their corresponding uncertainties.

The elastic events is simulated using the montecarlo ELASTIC DISPERSION SOFTWARE, developed by J. Villamil [19], that takes the expected distribution of the transferred momentum (eq 5.20 named Block Function) and generates the positions where the roman pots are hit. This simulation includes, according to the beam parameters, a random angle α that brings the divergence of each beam of particles. The lattice implemented to obtain the detectors parameters is the beam injection lattice (“MAD” Version: 8.16/6 Run: 02/01/05 14.45.53). CHAPTER 6. SIMULATION DESCRIPTION 56

Figure 6.3: Range for the ﬁt in the block function.

6.2.1 Distribution of the Transferred Momentum

From the data of the Experiment E710 [1] and the Block Function [19] it is possible to have an expected distribution of the transferred momentum (t) for the elastic events. This distribution is showed in ﬁgures 6.3(taken from [1]) and 6.4 that is the original distribution implemented in the ELASTIC DISPERSION SOFTWARE. The inverse method MonteCarlo technique for the cumulative function is used to obtain the distributions in the detectors, evaluated in a short interval of transferred momentum |t|.

Figure 6.4 presents the distributions of the transferred momentum changing the positions of the A2D pot of the FPD subdetector; note that all positions represented in the ﬁgure have the same entries, this means that the luminosity is changing (the interception point is always diﬀerent).

In order to have more results in less operation time a cut in the cumulative function was performed. Only events with a transferred momentum of |t| < 0.55 (the forward region) are generated, which is the region where the nuclear contribution is large, and allows us to obtain the total cross-section from an extrapolation. Distributions for CHAPTER 6. SIMULATION DESCRIPTION 57

Momentum Transferred Distributions for PotA2D dt dN

104

103

Positions with 30000 entries 20σ 102 18σ 16σ 14σ 10 12σ 10σ

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 |t| [(GeV/c)^2]

Figure 6.4: Distributions of the expected transferred momentum At different locations of the FPD roman pot A2D, changing the luminosity and with an emittance of =10π. this case and ready for the fit are presented in figure 6.5.

The diﬀerence besides the cut of the cumulative function, between ﬁgures 6.4 and 6.5, is that in this latter case all distributions bring the same intercept in order to compare the uncertainties of the total cross-section changing the positions of the roman pots, this also means that the luminosity in all cases is the same. A change in the roman pot position, in a direction away from the beam-line, with the same luminosity implies a smaller number of events in the distribution (Fig. 6.5 only shows the entries forthepotP1Ulocatedatposition10σ,whereσ is the beam size).

In order to achieve the correct uncertainty in the slope and extrapolation point of the curve obtained in each roman pot, it is necessary to make two corrections (for each FPD location simulated): one from the geometrical acceptance of the detector, which is explained in following section, and other because of the beam size divergence.

The analysis presented in this document was developed using ROOT 3 so the dis-

3ROOT is An object oriented framework for large scale data analysis [24] CHAPTER 6. SIMULATION DESCRIPTION 58

Momentum Transferred Distributions for Pot P1U

] 105 dt dN Log[ 104

103

Positions with 33568 entries 20σ 102 18σ 16σ 14σ 10 12σ 10σ

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 |t| [(GeV/c)^2]

Figure 6.5: Distributions with =10π changing P1U position. Only the entries for the roman pot at 10σ are reported (33568). tributions in each roman pot of the FPD are interpreted as histograms. For each position of a run, the histograms are denoted by:

• ideal, the histogram obtained from the run with a beam of size equal to zero.

• outcome, the histogram obtained from the run with a beam size using =10π or 15π

• acce, the histogram corrected by geometrical acceptance.

• pos, the ﬁnal corrected histogram for each position.

Each bin of the acce histogram is calculated, with the previous knowledge of a weight (acceptance at the corresponding bin), by:

outcome acce = (6.3) weight CHAPTER 6. SIMULATION DESCRIPTION 59

The histogram outcome is the result of a convolution between a zero and a Gaussian distribution of the beam size. In order to have only the Gaussian distribution of the beam size the following coeﬃcient is calculated:

outcome c = (6.4) bs ideal

Hence the ﬁnal corrected or deﬁnitive histogram would be:

acce pos = cbs outcome = (6.5) cbs ∗ weight

The standard propagation of error formula tells the error bars (after simplifying):

2 2 ∂c ∂c σ = bs σ2 + bs σ2 cbs ∂outcome outcome ∂ideal ideal 2 1 2 acce 2 2 2 = σacce + (σoutcome + cbsσideal) cbs √ outcome σoutcome 2 σpos = (6.6) cbs ∗ wei

The corresponding ﬁt to obtain the total cross-section is calculated from the histogram pos, using eq 2.11, and their corresponding uncertainty is explained at the end of this chapter.

6.2.2 Calculation of the Geometrical Acceptance of the FPD

The acceptance adjustment consists of taking into account the real contribution of one event with a ﬁx four-momentum t. Each transferred momentum t sweeps an ellipse in the detector given as:

x2 y2 t = 2 + 2 (6.7) Leffx Leffy with x and y as the coordinates, and Leffx and Leffy are the corresponding effective lengths in each axis.Diﬀerent transferred four-momentums produce diﬀerent CHAPTER 6. SIMULATION DESCRIPTION 60

ellipses, which sweep diﬀerent areas or angular distributions in the detector. Figure 6.6 presents, on the right side, an schematic view of the ellipses and areas; on the right side, a common angular region of the detectors used in the triggering is presented.

Figure 6.6: Schematic View of the FPD Acceptance At the left is the common angular region of an elastic event trigger. At the right the detector located at positions 10 and 12σ covers diferent ellipses. For each position each t covers a diﬀerent area in the detector.

Taking a homogeneous angular distribution along 2π to obtain the acceptance of the detector, the relation that must follow is dA = dφ/2π. This calculated acceptance is only geometrical since the eﬃciency of the detectors ﬁbers is ignored. The value number of the acceptance is called the weight of each four-momentum t.

The correction by acceptance is done in each bin of the histogram that represents the distribution of the transferred momentum as, with the notation of the above section:

outcome acce = (6.8) weight the corresponding error bar is: √ outcome entries acce error bar = (6.9) weight CHAPTER 6. SIMULATION DESCRIPTION 61

common Acceptance. 10σ (blue) 12σ (red) 14σ (pink) 16σ (green)

0.3

0.25

0.2

0.15 Acceptance 0.1

0.05

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 t [GeV/c]^2

Figure 6.7: Acceptance changing positions for an emittance of =10π

Changing the positions of the FPD roman pots we obtain the acceptance represented in ﬁgures 6.7 and 6.8, for the common area PU-AD4 with an emittance of =10π and 15π respectively. The acceptance decrease when the roman pots are moving away of the beam-line. With a greater emittance of =15π the new position 10σ (σ means the beam size) is further out than the 10σ with an emittance =10π (since the emittance increases the beam size).

common Acceptance. 10σ (blue) 12σ (red) 14σ (pink) 16σ (green)

0.25

0.2

0.15 Acceptance 0.1

0.05

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 t [GeV/c]^2

Figure 6.8: Acceptance changing positions for an emittance of =15π

4PU-AD means the coincidence of the roman pots P1U, P2U, A1D and A2D. In section 4.2.1 the FPD roman pots are discussed CHAPTER 6. SIMULATION DESCRIPTION 62

6.2.3 Fiducial Cuts

Since the FPD subdetector at DØ Detector has eighteen roman pots, for this dissertation a less number of the detectors are used in the elastic trigger. As ﬁgure 6.9(taken from [25]) shows an elastic event could be obtained from the coincidence of A2U, A1U, P1D and P2D, it is denoted as AU-PD; the symmetric combination AD-PU is also possible.

In this dissertation, both coincidences AU-PD and AD-PU are studied and for these roman pots the results and total cross-section uncertainties are reported in the following chapters. The common angular area of the coincidences AD-PU are reported in tables 6.1 and 6.2, for an emittance of 10π and 15π respectively.

Figure 6.9: Elastic Trigger (schematic). CHAPTER 6. SIMULATION DESCRIPTION 63

Pos Common area Xmax Xmax Ymin Ymin Ymax Ymax 2 [σ] tmin < |t|

Table 6.1: Common area region for AD-PU and =10π

Xmin in all the cases is zero

6.3 Simulation Study of Inelastic Events

As mentioned in sec 6.1, for the study presents in this dissertation, the inelastic processes are dividing in:

1. single diﬀractive p processes. The total number of these events is denoted as

Nsd,p.

2. single diﬀractivep ¯ process. The total number of these events is denoted as Nsd,p¯.

3. double pomeron exchange processes. The total number of these events is de-

noted as Ndpe.

4. non-diﬀractive processes. The total number of these events is denoted as Nnd.

Because there is a symmetric relation between the single diﬀractive processes p and p¯, and hence a factor of 2 brings the total number of single diﬀractive events. The choice of thep ¯ side is convenient because in that side there are more FPD roman pots located . The total number of inelastic processes stays now as:

Ninel =2Nsd + Nnd + Ndpe (6.10) CHAPTER 6. SIMULATION DESCRIPTION 64

Pos Common area Xmax Xmax Ymin Ymin Ymax Ymax 2 [σ] tmin < |t|

Table 6.2: Common area region for AD-PU and =15π

Xmin in all the cases is zero

The double pomeron exchange process has a low cross-section, a reasonable guess for the hard double pomeron cross-section is about 1% of the hard diﬀractive cross-section (≈ 0.03 µb), so its contribution of the ﬁnal number of inelastic events is despicable and will ignored for the remaining analysis.

Hence the ﬁnal total number of inelastic events measured by a detector is:

Ninel =2Nsd + Nnd (6.11)

with Nsd and Nnd are also the number of detected events.

All QCD processes are generate using PYTHIA (sec C.3), as mentioned. The classification of sec 6.1 labels each number of events with a corresponding flag of the processes. After identifying them, we measure the detected events using a different trigger for each process. For the measurement of single diffractivep ¯ processes we use thep ¯ side of the FPD subdetector and the Luminosity Monitor South of the DØ Detector. The measurement of the non-diffractive processes is doing with both Luminosity Monitors. CHAPTER 6. SIMULATION DESCRIPTION 65

The analysis of the non-diﬀractive processes is made with the PYTHIA generation data of the above paragraph but for the diﬀractive processes simulation the generator POMWIG were used. Details of these generators software are discussed in appendix C.

In order to have the most exact approximation of the real σtot measurement we use the DØ GEANT Simulation of the Total Apparatus Response (DØgstart)5 that include the Tevatron lattice and the detectors around the interaction point DØ, this permits us to obtain the measurements taking by the Luminosity Monitors. Since the FPD

is out of the DØ Detector we use a PROPAGATOR FUNCTION, developed by J. Molina (discussed in the appendix B), for the measurements of the particles that remained intact after the collisions.

The study of the inelastic processes is focused in the single diﬀractivep ¯ process, in which the FPD subdetector at diﬀerent locations correspond with the positions evaluated in the MonteCarlo Elastic Study. Main results in the FPD acceptance for this process are discussed in the following chapter.

6.3.1 Beam Pipe Eﬀect View using PYTHIA and GEANT4

As a ﬁrst understanding of the Tevatron lattice, we want to establish the beam pipe eﬀect in the measurements taken by the luminosity monitors that are outside of the Tevatron pipe.

We start by generating a collision proton-antiproton collision with a center-of-mass energy of 1.96TeV using PYTHIA. This software allows to simulate the speciﬁc sub-

processes those are of interest. In this section the Transverse Momentum Pt, Pseudo-

5The standard programs of the DØgstart simulation using in this dissertation were obtained from works of L. Mendoza (PhD student at Universidad de los Andes) see details in appendix C.1. The run of the programs and their corresponding analysis were developed in Fermilab Computers from a remote conection. CHAPTER 6. SIMULATION DESCRIPTION 66 rapidity η and Multiplicity Distributions are reported. They are obtained from the single diﬀractive processes with p andp ¯ intact separately, and from inelastic processes.

