analysis of the inclusive gaugino pair channel at the cms ...thesis/data/iekp-ka2