The information of the generated particles after the collision by PYTHIA is used to propagate them to the LM detector by using GEANT4, which is a package for the simulation of the passage of particles through mattter (discussed in the last appendix of this document). The lattice implemented here consisted of a vacuum medium with a beryllium tube that the particles cross to arrive the luminosity monitors. The tube had an inner radius of 2.5781cm and an outer radius of 2.667cm as it is shown in figure 6.10 and corresponds to the Tevatron pipe characteristic. Figures 6.12 and 6.11 show the particle traces of a single diffractive and an inelastic process that correspond to the triggers defined in sec.6.1.

The interface between PYTHIA and GEANT4 is the standard HEPEvtInterface (High Energy Event Interface). The physics simulated corresponds to the QGSP Educated guess physics list, which includes electro-magnetic and hadronic interactions.

Figure 6.10: Geometry View for Geant4 Simulation of the Beam Pipe. Luminosity monitors, beam pipe and the coordinates plane

Figure 6.11: Single Diﬀractive Soft Event

Figure 6.12: Inelastic event CHAPTER 6. SIMULATION DESCRIPTION 67

Seudorapidity Distributions for Luminosity Monitors Just after beam pipe - GEANT4 Just after collision - PYTHIA Seudorapidity Distributions for Luminosity Monitors Just after beam pipe - GEANT4 Just after collision - PYTHIA 103 Entries = 6481

103 Entries = 6604

102

10 10

1 -10 -8 -6 -4 -2 0 2 4 6 8 10 1

-10 -8 -6 -4 -2 0 2 4 6 8 10

Figure 6.13: Single Diﬀractive (X+¯p), η Figure 6.16: Single Diﬀractive (p+X), η Distribution Distribution

Transverse Momentum (Direction) for Luminosity Monitors Just after beam pipe - GEANT4 Just after collision - PYTHIA Transverse Momentum (Direction) for Luminosity Monitors Just after beam pipe - GEANT4 Just after collision - PYTHIA

3 Entries = 6481 10 104 Entries = 23525

102 103

10 102

10 1

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Figure 6.14: Single Diﬀractive (X+¯p), pt Figure 6.17: All QCD processes, Pt Dis- Distribution tribution

Transverse Momentum (Direction) for Luminosity Monitors Just after beam pipe - GEANT4 Just after collision - PYTHIA Seudorapidity Distributions for Luminosity Monitors Just after beam pipe - GEANT4 Just after collision - PYTHIA Entries = 6604 103 Entries = 23525 103

102

1 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-10 -8 -6 -4 -2 0 2 4 6 8 10

Figure 6.15: Single Diﬀractive (p+X), p t Figure 6.18: All QCD processes, η Distri- Distribution bution

Multiplicity Distributions for Luminosity Monitors Just after beam pipe - GEANT4 Just after collision - PYTHIA

Entries = 2001

102

0 20 40 60 80 100 120 140

Figure 6.19: Single Diﬀractive (p+X) CHAPTER 6. SIMULATION DESCRIPTION 68

Multiplicity Distributions

As we expected the beam pipe eﬀect produces the creation of new particles that increase the acceptance of the inelastic events in the Luminosity Monitors. Figures 6.19, 6.20 and 6.21 present the multiplicity distributions before an after the beam-pipe for each process.

Multiplicity Distributions for Luminosity Monitors Just after beam pipe - GEANT4 Just after collision - PYTHIA

Entries = 2001

102

0 20 40 60 80 100 120 140

Figure 6.20: Single Diﬀractive (X+¯p)

Multiplicity Distributions for Luminosity Monitors Just after beam pipe - GEANT4 Just after collision - PYTHIA

2 10 Entries = 2001

0 20 40 60 80 100 120 140

Figure 6.21: MSEL=2 Inelastic process

Results of the acceptance of the luminosity monitors are presented in table 6.3.1. The Luminosity Monitors (LM) south correspond to the luminosity monitor installed in CHAPTER 6. SIMULATION DESCRIPTION 69

the proton side after the collision.

Process Acceptance LM north[%] Aceptance LM south[%] Single Diﬀractive X+¯p 78.7606 49.1754 Single Diﬀractive p+X 49.2754 79.4103 All inelastics 90.1549 89.2554

Table 6.3: LM acceptance using a tube of beryllium

6.4 The Total Cross-Section Uncertainty

As we discussed in sec.2.3 the total cross-section measurement is given by eq 2.11: A σtot = C A (6.12) B + Ninel 16π2c2 where C is a constant value equal to C = 1+ρ2 , A and B correspond to a ﬁt in the dNel −Bt elastic distribution of the transferred four-momentum expressed as dt = A exp ,

B is called the slope and Ninel is the number of inelastic events.

The corresponding derivatives for the evaluation of errors are:

∂σtot C − C CNinel = A 2 = 2 ∂A B + Ninel (A/B + Ninel) (A/B + Ninel) 2 2 ∂σtot CA /B = 2 ∂B (A/B + Ninel) ∂σtot − CA = 2 ∂Ninel (A/B + Ninel)

using the usual propagation of errors formula, the total cross-section uncertainty ∆σtot is obtained as: C 2 2 4 2 2 2 ∆σtot = 2 Ninel∆A +(A/B) ∆B + A ∆Ninel (6.13) (A/B + Ninel) The total number of inelastic events, eq 6.11, is corrected by the acceptance (the acceptance calculation is discussed in the following chapter) of each process according CHAPTER 6. SIMULATION DESCRIPTION 70

with the classiﬁcation of events strategy. Since two diﬀerent MonteCarlo are used, the inelastic events for the total cross-section measurement is expressed or normalized in terms of the number of elastic events as:

d0g d0g 2Nsd /Accep.sd + Nnd /Accep.nd Ninel = d0g Nelas (6.14) Nelas d0g where Nsd is the number of detected single diﬀractive (sd) processes obtained us-

ing PYTHIA in the d0gstar simulation, Accep.sd is the corresponding acceptance of d0g the (sd) processes, Nnd is the number of detected non-diﬀractive nd processes using

PYTHIA in the d0gstar simulation, Accep.nd is the acceptance of the nd processes, d0g Nelas is the number of sent elastic events produced using the PYTHIA as the generator in the d0gstar simulation, and Nelas is A/B the corresponding number of elastic events generated by the ELASTIC DISPERSION SOFTWARE.

The uncertainty in the number of inelastic events (∆Ninel ) is obtained with the usual error formula, assuming that the acceptance has not uncertainty because with a Mon- teCarlo simulation is possible to reduce the uncertainty to an neglected contribution: 2 2 ∗ 2 d0g 1 d0g ∆Ninel = Nelas d0g Nsd + d0g Nnd Accep.sdN Accep.ndN elas elas 0 0 N 4N d g N d g = elas ∗ sd + nd (6.15) d0g A2 A2 Nelas ccep.sd ccep.nd

The total acceptance of the single diﬀractive process Accep.sd is calculated considering that the acceptance in the FPD is independent of the acceptance in the LM. This implies that the ﬁnal acceptance is the product of the individual acceptances. Chapter 7

Inelastic Acceptance Simulation Results

The DØ Geant Simulation of the Total Apparatus Response (DØgstar) is used for

the measurement of inelastic events rate Ninel on the Luminosity Monitors (LM) while a PROPAGATOR FUNCTION (appendix.B) is used for the measurement on the FPD, as mentioned in the preceding chapter.Closer results to real experiments can be achieved by following this strategy. In this chapter the inelastic events acceptance results for the LM and FPD changing the roman pot position are presented.

The geometrical acceptance of each detector is considered while ineﬃciencies of the individual roman pot modules are neglected. This means that for a single particle the acceptance to an event is one if the detector is hit and otherwise is zero. The acceptance is evaluated as:

N accep = detec (7.1) Nsent

where Ndetec is the number of events that hit the detector and Nsent is the number of events sent to the detector.

71 CHAPTER 7. INELASTIC ACCEPTANCE SIMULATION RESULTS 72

The uncertainty in the acceptance can be obtained from the usual formula of propagation of errors. First a rewriting of the acceptance is needed in order to obtain the appropriated value of uncertainty, knowing that there is only error in the events detected; the number of sent events is an exact value. The acceptance could be written as:

N N accep = detec = detec (7.2) Nsent Ndiff + Ndetec where Ndiff = Nsent − Ndetec, the usual formula of propagation of errors implies:

2 2 ∂accep ∂accep ∆accep = N + N ∂N detec ∂N diff detec diff 2 2 ∆ N = N + − N (∆ + N)2 detec (∆ + N)2 diff

Ndetec Ndiff = 3 (Ndetec + Ndiff ) the distribution of the number of detected events is expected to have a Gaussian √ shape, for this, the uncertainty of Ndetec is Ndetec. Hence, the uncertainty or error in the acceptance can be obtained as:

Ndetec (Nsent − Ndetec) ∆accep = 3 (7.3) Nsent

7.1 Acceptance of LM for Each Process

The Luminosity Monitors acceptance is calculated using the DØ Geant Simulation of the Total Apparatus Response (DØgstar) with PYTHIA as the generator of events (the d0gstar simulation was running in the Fermilab cluster of the DØ Experiment from remote connection, refer to sec. C.1). To consider a hit in a luminosity monitor counter it is required that:

1. The multiplicity of the luminosity monitors counters are high. This means that a considerable number of luminosity monitor cells were on. This clears part of CHAPTER 7. INELASTIC ACCEPTANCE SIMULATION RESULTS 73

η_plot Azimutal angle distribution φ_plot Seudorapidity distribution Entries 82528 Entries 82528

] Mean 2.541 Mean 3.124 2200φ η dN d

dN d RMS 2.014 RMS 1.815 2000

Log[ 1800 1600 1400 1200 1000 800 103 600 400 200 0 -10-8-6-4-20246810 -10123456 |η| [rad] |φ| [rad]

Energy distribution energy_plot Momentum Transverse distribution pT_plot Entries 82528 Entries 82528 5 ] 5 Mean 17.71 ] Mean 0.3013 10 10

dN RMS 69 RMS 0.3886 dE dN dp_t

Log[ 4 4 10 10 Log[

103 103

102 102

10 10

1 0 100 200 300 400 500 600 700 800 900 02468101214 |E| [GeV] |p_t| [(GeV/c)]

Figure 7.1: Distributions measured by Luminosity Monitor South.

the possible background events, for example when a cosmic ray could turn on a cell.

2. There are energy deposited in the calorimeter cells after crossing the luminosity counters.

Plots of the distributions measured for the main physical variables (pseudorapidity, azimutal angle and transverse momentum, respectively) of the particles and the energy deposited in the calorimeter cells, for the events detected by the Luminosity counter located in the south side of the collision, with the conditions explained in the above paragraphs and with a total of 10000 events sent, are shown in ﬁg7.1.

The acceptance and efficiency of the Luminosity Monitors for 10000 Events, according with each process is reported in table 7.1. The greatest acceptance value of the Luminosity Monitors is for the non-diffractive processes and corresponds with the efficiency measured for Run II (90.9% ± 1.8%) and reported in [26]. The Luminosity CHAPTER 7. INELASTIC ACCEPTANCE SIMULATION RESULTS 74

Monitors acceptance is 50% greater than the FPD acceptance of the intact particle, for a single diﬀractivep ¯ process, as reported in the following section.

Process Percentage Num Eve Acceptance and Effi. of total events Detected for LM Elastic 27.95% single diffrac. p 10.95% 849 0.77±0.013 single diffrac.p ¯ 10.80% 812 0.75±0.013 Non Diffrac. 49.86% 4234 0.85±0.005 DPE 0.400% 19 0.47±0.079

Table 7.1: Acceptance of the Luminosity Monitors for 10000 events Results obtained using the DØgstar with a PYHIA card ﬁle as the generator

For the Double Pomeron Exchange (DPE) process we note that certain particles reach the luminosity monitors, then the particles produced had a big energy an a pseudorapidity of 2.7 < |η| < 4.4. Recall that the expected behavior is to have two intact particles, one at least with energy diﬀerent of 980GeV, which produced two jets in the central axis of the collision those not necessarily hit the LM.

The acceptance of the DPE process is ignored in the ﬁnal calculation of the total cross- section, as discussed in the previous chapter, because its contribution is despicable since this process has a low cross-section compare with the others processes.

7.2 Single Diﬀractive FPD Acceptance Changing Positions

The acceptance of the FPD subdetector for the single diﬀractivep ¯ processes, using the PROPAGATOR FUNCTION (appendix B) with the events generated by POMWIG, are presented in the tables of this section. Although there is a change in the generator CHAPTER 7. INELASTIC ACCEPTANCE SIMULATION RESULTS 75 used for the results reported in the previous section, the number of single diﬀractive p¯ processes is preserved.

Pot Events Acceptance A1U 128 0.12 ± (9.8x10−3) A2U 85 0.08 ± (8.2x10−3) A1O 160 0.15 ± (11x10−3) A2O 151 0.14 ± (10x10−3) A1D 102 0.09 ± (8.9x10−3) A2D 79 0.07 ± (7.9x10−3) A1I 146 0.14 ± (10x10−3) A2I 137 0.13 ± (10x10−3) D1 366 0.34 ± (14x10−3) D2 325 0.30 ± (14x10−3) A spectrometer 452 0.42 ± (15x10−3) D spectrometer 318 0.29 ± (14x10−3) Any spectrometer 614 0.57 ± (15x10−3)

Table 7.2: FPD acceptance at 10σ,with =10π Total ofp ¯ sent: 1084

A POMWIG card is used instead of a PYTHIA card because it is necessary to have the most precise and random physical quantities of the intact particles, as mentioned in the preceding chapter; an example that compares these two generators is introduced at the end of this chapter.

A completed list of the 8 roman pots, (A1U, A2U, ..., D1 and D2) of the FPD subdetector located at thep ¯ side, with its corresponding acceptance is present in table 7.2. This data correspond to an emittance of =10π and a total of 1084p ¯ sent produced in a simulation of single diﬀractivep ¯ processes. There are also the results CHAPTER 7. INELASTIC ACCEPTANCE SIMULATION RESULTS 76 of each spectrometer acceptance:

• A spectrometer hit means a hit in A1U and A2U, or a hit in A1I and A2I, ..., i.e. There are coincidences between A1 and A2.

• D spectrometer hit means a hit in D1 and a hit in D2.

• Any spectrometer hit means that at least one of the spectrometer is hit in the current event.

Changing the location of the FPD roman pots, the acceptance change as reported in table 7.3. The detector acceptance decrease when the roman pots are located in a further out position from the beam line, as expected. The change of two units (in the beam size σ) in the positions produced a change of 15% in the acceptance for 10 to 12 σ while only a change of 2% in acceptance is presented from 16 to 18σ.

Pos Detector Events Det. Acceptance 10 σ Any spectrometer 614 0.57 ± (15x10−3) 12 σ Any spectrometer 509 0.47 ± (15x10−3) 14 σ Any spectrometer 429 0.40 ± (15x10−3) 16 σ Any spectrometer 366 0.34 ± (14x10−3) 18 σ Any spectrometer 312 0.29 ± (14x10−3)

Table 7.3: FPD acceptance summary, with =10π Total ofp ¯ sent: 1084

Tables 7.4 and 7.5 present the same parameters discussed above but with an emittance of =15π. The change to a higher emittance produced a lost in the acceptance of the FPD roman pots but preserved the relationships statement in the above paragraphs. CHAPTER 7. INELASTIC ACCEPTANCE SIMULATION RESULTS 77

Pot Events Acceptance A1U 99 0.09 ± (8.7x10−3) A2U 58 0.05 ± (6.8x10−3) A1O 106 0.10 ± (9.0x10−3) A2O 97 0.09 ± (8.7x10−3) A1D 80 0.07 ± (7.9x10−3) A2D 55 0.05 ± (6.7x10−3) A1I 105 0.10 ± (9.0x10−3) A2I 99 0.09 ± (8.7x10−3) D1 346 0.32 ± (14x10−3) D2 315 0.29 ± (14x10−3) A spectrometer 309 0.28 ± (14x10−3) D spectrometer 296 0.27 ± (13x10−3) Any spectrometer 495 0.46 ± (15x10−3)

Table 7.4: FPD acceptance at 10σ,with =15π Total ofp ¯ sent: 1084

7.3 Pots located at high β Store

The acceptance presents in table 7.6 corresponds to an additional ﬁxed location of the FPD roman pots. These positions are according with the measurements taking in the high β run at the Tevatron. These measurements were taking by FPD Group in February 2006 and might be useful for the measurement of the total cross-section, as discussed in sec 4.2. This table helps in the expected results after the corresponding analysis of the real data.

The value 0.48 for the FPD acceptance, with the parameters of the high β run, is in the interval of the acceptance obtained with the roman pots located between 10σ and 12σ with an emittance of 10π. In the following chapter, were the value of the posi- CHAPTER 7. INELASTIC ACCEPTANCE SIMULATION RESULTS 78

Pos Detector Events Det. Acceptance 10 σ Any spectrometer 495 0.46 ± (15x10−3) 12 σ Any spectrometer 402 0.37 ± (15x10−3) 14 σ Any spectrometer 333 0.31 ± (14x10−3) 16 σ Any spectrometer 269 0.25 ± (13x10−3) 18 σ Any spectrometer 245 0.23 ± (13x10−3)

Table 7.5: FPD acceptance summary, with =15π Total ofp ¯ sent: 1084

tions are reported in millimeters, we will note that the positions are corresponding, for this, a similar acceptance is expected.

In order to compare the generators of particle collisions POMWIG and PYTHIA, the table 7.7 is presented. A wrong distribution in the particle four-momentum of PYTHIA, discussed bellow, gives a diﬀerence of about 46% in the acceptance of the single diﬀractivep ¯ events in the FPD roman pots.

Pythia simulate the generation of particles by using a string-based fragmentation scheme that has a disfavored soft color interaction approach because of the non- perturbative color theory introduced. QCD perturbative theory do not apply when small angles are involved, as mentioned in cahpter 5.

In fact there is not a theory that explains the behavior of the diﬀractive processes at the forward region only phenomenological theories are used as approach. This is the big reason of why the FPD was introduced in Run II of the Tevatron, there is physics that do not understand yet. CHAPTER 7. INELASTIC ACCEPTANCE SIMULATION RESULTS 79

Pot Events Acceptance A1U 108 0.10 ± (9.1x10−3) A2U 64 0.06 ± (7.2x10−3) A1O 91 0.08 ± (8.4x10−3) A2O 87 0.08 ± (8.2x10−3) A1D 54 0.05 ± (6.6x10−3) A2D 47 0.04 ± (6.2x10−3) A1I 148 0.14 ± (10x10−3) A2I 148 0.14 ± (10x10−3) D1 368 0.34 ± (14x10−3) D2 329 0.30 ± (14x10−3) A spectrometer 346 0.32 ± (14x10−3) D spectrometer 323 0.30 ± (14x10−3) Any spectrometer 526 0.48 ± (15x10−3)

Table 7.6: FPD acceptance for High β run using POMWIG Total ofp ¯ sent: 1084 CHAPTER 7. INELASTIC ACCEPTANCE SIMULATION RESULTS 80

Pot Events Acceptance A1U 65 0.06 ± (7.3x10−3) A2U 53 0.05 ± (6.6x10−3) A1O 41 0.04 ± (5.9x10−3) A2O 37 0.03 ± (5.6x10−3) A1D 33 0.03 ± (5.3x10−3) A2D 31 0.03 ± (5.1x10−3) A1I 89 0.08 ± (8.5x10−3) A2I 89 0.08 ± (8.5x10−3) D1 161 0.15 ± (11x10−3) D2 160 0.15 ± (11x10−3) A spectrometer 210 0.20 ± (12x10−3) D spectrometer 153 0.14 ± (11x10−3) Any spectrometer 278 0.26 ± (13x10−3)

Table 7.7: FPD acceptance for High β run using PYTHIA Total ofp ¯ sent: 1067 Chapter 8

Statistical Errors for σtot,pp¯ Simulation Results

The study of the total cross-section uncertainty (∆σtot) is able to developed with the elastic events simulation joined with the results of the last chapter (inelastic acceptance). The FPD roman pots are moving farther out from the Tevatron beam-line in

order to established the change in the ∆σtot.

In this chapter, the total cross-section uncertainty obtained by taking into account only statistical errors is presented. The analysis and results are presented in three sections: Tables of ﬁts, tables of the uncertainty contribution of each term and Tables of the total cross-section uncertainty.

8.1 Tables of Fits

dNel The total cross-section measurement is obtained from an exponential fit as dt = A exp−Bt on the distribution of the transferred momentum measured in each detector (presented in fig 8.1), as mentioned in sections 2.3 and 6.2. The fitting region is with t<0.55GeV2 and the two parameters of the fit are the extrapolation to t =0, dN A= dt t=0 and the slope (in a logarithmic scale) B. In this section, the results of the fit obtained for the FPD located at 10σ,12σ and 14σ with an emittance of =10π

81 CHAPTER 8. STATISTICAL ERRORS FOR SIMULATION RESULTS σTOT,PP¯ 82

Momentum Transferred Distributions for Pot A1D

] 105 dt dN Log[ 104

103

Positions with 33368 entries 20σ 102 18σ 16σ 14σ 10 12σ 10σ

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 |t| [(GeV/c)^2]

Figure 8.1: Fit example for AD-PU detectors with =10π changing positions. are presented.

All the fits include the corrections by the geometrical acceptance of the detectors and convolution of the beam-size discussed in sec 6.2. The coincidences between the roman pots of the trigger and the acceptance values restrict the entrance of events in the histogram outcome to only the ones to has the t inside the common regions. Graphical examples of the fits (doing with the software package ROOT [24]) are presented in fig 8.2 and 8.3.

dN 2 Pot Pos t dt t=0 Slope χ /ndf [mm] [(GeV/c)2] [(GeV/c)−2] [(GeV/c)−2] P1U 3.01 0.17±0.50 13.44±0.052 -17.23±0.21 0.98 P2U 3.52 0.17±0.50 13.44±0.052 -17.24±0.21 1.05 A1D 6.24 0.17±0.50 13.44±0.051 -17.24±0.21 1.08 A2D 5.50 0.17±0.50 13.44±0.052 -17.25±0.21 1.05

Table 8.1: Fit table at 10σ with =10π

In the tables the value χ2/ndf is reported, where χ2 is obtained from the method of CHAPTER 8. STATISTICAL ERRORS FOR SIMULATION RESULTS σTOT,PP¯ 83

Momentum Transferred pos12sigA1D Momentum Transferred pos12sigA2D Entries 30854 Entries 30847 Mean 0.2371 Mean 0.2371 RMS 0.05338 RMS 0.05338 4 χ2 4 10 / ndf 19.75 / 17 10 χ2 / ndf 18.53 / 17 Prob 0.2873 Prob 0.3564 Constant 13.17 ± 0.04 Constant 13.17 ± 0.04 Slope -17.23 ± 0.14 Slope -17.23 ± 0.14

3 3 10 10

102 102 0.2 0.25 0.3 0.35 0.4 0.45 0.2 0.25 0.3 0.35 0.4 0.45

Momentum Transferred pos12sigP1U Momentum Transferred pos12sigP2U Entries 25005 Entries 24473 Mean 0.2382 Mean 0.2383 RMS 0.05349 RMS 0.05348 4 2 4 2 10 χ / ndf 20.88 / 17 10 χ / ndf 20.98 / 17 Prob 0.2317 Prob 0.2273 Constant 13.06 ± 0.04 Constant 13.04 ± 0.04 Slope -17.06 ± 0.15 Slope -17.06 ± 0.15

3 3 10 10

102 102

0.2 0.25 0.3 0.35 0.4 0.45 0.2 0.25 0.3 0.35 0.4 0.45

Figure 8.2: Fit example for AD-PU detectors at 12σ with =10π.

least squares and ndf is the appropriate number of degrees of freedom. Remember that, in order to compare a histogram with a hypothesis of their expectation values we have: N (n − v )2 χ2 = i i (8.1) v i=1 i where ni is the i-term of the vector n =(n1, ..., nN ) represented by the histogram (Poi- son distributed numbers), and vi = E[ni] is their corresponding expectation number. The ndf is equal to the number of measurements N minus the number of ﬁtted parameters.

The χ2 statistics is useful when we want to evaluate the agreement between the data and a hypothesis (without explicit reference) of a ﬁt (ni must be a large value or at 2 2 least ni > 5). Since the mean of the χ distribution is ndf we expected χ /ndf ∼ 1 for a good approximation.

In tables 8.1, 8.2 and 8.3 the parameters of the exponential ﬁt are reported, for the CHAPTER 8. STATISTICAL ERRORS FOR SIMULATION RESULTS σTOT,PP¯ 84

Momentum Transferred pos14sigA1D Momentum Transferred pos14sigA2D Entries 660 Entries 675 Mean 0.2548 Mean 0.2551

3 RMS 0.05497 3 RMS 0.05498 10 χ2 / ndf 7.746 / 11 10 χ2 / ndf 7.939 / 11 Prob 0.7359 Prob 0.7188 Constant 10.3 ± 0.3 Constant 10.42 ± 0.31 Slope -16.78 ± 1.06 Slope -17.22 ± 1.08

2 2 10 10

10 10

0.2 0.25 0.3 0.35 0.4 0.45 0.2 0.25 0.3 0.35 0.4 0.45

Momentum Transferred pos14sigP1U Momentum Transferred pos14sigP2U Entries 693 Entries 681 Mean 0.2547 Mean 0.2547 3 RMS 0.05494 RMS 0.0549 χ2 3 χ2 10 / ndf 9.006 / 11 10 / ndf 8.016 / 11 Prob 0.6213 Prob 0.7119 Constant 10.37 ± 0.31 Constant 10.46 ± 0.31 Slope -17.03 ± 1.07 Slope -17.34 ± 1.06

102 2 10

0.2 0.25 0.3 0.35 0.4 0.45 0.2 0.25 0.3 0.35 0.4 0.45

Figure 8.3: Fit example for AD-PU detectors at 14σ with =10π.

combination PU-AD of the FPD roman pots located at 10, 12 y 14 times the beam- size (σ)withanemittanceof =10π. Each ﬁt parameter has its corresponding uncertainty. In all cases we obtain a χ2/ndf close to one; this correlation is worse when the roman pots are moving far away of beam-line.

8.2 Table of each term uncertainty contribution dN In this section, the uncertainty contributions from the intercept dt t=0,slopeand number of inelastic events to the total cross-section uncertainty are presented.

Table 8.4 presents the uncertainty contribution of each term for the combination PU- AD of the FPD roman pots located at 10, 12 y 14 times the beam-size (σ)withan emittance of =10π. The number of entries in each histogram decreases with an outer position, because there are lesser hits in the detectors when the acceptance CHAPTER 8. STATISTICAL ERRORS FOR SIMULATION RESULTS σTOT,PP¯ 85

dN 2 Pot Pos t dt t=0 Slope χ /ndf [mm] [(GeV/c)2] [(GeV/c)−2] [(GeV/c)−2] P1U 3.61 0.19±0.50 12.86±0.056 -16.91±0.22 1.13 P2U 4.22 0.19±0.50 12.84±0.056 -16.88±0.22 1.28 A1D 7.49 0.19±0.50 13.03±0.055 -17.23±0.22 1.01 A2D 6.60 0.19±0.50 13.03±0.055 -17.24±0.22 0.95

Table 8.2: Fit table at 12σ with =10π

dN 2 Pot Pos t dt t=0 Slope χ /ndf [mm] [(GeV/c)2] [(GeV/c)−2] [(GeV/c)−2] P1U 4.21 0.22±0.50 13.01±0.100 -17.16±0.35 1.27 P2U 4.93 0.22±0.50 13.01±0.098 -17.15±0.34 1.34 A1D 8.74 0.22±0.50 13.01±0.099 -17.17±0.34 1.37 A2D 7.70 0.22±0.50 13.01±0.098 -17.16±0.34 1.32

Table 8.3: Fit table at 14σ with =10π

decrease and the luminosity remain constant for all the positions.

The difference in the number of entries of histograms with the same position and different detector are explained by the different cuts made. Besides the acceptance common area we cut entries with positions with 0.25mm inside the common area for PU while 0.1mm for AU, these for the case with the FPD roman pots located at 10σ. For 12σ we change the common area only 0.1mm for PU. In the case of 14σ we cut justthecommonareabecausewehavelessstatistic and more cuts are inappropriate.

The highest uncertainty contribution, reported in the table presented in this section, comes from the number of inelastic events Ninel no matter in what position are FPD roman pots located. In sec 6.4 the variables involved in each contribution could be appreciated. CHAPTER 8. STATISTICAL ERRORS FOR SIMULATION RESULTS σTOT,PP¯ 86

For the FPD roman pots located at 10σ the contribution of the inelastic events uncertainty is more than two times the contribution of the others terms. dN 2 Pos Entries from dt t=0 from Slope from Ninel χ /ndf Pot [σ] [mb] [mb] [mb] 10 33331 0.22 0.20 1.01 0.98 P1U 10 33319 0.22 0.20 1.01 1.05 P2U 10 33486 0.22 0.20 1.01 1.08 A1D 10 33536 0.22 0.20 1.01 1.05 A2D

12 16544 0.24 0.21 1.05 1.13 P1U 12 15947 0.24 0.21 1.05 1.28 P2U 12 20252 0.24 0.21 1.07 1.01 A1D 12 20106 0.24 0.21 1.07 0.95 A2D

14 8118 0.44 0.33 1.13 1.27 P1U 14 8133 0.43 0.32 1.13 1.34 P2U 14 8197 0.43 0.32 1.13 1.37 A1D 14 8162 0.43 0.32 1.13 1.32 A2D

Table 8.4: Each term uncertainty contribution with =10π

8.3 Total cross-section uncertainty results

The ﬁnal total cross-section uncertainty for the cases explored in the above sections are reported in table 8.5, from only the histogram error bars this means the statistical errors. The statistical uncertainty found for the total cross-section is almost 50% of the reported total uncertainty of the real experiments.

An increase of 8% in the total cross-section uncertainty is produced when the position of the FPD roman pots change in two units of beam-size from 10 to 12. An increase CHAPTER 8. STATISTICAL ERRORS FOR SIMULATION RESULTS σTOT,PP¯ 87

of 12% in ∆σtot is produced between the change in the location from 12 to 14 σ. dN Pos Pos ∆ dt t=0 Slope σtot ∆σtot Pot [σ] [mm] [(GeV/c)−2] [(GeV/c)−2] [mb] [mb]

10 3.01 0.053 17.34±0.21 73.75 1.06 P1U 10 3.52 0.053 17.41±0.21 74.04 1.06 P2U 10 6.24 0.052 17.08±0.21 72.67 1.04 A1D 10 5.50 0.052 17.07±0.21 72.60 1.04 A2D

12 3.61 0.056 16.91±0.22 71.95 1.10 P1U 12 4.22 0.056 16.88±0.22 71.81 1.10 P2U 12 7.49 0.055 17.23±0.22 73.29 1.12 A1D 12 6.60 0.055 17.24±0.22 73.32 1.12 A2D

14 4.21 0.100 17.16±0.35 72.99 1.26 P1U 14 4.93 0.098 17.15±0.34 72.97 1.25 P2U 14 8.74 0.099 17.17±0.34 73.05 1.25 A1D 14 7.70 0.098 17.16±0.34 72.99 1.25 A2D

Table 8.5: The total cross-section uncertainty with =10π

8.4 Changing emittance

With the same methodology as above, the following tables for an emittance of =15π are presented. Since the roman pots are farther out from the Tevatron beam-line com- paredwiththecaseof =10π the uncertainty of the total cross-section increases and the correlation χ2/ndf is lost, becuase the low statistics presented after the ﬁducial cuts, although a smaller number of bins in the histogram was implemented.

A change in the desired luminosity is produced when the emittance changes. It is almost impossible to predetermine the number of total events that must be sent to the detector to obtain an exactly desired number of entries in the histograms. 750000 CHAPTER 8. STATISTICAL ERRORS FOR SIMULATION RESULTS σTOT,PP¯ 88 collisions produced the last sections results (31000 entries) with an emittance =10π while 2000000 collisions (2.7 times more) produced about the same 34000 entries for =15π.

dN 2 Pot Pos t dt t=0 Slope χ /ndf [mm] [(GeV/c)2] [(GeV/c)−2] [(GeV/c)−2] P1U 3.69 0.26±0.50 14.28±0.077 -16.78±0.23 0.82 P2U 4.32 0.26±0.50 14.29±0.077 -16.79±0.23 0.79 A1D 7.65 0.26±0.50 14.28±0.077 -16.76±0.23 0.77 A2D 6.74 0.26±0.50 14.28±0.078 -16.77±0.24 0.72

Table 8.6: Fit table at 10σ with =15π.

dN 2 Pot Pos t dt t=0 Slope χ /ndf [mm] [(GeV/c)2] [(GeV/c)−2] [(GeV/c)−2] P1U 4.43 0.35±0.50 14.39±0.28 -17.00±0.69 0.88 P2U 5.18 0.35±0.50 14.40±0.28 -17.03±0.70 0.82 A1D 9.18 0.35±0.50 14.36±0.28 -16.92±0.70 0.80 A2D 8.09 0.35±0.50 14.39±0.29 -16.99±0.72 0.69

Table 8.7: Fit table at 12σ with =15π

The highest uncertainty contribution is again from the number of inelastic events with an emittance of =15π. CHAPTER 8. STATISTICAL ERRORS FOR SIMULATION RESULTS σTOT,PP¯ 89

dN 2 Pot Pos t dt t=0 Slope χ /ndf [mm] [(GeV/c)2] [(GeV/c)−2] [(GeV/c)−2] P1U 5.17 0.33±0.5 14.34±0.19 -16.92±0.50 0.98 P2U 6.05 0.33±0.5 14.36±0.19 -16.96±0.49 0.95 A1D 10.7 0.33±0.5 14.31±0.19 -16.84±0.50 0.96 A2D 9.44 0.33±0.5 14.35±0.20 -16.92±0.52 0.93

Table 8.8: Fit table at 14σ with =15π

dN 2 Pos Entries from dt t=0 from Slope from Ninel χ /ndf Pot [σ] [mb] [mb] [mb]

10 34532 0.299 0.220 1.06 0.817 P1U 10 34499 0.301 0.222 1.06 0.795 P2U 10 34617 0.301 0.222 1.06 0.771 A1D 10 34823 0.305 0.225 1.06 0.726 A2D

12 14307 1.100 0.651 1.15 0.886 P1U 12 14280 1.110 0.659 1.15 0.818 P2U 12 14393 1.110 0.659 1.14 0.805 A1D 12 14398 1.150 0.685 1.15 0.693 A2D

14 3527 0.757 0.469 1.23 0.978 P1U 14 3576 0.751 0.467 1.23 0.949 P2U 14 3585 0.76 0.475 1.22 0.964 A1D 14 3530 0.782 0.488 1.23 0.929 A2D

Table 8.9: Each term uncertainty with =15π CHAPTER 8. STATISTICAL ERRORS FOR SIMULATION RESULTS σTOT,PP¯ 90

dN Pos Pos ∆ dt t=0 Slope σtot ∆σtot Pot [σ] [mm] [(GeV/c)−2] [(GeV/c)−2] [mb] [mb]

10 3.69 0.077 16.78±0.23 71.37 1.12 P1U 10 4.32 0.077 16.79±0.23 71.42 1.12 P2U 10 7.65 0.077 16.76±0.23 71.29 1.12 A1D 10 6.74 0.078 16.77±0.24 71.34 1.12 A2D

12 4.43 0.281 17.00±0.69 72.34 1.72 P1U 12 5.18 0.284 17.03±0.70 72.44 1.73 P2U 12 9.18 0.283 16.92±0.70 71.96 1.72 A1D 12 8.09 0.294 16.99±0.72 72.28 1.76 A2D

14 5.17 0.194 16.92±0.50 71.97 1.51 P1U 14 6.05 0.192 16.96±0.49 72.15 1.51 P2U 14 10.7 0.195 16.84±0.50 71.65 1.51 A1D 14 9.44 0.200 16.92±0.51 71.98 1.53 A2D

Table 8.10: The total cross-section uncertainty with =15π

8.5 High-β-Store results

The analysis of the ﬁrst three chapters also applies to the results obtained from the parameters of special run of the Tevatron at High-β. The results of the statistical errors are presented in tables 8.12 and 8.11 for the FPD roman pots located at the High-β-Store.

The coincidences between the detectors are diﬀerent from the above sections in order to reach the highest acceptance of the high β run. In this case the trigger is the combination AU-PD.

Table 8.11 shows a χ2/ndf close to 1, which implies a good ﬁt for the distribution obtained. Also the uncertainty contribution of each term of the total cross-section CHAPTER 8. STATISTICAL ERRORS FOR SIMULATION RESULTS σTOT,PP¯ 91

dN 2 Pos Entries from dt t=0 from Slope from Ninel χ /ndf Pot [mm] [mb] [mb] [mb] 6.04 32415 0.13 0.13 1.04 1.08 P1D 6.05 32415 0.13 0.13 1.04 1.11 P2D 4.05 32415 0.13 0.13 1.04 1.06 A1U 3.54 32415 0.13 0.13 1.04 1.15 A2U

Table 8.11: High β run uncertainty contribution of each variable with =10π uncertainty is reported, again the highest uncertainty is from the inelastic events contribution.

Table 8.12 presents the ﬁt parameters, total cross-section, total cross-section uncertainty obtained for each roman pot. The total cross-section uncertainty obtained is again 50% of the reported total uncertainty of experiments.

2 dN Pos χ /ndf dt t=0 Slope σtot ∆σtot Pot [mm] [(GeV/c)−2 ] [(GeV/c)−2 ] [mb] [mb]

6.04 1.08 0.11±0.032 16.86±0.1378 71.72 1.053 P1D 6.05 1.11 0.11±0.032 16.86±0.1366 71.73 1.053 P2D 4.05 1.06 0.11±0.032 16.86±0.1367 71.72 1.053 A1U 3.54 1.15 0.11±0.031 16.88±0.1351 71.80 1.053 A2U

Table 8.12: High β run results with =10π Chapter 9

Systematic Errors for σtot,pp¯ at √ s =1.96TeV Results

In the following tables the total cross-section is recalculated with a shift in one physical quantity depending in the type of systematic error involved. Two systematic errors are included: the systematic error due to the position of the detectors measurement and the other due to the eﬀective length measurement.1

The measured position of the detector has an uncertainty of 300µm hence we calculate the new σtot if the position of the detectors is 300µm above and bellow the initial reference value. Only changes in the positions on y-axis are relevant for our study.

The uncertainty in the eﬀective length measurement is about 1%. An analogous strategy of the above paragraph is used to obtained the systematic error from the eﬀective length.

The number of inelastic events is constant in all the tables reported in this section. Since, although a change in the FPD roman pots exist, the non-diﬀractive events measured by the luminosity monitors are dominant and independent of the FPD ro-

1With the change in one detector parameter the common area of the triggering changes; this means that the measurement in each detector also change.

92 √ CHAPTER 9. SYSTEMATIC ERRORS FOR AT TEV RESULTS σTOT,PP¯ S =1.96 93

man pots positions.

The uncertainty produced due to the positions of the detector measurement, with an emittance of =10π, is reported in table 9.1 for the roman pots A1D y P1U. An appropriated value of the χ2/ndf is presented for locations at 10π and 12π.

dN 2 Position dt t=0 Slope χ /ndf σtot ∆σtot Pot [(GeV/c)−2] [(GeV/c)−2] [mb] [mb]

10σ ±∆pos 13.45±0.05 17.25±0.21 1.07 73.06 0.058 A1D

10σ ±∆pos 13.45±0.05 17.26±0.21 0.98 73.04 0.070 P1U

12σ ±∆pos 13.44±0.06 17.22±0.24 1.03 72.92 0.063 A1D

12σ ±∆pos 13.43±0.06 17.19±0.24 0.99 72.79 0.075 P1U

14σ ±∆pos 13.46±0.13 17.3±0.42 1.61 73.12 0.149 A1D

14σ ±∆pos 13.45±0.14 17.28±0.44 1.49 73.01 0.173 P1U

Table 9.1: New σtot from position uncertainty with =10π

The systematic errors due to the effective length uncertainty are reported in table 9.2. The total cross-section uncertainty does not change when the FPD roman pots are moving; the independent relation between the effective length and the FPD roman pots locations explains that. Also it is reported that the systematic error due to the effective length depends on the coordinate-axis (greater in x-axis than in y-axis). Additional tests were developed for a higher value of the effective length uncertainty. An change of 0.31mb in the total cross-section were found for the FPD roman pots located at 10σ with an emittace of 15π. These results are not reported because of the bad correlation found, as presented in the preceding chapter.

In the case of the High-β-Store positions similar results were found. The corresponding results are reported in table 9.3. A goog correlation number χ2/ndf is presented. √ CHAPTER 9. SYSTEMATIC ERRORS FOR AT TEV RESULTS σTOT,PP¯ S =1.96 94

dN 2 Pos Eﬀective ∆ dt t=0 Slope χ /ndf σtot ∆σtot Pot [mm] Length [(GeV/c)−2] [(GeV/c)−2] [mb] [mb]

10σ Leﬀx ±∆leff 13.43±0.052 17.20±0.21 1.03 72.82 0.18 A1D

10σ Leﬀx ±∆leff 13.43±0.053 17.19±0.21 0.92 72.80 0.18 P1U

10σ Leﬀy ±∆leff 13.44±0.051 17.23±0.21 1.08 72.99 0.01 A1D

10σ Leﬀy ±∆leff 13.44±0.052 17.23±0.21 0.98 72.96 0.01 P1U

12σ Leﬀx ±∆leff 13.43±0.059 17.18±0.23 1.06 72.77 0.17 A1D

12σ Leﬀx ±∆leff 13.43±0.060 17.17±0.23 0.96 72.69 0.17 P1U

12σ Leﬀy ±∆leff 13.44±0.059 17.22±0.23 1.08 72.93 0.01 A1D

12σ Leﬀy ±∆leff 13.43±0.060 17.20±0.23 1.00 72.86 0.01 P1U

14σ Leﬀx ±∆leff 13.43±0.100 17.19±0.34 1.23 72.82 0.12 A1D

14σ Leﬀx ±∆leff 13.42±0.100 17.16±0.34 1.14 72.66 0.21 P1U

14σ Leﬀy ±∆leff 13.44±0.100 17.23±0.34 1.24 72.99 0.04 A1D

14σ Leﬀy ±∆leff 13.43±0.100 17.20±0.34 1.16 72.83 0.04 P1U

Table 9.2: New σtot from eﬀective length uncertainty with =10π

dN 2 Pos Eﬀective ∆ dt t=0 Slope χ /ndf σtot ∆σtot Pot [mm] Length [(GeV/c)−2] [(GeV/c)−2] [mb] [mb]

6.04±∆pos Leﬀ 13.89± 0.034 -16.844±0.1424 1.006 71.65 0.0727 P1D

4.05±∆pos Leﬀ 13.89±0.032 -16.850±0.139 1.045 71.67 0.0527 A1U

6.04 Leﬀ±∆leff 13.89±0.033 -16.851±0.1406 1.000 71.65 0.0752 P1D

4.05 Leﬀ±∆leff 13.89 ±0.032 -16.887± 0.138 1.026 71.67 0.16990 A1U

Table 9.3: New σtot from sistematic uncertainty for the High-β-Store positions An emittance of =10π is used. Chapter 10

Background Analysis and Results

Two main types of backgrounds are recognized. The background coming from the particle bunches crossing as multiple interactions and from the halo eﬀects. In this analysis the collective eﬀects of the bunch are ignored, hence the study of having collision of particles within the same beam, is out of this discussion.

The analysis and estimated percentages of background presented in this chapter correspond to the High-β-Store of the Tevatron, made in February 15th 2006. In the ﬁrst section the multiparticle interaction is discussed. The halo background for the inelastic processes is analyzed in the second section of this chapter.

The measured data of the special run at high β is reported in the table 10.1. The special run of the Tevatron were developed with a beam injection lattice, also there was only one bunch crossing every 21µs, as mentioned in sec 4.2.

10.1 Multiple Interactions

A multiple interaction event produces a wrong classiﬁcation of events. This occurs when two or more interactions are presented in the bunch crossing. There are two types of multiple interactions that are of concern:

95 CHAPTER 10. BACKGROUND ANALYSIS AND RESULTS 96

Pot Position[mm] Wanted Position[mm] Rate [KHz] D1I 36.03 35.92 2.12 D2I 32.55 32.48 2.59 A1U 38.18 37.96 2.42 A1D 38.29 38.11 1.55 A1I 38.92 39.00 1.28 A1O 27.58 28.15 3.86 A2U 37.52 37.62 1.15 A2D 38.45 38.35 1.34 A2I 38.47 38.68 1.82 A2O 30.48 30.50 4.07

Table 10.1: High β run Tevatron parameters for FPD roman pots atp ¯ side With L=0.29x1030 cm−2s−1. D0 Beam Halo [KHz] P halo=1.05 and A halo=0.09. D0 Beam Position (mm) xpos=-0.079 ypos=0.145

• The superposition of a hard single diﬀractive event with a minimum bias event1.

• The superposition of a standard single diﬀractive event with a hard scattering event (pile-up background).

The probability of a multiple interaction is obtained from the cross-section, which could be interpreted as a probability in accordance with the discussion of chapter

2. From [13] the probability P(n=0) of no extra interaction in addition to a hard scattering is calculated as:

n¯ = L σT/NB (10.1)

−n¯ P(n=0) =exp (10.2)

wheren ¯ is the average number of extra interactions, L is the instantaneous luminosity, σ is the total cross section and T the period of bunch crossing and NB is the 1A minimum vias event is considered as an event taking without trigger in the DØ Experiment CHAPTER 10. BACKGROUND ANALYSIS AND RESULTS 97

number of bunches.

The probability of no extra interaction P(n=0) for each processes is presented in table 30 −2 −1 10.2 for the special run at high β with L=0.29x10 cm s , NB=1 and T=21µs . The cross-sections in the table are consider the expected cross-sections of the events and correspond with the cross-sections used in PYTHIA (reported in table 2.1).

Physical Process Cross Section [mb] P(n=0) Total 73.98 0.64 Elastic 15.02 0.91 Single diffractive X+¯p 6.24 0.96 Single diffractive p+X 6.24 0.96 Double diffractive 7.45 0.96 Inelastic, non-diffractive 39.03 0.79

Table 10.2: Pythia Cross-Sections Values

The probabilities of having a multiple interaction are 0.0874, 0.037 and 0.21 for elastic, diﬀractive and non-diﬀractive processes respectively. These values are quite lower 31 −2 −1 than the results for normal operations (L=2x10 cm s and NB=36) 0.84, 0.07, 0.634.

An injection lattice reduce the background of multiple interactions, because it has a lower luminosity, as presented in the above paragraph.

10.2 Halo Background

The number of events or reactions in a collision per second, could be estimated from the deﬁnition of the luminosity (eq 3.12), this rate will be considered without back- CHAPTER 10. BACKGROUND ANALYSIS AND RESULTS 98

ground. Using the real data taking by the FPD roman pots at the high β store on February 2006 and the results of the previous chapters, an estimation of the background present in the pp¯ collisions at the Tevatron with a center-of-mass energy of 1.96 TeV could be achieve.

The signal without background is (according with eq 3.12):

N σL R = = t s R = σL (10.3)

where R is the number of events or reactions in a collision per second, N is the total number of events, t is and interval of time, σ is the cross-section, L is the integrated luminosity and L is the instantaneous luminosity.

The signal with background is expressed as:

Prob R = backg (10.4) backg T where Rbackg is the estimated number of events or reactions with background in a collision per second, Probbackg is and T is the period of beam crossing.

This type or background is called halo background because the noise signals belong to the beam of the accelerator. Since the beam is not a straight line but has a Gaussian form, some particles in frontier or outside the buckets (discussed in sec 3.2) hit the detectors before the real collision.

Possible sources of beam halo include: mismatched beam optics (bucket leakage), nonlinear elements out of the reconstruction calculations, space charge eﬀects (inter- beam), beam-beam eﬀects, Coulomb scattering on the residual gas and more. The reduction mechanisms of halo include collimation or scraping, channeling and shield- ing at the Tevatron CHAPTER 10. BACKGROUND ANALYSIS AND RESULTS 99

An estimated percentage of the presented halo background in each process is obtained in this chapter by comparing the expected frequency of the processes produced and the frequency or rate of background in each cycle of bunch crossing.

An acceptance correction is taken into account in the signal with background and the highest rate measured in the pots is the used rate for the estimations.

The trigger system of DØ Detector has the so called halo bit ﬂag that prevents the halo background. For elastic events this system reduces most of the background because of the easy topology of the event. The halo background of the inelastic processes, which has the highest statistical error contribution, is studied as follows.

Halo Background in Single Diﬀractive Processes

The probability of having a signal with background in a single diﬀractive process PbgSD depends on the detector that produced the signal. In this dissertation, the single diﬀractive process measurement is obtained from simulations of the measurements on the FPD and luminosity monitors of DØ Experiment. Since each detector is independent of the other, the probability is estimated from:

PbgSD = Pbg,F P D Pbg,LM R R = pot LM F F 2 = Rpot RLM T (10.5)

where Pbg,F P D is the probability of having a halo hit in any roman pot in thep ¯ side.

Pbg,LM is the probability of having a halo hit in the luminosity monitors (LM). F is the frequency of a collision in the Tevatron that is calculated from the period of collision T established as 21µs for the high β run (with only one bunch colliding).

Rpot and RLM are the number of events or reactions detected, by the FPD roman CHAPTER 10. BACKGROUND ANALYSIS AND RESULTS 100 pots and the luminosity monitor, per second, respectively.

The probabilities Pbg,F P D and Pbg,LM are understood with the usual deﬁnition as the ratio of the number of actual occurrences to the number of possible occurrences. Hence, the estimated number of events or reactions with background in a collision

per second (RbgSD), eq 10.4, is:

Prob R = backg = R R T bgSD T pot LM

RbgSD =(4KHz)(1KHz)(21µs)=84Hz (10.6)

assuming a rate of 1KHZ for the luminosity monitor counters.

The signal frequency without background is estimated from eq 10.3. The cross-section introduced in table 2.1:

30 −27 Rsd = Lσsd =(0.29x10 )(6.2x10 ) = 1798Hz (10.7)

The expected signal is corrected by the acceptance of each detector obtained in chapter 7

RSD = Rsd Accefpd AcceLM = (1798Hz)(0.48)(0.75) = 647Hz (10.8)

13% of background is estimated to be in the signal of a single diﬀractive process.

Halo Background in Non-Diﬀractive Processes

The simulation of the non-diﬀractive processes (ND) measurement, in this dissertation, is obtained by both luminosity monitors counters, as mentionated in cahapter 6. The trigger demands at least one hit in the Luminosity Monitor counter of each side of the collision. Since the measurements by the Luminosity Monitor south (LMs) are independent of the measurements by the Luminosity Monitor north (LMn), the

probability of having a signal with background in a non-diﬀractive process PbgND is: CHAPTER 10. BACKGROUND ANALYSIS AND RESULTS 101

PbgND = Pbg,LMs Pbg,LMn R R = LMs LMn F F 2 = RLMs RLMn T (10.9)

where Pbg,LMs and Pbg,LMn is the probability of having a halo hit in the luminosity

monitors south and north, respectively. RLMsand RLMn are the number of events or reactions detected per second by in the LM south and north, respectively. As the above paragraphs, F is the frequency of a collision in the tevatron that can be calculate from the period of collision T that is 21µs for the high β run (with only one bunch colliding).

Hence, the estimated number of events or reactions with background in a collision

per second (RbgND), eq 10.4, is:

Prob R = backg = R R T bgND T LMs LMn

RbgND =(1KHz)(1KHz)(21µs)=21Hz (10.10)

assuming a rate signal of 1KHZ for each luminosity monitor counter.

The signal frequency without background is estimated from eq 10.3. The cross-section introduced in table 2.1:

30 −27 Rnd = Lσnd =(0.29x10 ) (39x10 ) = 11310Hz (10.11)

The expected signal is corrected by the acceptance of the luminosity monitors for the corresponding process obtained in chap.7

RND = Rnd AcceLMs AcceLMn = (11310Hz)(0.85)(0.85) = 8171Hz (10.12)

0.26% of background is estimated to be in the signal of a non-diﬀractive process. Chapter 11

Conclusions

√ A feasibility study of the pp¯ total cross-section at s =1.96 TeV using the FPD sub-detector at DZero Experiment was developed in this dissertation. The luminosity independent method was the technique used to obtain the total cross-section measurement. This method allowed us to avoid the uncertainty of the luminosity measurement (about 6% to 7%).

Inelastic and elastic events from the proton-antiproton collisions were studied separately. In both cases Monte-Carlo simulations were used in order to obtain the acceptance when the position of the Forward Proton Detector (FPD) changed.

For the inelastic events we run DØgstar (DØ Geant simulation of the total apparatus response) with the data generated by PYTHIA. All QCD processes: elastic, single diffractive, double diffractive and non-diffractive, were simulated. The Luminosity Monitors at DØ Detector are used to detected the inelastic events and the FPD to label the intact antiprotons and protons of the collisions. This allowed to classify the events and obtain their corresponding acceptance. The single diffractivep ¯ processes were studied using POMWIG as the generator, in order to obtain the FPD acceptance including the pomeron model of the Regge Theory.

The elastic events and the ﬁnal value of the total cross-section were studied using

102 CHAPTER 11. CONCLUSIONS 103

the expected distribution of transferred momentum in each FPD roman pot. An injection lattice was implemented in order to have a low luminosity and hence locate the FPD as close as possible to the beam line. We present the results obtained with an emittance of 10π and 15π beam having the FPD sub-detector located at diﬀerent positions, as well as the results for the parameters of the High-β-Store at the Tevatron (took in February 2006).

For this dissertation, we conclude that a change in 2 beam sizes (σ) in the vertical position of the FPD roman pots implies a change of 15% in their acceptance if they position are close to the beam line (10 to 12 σ) while only a change of 2% in acceptance is presented when the FPD changes from 16 to 18σ. When the FPD roman pot location is closer to the beam-line the acceptance is higher.

From the study of elastic and inelastic statistical errors separately, we conclude that the main source of statistical uncertainty is from the inelastic events. And when the FPD change the location to a position futher out of the beam line the correlation of the data is lost and the uncertainty increase.

Also, the systematic error due to the eﬀective length is greater than the uncertainty found from the systematic error due to the position of the detector measurement, in about 50%. It is explained by the use of the eﬀective lenght to obtain the common angular region of the detectors that involved also the measured position.

Adding in quadrature the statistical errors (∆esta) and systematics errors (∆sisP os from the position measurement and ∆sisLeff from the eﬀective measurement), the total uncertainty of pp¯ total cross-section is stablished as reported in table 11.1. The table is divided by the results from positions 10, 12 and 14σ with an emittance of 10π,wheresigma is the beam size. In this dissertation, an uncertainty 50% lesser than 2mb, which is the uncertainty reported by real experiments at the Tevatron, is obtained for these cases. CHAPTER 11. CONCLUSIONS 104

Det Pos σtot ∆esta ∆sisP os ∆sisLeff ∆σtot [mm] [mb] [mb] [mb] [mb] [mb]

P1U 3.01 73.0 1.05 0.0580 0.180 1.07 A1D 6.24 73.0 1.05 0.0698 0.182 1.07 P1U 3.61 72.9 1.06 0.0753 0.174 1.08 A1D 7.49 72.9 1.06 0.0631 0.174 1.08 P1U 4.21 72.8 1.14 0.1730 0.211 1.17 A1D 8.74 72.9 1.14 0.1490 0.124 1.16

Table 11.1: Summary of the Total Cross-Section for diﬀerent positions of the FPD The ﬁnal uncertainty is reported as well as the corresponding statistical and systematic uncertainty contributions.

Det Pos σtot ∆esta ∆sisP os ∆sisLeff ∆σtot [mm] [mb] [mb] [mb] [mb] [mb]

P1D 6.04 71.7 1.05 0.0727 0.0752 1.05 A1U 4.05 71.7 1.05 0.0527 0.1690 1.06

Table 11.2: Total Cross-Section Uncertainty for the FPD located at the High-β-Store positions The ﬁnal uncertainty is reported as well as the corresponding statistical and systematic uncertainty contributions.

The uncertainty reported in table 11.2 and the percentage of background estimated in this dissertation (0.26% for non-diﬀractive processes and 13% for single diﬀractive processes) announce a good possibility to have a total cross-section measurement for the proton-antiproton collisions at the Tevatron energy, using the data of the High- β-Store took on February 2006, with a lesser uncertainty than the reported for the experiments E710, CDF y E811. Bibliography

[1] N. Amos et al. E-710 Collaboration. Phys. Rev. Lett., 1992.

[2] F.Abe et al. CDF Collaboration. Phys. Rev. D, 1994.

[3] C. Avila et al. E-811 Collaboration. Phys. Lett. B, 1999.

[4] J.R. Cudell. Phys. Rev. Lett., 2002.

[5] F. Ferro TOTEM Collaboration.

[6] Elementary Particles and Their Interactions. 1998.

[7] Quantum mechanics. 1977.

[8] Collider Physics.

[9] Stilianos Isaak Kesisoglou. Search for Gauge Mediated Supersymmetry.PhD thesis, Brown University, 2005.

[10] Particle Accelerator Physics. 1998.

[11] http://www bd.fnal.gov/runII/index.html. Run ii handbook,tevatron. Technical report, Fermilab, 2006.

0 0 → 0 [12] Paul Wijnand Balm. Measurement of the Bd lifetime using Bd J/ΨKs decays at DØ. PhD thesis, Universiteit van Amsterdam, 2004.

[13] A. Brandt et al. Fpd detector at d0. Technical report, FERMILAB, 1997.

105 BIBLIOGRAPHY 106

[14] http://www.fnal.gov/pub/now/live events/explain det dzero.html. Explaining the d0 detector. Technical report.

[15] C. Avila´ et al. Revista Colombiana de F´ısica, 2004.

[16] http://www-d0.fnal.gov/ avila/daqfpd.htm. Fpd trigger. Technical report, Fer- milab.

[17] Chyi-Chang Miao and D Collaboration. The d0 run ii luminosity monitor. Nu- clear Physics B - Proceedings Supplements, 1999.

[18] Luminosity Monitor at D0 experiment http://www.hep.brown.edu/lm/detector.htm.

[19] Jairo Villamil. Mediciones de dispersion elastica con el detector fpd en el exper- imento d0. Universidad de los Andes, 2002.

[20] D0gstar. Standard pythia card ﬁles obtained from the mcpp montecarlo at fermilab machines. (http://www-d0.fnal.gov/computing/montecarlo/montecarlo.html).

[21] High-Energy Particle Diﬀraction. 2002.

[22] Review of particle physics. Phys. Lett. B, 2004.

[23] Jaime Alfredo Betancourt Minganquer. Medicion de la seccion eﬁcaz diferencial √ elastica pp¯ a s=1.96tev. Master’s thesis, Universidad de los Andes, 2004.

[24] ROOT is An object oriented framework for large scale data analysis. From the cern laboratory (http://root.cern.ch/).

[25] M. Martens. Fpd trigger. Technical report, Trigger Workshop.

[26] Tamsin Edwards. Diﬀractively produced Z bosons in the muon decay channel in pp¯ collisions at s = 1.96 TeV, and the measurement of the eﬃciency of the DØ Run II Luminosity Monitor. PhD thesis, University of Manchester, 2006. Appendix A

The FPD Elastic Dispersion Function

The measurement of the total cross-section presented in this dissertation is obtained using the ELASTIC DISPERSION SOFTWARE wrote by J. Villamil [19]. An introduction of this function is presented in this chapter. The detectors parameters and the cumulated function in this dissertation diﬀer from the original version.

A.1 Input parameters

The input of the ELASTIC DISPERSION function are divided in three files explained as follows: The cumulated function of the expected distribution of the transferred momentum in the file acumul.txt, the beam parameters in the file parn.txt and the detectors parameters in detectors.txt. The information of these files will be explained in the following paragraphs.

The acumul.txt is a two column file, the first column is a random number and its corresponding transferred momentum t is in the second column. The random numbers belong to [0, 1] and are arranged from the lesser to the greater. These form the cumulative function, that is calculated from the expected distribution, obtained in eq 5.20 and represented in figure 6.4, using the inverse method MonteCarlo technique. In the dissertation presented in this document the elastic momentum distribution are 2 calculated with π = atan(1.0)*4, (c) =0.38938572, α=1/137.039, ρ=0.15, σtot=72.0 and b=17.0.

The parn.txt file contains two rows, the first one for the antiproton beam information and the second for the proton beam information. Each row has five columns corresponding with the beam size in x-axis, the beam size in y-axis, the offsets of the collision point in x-axis, y-axis and z-axis, respectively. A Calibration of these parameters is necessary before the study. The calibration consist in obtain a Gaussian distribution with center in zero (0) from the subtractions of the coordinates on closed detectors. For example, for the pots P1U and P2U:

107 APPENDIX A. THE FPD ELASTIC DISPERSION FUNCTION 108

effLengthP 1U subtraction = coordinateP 2U − coordinateP 1U (A.1) effLengthP 2U where effLength is the effective length measure in each pot and coordinate is the value of x or y depending of the axis that be evaluated. These coordinates are the output of the ELASTIC DISPERSION SOFTWARE. The calibration begins with the expected beam size divergence σ according with the Tevatron parameters. Since we know the case with emittance of 20π and the values of normal run data, we can obtain the first values of the beam size divergence for the case of injection by:

emittance βinjection σ = σ20π (A.2) 20 βnormal

In the ﬁle detectors.txt the physical parameters of the detectors are included. involved in a beam injection lattice, we use the information from the “MAD” Version: 8.16/6 of the Run: 02/01/05 at 14.45.53. This ﬁle has 18 rows and 13 columns. The 18 rows correspond with the number of detectors (D2I, .., P2O) and the 13 columns correspond with:

• One column for the quadrant denoting: up=+1, down=-1, outer=+2, inner=- 2. The second column for the side: -1 and 1 for antiproton and proton side, respectively.

• One column for x detector resolution deltax. The following column is for the y detector resolution deltay. We ﬁx a value of zero in both cases.

• A column for the detector size in x-axis tamx in mm. Another column for the y-axis tamy. In both cases a value of 17.390 mm was setup.

• The eﬀective length measure in each axis are present in the two columns, at ﬁrst in x-axis then in y. The values working in this dissertation can be found in tables 4.2 and 4.3 1.

• The transport matrix elements: m01 xandm01y discussed in sec.3.7 are in the next two columns. Tables 4.2 and 4.3 also present the establish values for our study.

• The following two columns correspond with the beam width in each axis: sigx(mm) and sigy(mm).

• Finally the name of the corresponding pot is presented.

1The original version of the program run with the eﬀective length in mm. APPENDIX A. THE FPD ELASTIC DISPERSION FUNCTION 109 A.2 Obtaining the ﬁnal position in the detectors

The input parameters discussed in the above section are constant in a single run of the program. A run consist in a certain number of elastic events to be studied. Not all the events are in the desired trigger that is why the run time of the program is large. For example 1300000 events produce only 30000 entries for analysis. The procedure of a single event process is explain as follows.

Using the inverse method MonteCarlo technique for the cumulated function, an random number a.n from an uniform distribution is generated to obtain a transferred momentum t. Its corresponding azimuthal angle φ is obtained from a second random number generated between 0 and 2π.

From t one gets the polar angle θ measured from the elastic collision point, as: √ θ = t/pbeam (A.3) with pbeam = 980 that has the correct dimensional units. This approximation eq A.3 is valid for the energy involved in the proton-antiproton collision at the Tevatron, that is discussed in chapter 5 and corresponds to the eq.5.13.

For a Cartesian plane in each detector, the polar angles are:

θx = θ cos φ

θy = θ sin φ (A.4)

adding the beam divergence

θu+=(a.n. σdivergence)(A.5)

where u stands for x or y, σdivergence is the beam size from the calibration and a.n. is an uniform random number between 0 and 12 (see details of the generation of this number in the J. Villamil Thesis [19]). It is also possible to add also: the detector resolution, and the beam oﬀset from the collision point in x and y. For our study we ignore all these.

With the polar angle in each detector, the ﬁnal coordinates (x,y) can be establish as:

x = Leff x θx

y = Leff y θy where Leff are the corresponding eﬀective length measured for each detector and obtained from the ﬁle detectors.txt.

If the position is inside the detector size, a hit is considered in that detector. A line in the ﬁle detected.txt is printed with the 18 positions obtained if there are hits in APPENDIX A. THE FPD ELASTIC DISPERSION FUNCTION 110

both sides of the collision point. The 18 positions are the positions in each detector arranged in order of the ﬁle detectors.txt. A position of (0,0) is consider as a not hit in the detector.

A.3 The output distribution

There is a factor to take into account when a simulation runs with real data: the convolution between the distribution of beam width and the distribution of the dispersion. Since the beam has a Gaussian distribution width (it is not a thin line), the output events are dispersed with a higher t of the one than they really have. The resulting histogram, in logarithmic scale, has a lesser slope than the expected one as show in tables A.1 and A.2. The histogram names correspond which the denotation introduced in sec.6.2: • ideal the histogram obtained from the run with a beam of size equal to zero.

• outcome the histogram obtained from the run with a beam size using an emittance =10π or 15π

• acce the histogram corrected by geometrical acceptance.

• pos the ﬁnal corrected histogram for each position.

2 tmin

Table A.1: P1U ﬁts with =10π at 10σ

For example, the outcome histogram in table A.1 has a difference of one unit in the slope, with respect to the final corrected histogram (pos ). The χ2/ndf present a steep change that finished with a value close to 1 that is the expected one. The correction of the convolution phenomena is explained in sec 6.2.

The convolution eﬀect and the χ2/ndf steep change are also present with the change of the location of the FPD roman pots, as shown in table A.3, but the acceptance correction plays a more important roll because there is a decrease in the number of entries. As far away of the beam line the corrected histogram pos diﬀers in 2 and 3 units of the outcome. APPENDIX A. THE FPD ELASTIC DISPERSION FUNCTION 111

2 tmin

Table A.2: Roman Pot ﬁts with =10π at 10σ

2 tmin

Table A.3: P1U and A1D ﬁts with =10π changing positions Appendix B

The FPD Propagator Function

This is a software developed by J. Molina1. It consists in two main functions that propagate a particle from the interaction point of the proton-antiproton collision at the Tevatron to the roman pots that constitute the FPD subdetector of DZero experiment. These functions are Propagate p and Propagate pbar according to the Tevatron lattice side to be evaluate.

The program uses the transportation matrix step by step on the Tevatron Lattice. Table B.1 presents the Tevatron lattice for thep ¯ side.

B.1 Input Parameters

The PROPAGATOR FUNCTION receives the following physical information of each particle (p orp ¯):

1. charge=q

2. fractional momentum loss=xsi

3. polar angle =θ

4. azimuthal angle = φ

5. vertex position= vax,vay,vaz Only thep ¯ side is used in this dissertation. The corresponding input data is obtained from POMWIG, a standard higher energy MonteCarlo generator, discussed in the following chapter. Figure B.1 presented the distributions of two enters parameters of the propagator function.

The coordinate system of POMWIG (and PYTHIA) diﬀers from the using in the PROPAGATOR FUNCTION: although in thep ¯ side the coordinate z is negative, the correct

1Graduate student at Fermilab working in the FPD group

112 APPENDIX B. THE FPD PROPAGATOR FUNCTION 113

Polar angle distribution θ_plot Azimutal angle distribution φ_plot Entries 1956 Entries 1956 ]

θ Mean 0.394 Mean 3.192 φ d dN d RMS 0.2101 dN RMS 1.844 Log[

2 10 102

0 0.5 1 1.5 2 01234567 θ [mrad] φ [rad]

Figure B.1: Enter parameters for the Propagator Function

enter parameters are with pz positive and θ measure from the z-negative axis.

Additionally we must change the positions in the transverse plane of each roman pot according to the simulation of elastic events. This is doing in “param.dat”.

B.2 Output Adjustment

We change the original version to output the acceptance (with its uncertainty) of each spectrometer separated and joined as reported in chapter 7. The PROPAGATOR FUNCTION gives 1 in each station if the particle hit any detector, otherwise 0. For each station there is a ﬂag that gives the information if there were a hit, also it is possible to have the position where the particle cross each detector. APPENDIX B. THE FPD PROPAGATOR FUNCTION 114

Process Distance in -Z [m] Drift 7.62 Focusing 3.35 Drift 0.88 Defocusing 5.89 Drift 0.88 Focusing 3.35 Drift 1.36 Pots: A1U y A1D Total 23.33 Drift 0.15 Pots: A1I y A1O Total 23.46 Drift 0.53 Drift sep 2.57 Drift 0.19 Drift sep 2.57 Drift 0.19 Pots: A2I y A2O Total 29.51 Drift 0.15 Pots: A2U y A2D Total 29.66 Drift 2.87 Dipole 6.12 Drift 0.28 Dipole 2.87 Drift 0.28 Dipole 6.12 Drift 1.89 Pot: D1 Total 50.12 Drift 2.25 Pot: D2 Total 52.36

Table B.1: Tevatron latticep ¯ side Appendix C

Computation Tools

A brief introduction to how to use the DØ Geant Simulation of the Total Apparatus Response (DØgstar) and the standard software in high energy physics discussed in this dissertation, POMWIG, PYTHIA and GEANT4, is presented in this chapter1. A UNIX environment was used in all cases. Refer to details in the physics and reference manuals of these software reported in each section. A CD is available with this document, where the code of main programs and results are presented.

C.1 Notes of using DØgstar

The simulation of the DØ Detector (discussed in sec 4.1), called the DØ Geant Simulation of the Total Apparatus Response (DØgstar), includes all materials and the magnetic field map of the real detector and creates a response up to the level of the data obtained from the real Data Acquisition System. A brief introduction of what is Geant is presented at the end of this chapter. Figure C.1 shows the data flow of the DØgstar. The phases of the simulation are divided in seven main packages, that can run independently but in an order that the output file of first one is the input of the second and so on:

1. The physics event generation d0gen package works with the standard high energy format called HEPEVT. It contains information of each particle status, particle identiﬁers, mother-daughter relationships, particle four-momentum and vertices.

2. d0geo creates the rz-ﬁels of the DØ Detector geometry for the geant simulation. An overview of the geometry for the Luminosity Monitors Counters, used in this dissertation, is presented in ﬁgure C.2.

3. d0kin initialized the kinematics variables for the geant simulation.

1A Leading Order approximation is used for the solution of the diﬀerential equations in these software.

115 APPENDIX C. COMPUTATION TOOLS 116

4. The GEANT tracking and hits generation are done with the d0sim package. Hit information is stored when the particle goes through a detector sensitive volume and this volume is deﬁned as a detector element. Secondary particles (daugh- ters) are stored if the interaction takes place in the tracker cavity (74 cm radius and 139cm long) and the mother has pt >pTcut (with pTcut=1.0GeV) or if the interaction takes place for muon with pt > 5 pTcut via decay, Bremsstrahlung, pair production or hadronic interaction. 5. The raw data simulation package is called d0raw. It performs event pile-up, noise and hit digitization. 6. The event reconstruction d0rec package works with the following order: reconstruction in calorimeters, reconstruction in muon chambers, reconstruction in the Tracker and ﬁnally the global reconstruction.

7. The event analysis package is d0ana. An explanation of the main steps is enumerated bellow.

Figure C.1: The data ﬂow for the D0gstar

The standard programs and codes of the DØ Geant Simulation of the Total Appa- ratus Response used in this dissertation, were obtained from works of L. Mendoza (PhD student at Universidad de los Andes). Fermilab Computers were used to run the programs and to analyse their corresponding results, from a remote connection. The main steps to obtain the results reported in this dissertation are:

1. To establish which generator of particle collisions will be used, in our case PYTHIA or POMWIG, and in what processes are one interested (name variable and number). With the corresponding CARD FILE, one run the d0mcpp- p1709 montecarlo program and obtains the data of the generated processes, in APPENDIX C. COMPUTATION TOOLS 117

a high energy standard format. This creates the ﬁle events.dat2,whichisone of the enter parameters to the total simulation.

2. With the corresponding link to the events.dat ﬁle and the desired conditions i.e. number of events to be produced, the geant simulation of the DØ Detector is able to run. We used the so called mcrunjob and because of the speciﬁc information that this simulation has, the results demand much time. A thousand of events take about three days to bring information. This package generates a folder (dest/) with the output data.

3. A rootupla (ﬁle .root) is produced from the output folders of the geant simulation. The used software is the Treemaker p18.05.00 and take approx 20 minutes to analysis 10000 events.

4. The analysis of the data saved in a rootupla is done with the Common Analysis Format (CAF), which is a software tool based on ROOT3 and allows to obtain the histograms and data from the simulation. For this dissertation we used the version p1807 and we made a separated analysis for the data from the generation and after reconstruction (testmc and reco). (The rootupla name to be analysis is in the .conﬁg ﬁle)

Each item of the above list demands a different program, hence the first step in each one is the compilation of the so called environment variables (mostly include in a file .ENV) The compilation is done by source name.ENV in the command line. Each software package has the file Readme, where a quick guide is founded, and almost all has a file run.sh for the execution of the program. Studies with real data are developed with the same software tools in order to be sure of the comparison.

The manuals for the DØGEANT Simulation of the Total Apparatus Response can be found in: http://www-d0.fnal.gov/d0dist/dist/packages/d0gstar/devel/docs/ html/d0gstar.html. The standard software discussed in this section can be found in: http://www-d0.fnal.gov/computing/MonteCarlo/MonteCarlo.html

C.1.1 CARD FILES The control commands of the generations of events in the DØ Geant Simulation of the Total Apparatus Response are organized in ﬁles called CARD FILES. This structure allows a non-specialist user to obtain the desired simulation without running additional software.

2The number of events can setup in the ﬁle d0 mcpp gen/rcp/MCNewEvent.rcp and the printed events in the .cmd ﬁle. 3ROOT is a An object oriented framework for large scale data analysis. This software is implemented by the CERN and their basic structure is C++ [24]. The elastic study, in this dissertation, were developed using Root version 5.06. APPENDIX C. COMPUTATION TOOLS 118

Luminosity_detector Components_and_materials_in_the_D0GSTAR

L0BP

L0OR

L0 L0SC L0IR L0IP

L0FP

L0OM

L0IM Magenta_Scintillator L0OP Black_Aluminium

Figure C.2: The Luminosity Monitor geometry at DØgstar.

The card ﬁles are developed for a speciﬁc group of physical processes. The d0gen package includes cards for the study of Higgs, quark top, quark tau, bosons wz and more.

In particular for the QCD process, there are two cards: one using HERWIG as the generator of the particle collision (discussed in the following section), and the other using PYTHIA. Both generators are written in FORTRAN.

C.2 Notes of using POMWIG

POMWIG is a HERWIG simulation specially implemented for diﬀractive interactions that include the Regge Theory. A HERWIG is a Monte Carlo package for simulating Hadron Emission Reactions With Interfering Gluons. REfer to http://hepwww.rl.ac.uk/theory/seymour/herwig/ .

The card-ﬁle using by the D0gstart package allows to work all the processes gener- APPENDIX C. COMPUTATION TOOLS 119 ated by HERWIG. In particular we were interested in process 1500 where the pomeron simulation takes place.

Three possible structures of the Pomeron are able to simulate: the H1 pomeron stru- cure function for beam particle 1, the reggeon exchange structure and the one stablish by the user.

To obtain the results of this dissertation, the setup for the single diﬀractivep ¯ processes was established with the variable DIFF=1. The pomeron structure simulated was the H1 fuction, and the energy fraction lost for the proton because of the pomeron, was in the interval [0.0001,0.1]GeV.

Information of this software is in the website http://www.pomwig.com/, where the source ﬁles are also found.

C.3 Notes of using PYTHIA

PYTHIA is a standard physical particle generation software with emphasis on multiparticle production in collisions between elementary particles. It is frequently used for event generation in high energy physics. This computation tool is called An event generator for a large number of physics processes and is written in FORTRAN (The authors planning to release a version in C++).

A stand-alone installation of PYTHIA, in a computer with a Fortran compiler, is easy to achieve. In this dissertation the version 6.3 were used. The main steps of the installation are:

1. The source code is download from the oﬃcial webpage of Pythia: http://www.thep.lu.se/∼torbjorn/Pythia.html. In this case the 6.323 version were used.

2. A library phythia6323.o must be create from the source code. A procedure is typing in the command line terminal4 g77 -c pythia6323.f.

3. A ﬁle main.f must be written (in a Fortran structure) calling appropriately the routines of PYTHIA. For an initial try it is recommend downloading the examples. The main routines consist in the initialization of the system (PYINIT), the execution of the events (calling PYEVNT for each event) and the ﬁnal print (PYLIST).

4. The compilation of the program main.f includes in all cases the library created from the PYTHIA source ﬁle. The usual command for compilation is g77 main.f pythia6323.o.

4It can be use f77 instead of g77 APPENDIX C. COMPUTATION TOOLS 120

5. To run the simulation, execute the a.out file created from the compilation, as usual, in the command line terminal type ./a.out.SincePYTHIAworks with the high energy format called HEPEVT an interface with others standard software is easy to performs. Different files output can be obtain according the main.f.

The manuals and physics references are also founded in the website http://www.thep.lu.se/∼torbjorn/Pythia.html, where the basic routines of a simple main are explained as well as the meaning and values of the variables. A proton antiproton collision with a center-of-mass energy of 1.96TeV is written in the main program as CALL PYINIT(’CMS’,’p’,’pbar’,1960D0) corresponding to the general instruction CALL PYINIT(frame,beam,target,win).

All QCD processes where simulated in this dissertation, the corresponding commands of the subprocesses involved are listed bellow:

1. - In order to be able of execute only one or certain types of processes, the variable MSEL is setup to 0. MSUB setup the number of the corresponding physical process. The QCD processes numbers are in the following list. When the variable is setup to 1 means that the current process is on (otherwise, 0 means that the process is oﬀ.)

(a) MSUB(92)=1 (single diffractivep ¯) (b) MSUB(93)=1 (single diffractive p) (c) MSUB(94)=1 (double diffractive) (d) MSUB(95)=1 y MSUB(96)=1 (low-pt scattering, semihard) (e) MSUB(11)=1, MSUB(12)=1, MSUB(13)=1, MSUB(28)=1, MSUB(53)=1, MSUB(68)=1 (Hard Process)

2. -A default and simpliﬁed command that includes all QCD process in the simulation is MSEL=2. Figure C.3 presents a distribution of the simulated events acoording with the numbers listed above.

C.4 Notes of using Geant4

Geant4 is A toolkit for the simulation of the passage of particles through matter.This powerful tool allows simulating detector responses and its ﬂow data structure follows the real physical experiments. It is also designed to take into account the requirements of space and cosmic ray applications, nuclear, heavy ion and radiation computations, and medical applications. The language of programming is C++, hence a complete reference manual of the classes involved are in APPENDIX C. COMPUTATION TOOLS 121

QCD Process distribution Subprocess_plot Entries 10001 Mean 66.22 dN 2500dn RMS 30.69

2000

1500

1000

500

0 0 102030405060708090100 n=number of the subprocess

Figure C.3: Pythia Processes for MSEL=2 with 10000 events http://geant4.cern.ch/bin/SRM/G4GenDoc81.csh?ﬂag=1.

In the website http://geant4.web.cern.ch/geant4/support/userdocuments.shtml an appropriated orientation of the installation and application of GEANT4 can be found. Manuals and Frequently Asked Questions (FAQ) from users with answers to them are also include in the website.

The installation of this toolkit is complex (respect to the installation of PYTHIA) and involved the installation of the CERN standard physics libraries. Besides, the default suggested installation of geant4 version 7.0.p01 does not work. The compilation and execution of the program is doing with a GNUmake ﬁle.

The more simply program must include the following routines in a main() ﬁle that used the principal class called G4RunManager:

1. The detector geometry deﬁnition, usual presented in src/DetectorConstruction.cc. This includes the dimension, form and materials of the detectors. Classes of basic geometrical ﬁgures are available. The materials are created from the basic physical properties.

2. The primary event, usually presented in: src/PrimaryGeneratorAction.cc. In this ﬁle is explained to the software, how the primary particle(s) in an event should be produced. There are two options to obtain the particles information of an event by another software generator or made a particle gun directly in Geant4. Interface HEPEVT, with the data obtain from PYTHIA, were used in order to simply the procedure of read a ﬁle and create a gun for each particle output by Pythia.

3. The physical processes list could be created, usually in: src/PhysicsList.cc. For the simulation results of this dissertation the QGSP Educated guess physics list were used. APPENDIX C. COMPUTATION TOOLS 122

Additionally, to visualized and event, a graphic interface must be installed. For this dissertation, the program used is DAWN (also OpenGL are standard graphic inter- faces) that produced a postscript file of the desire final state. The usual name of the include file for the visualization is the VisManager.cc.

The Geant4 package includes nice and different levels examples that illustrated the different configurations that this computation tool includes.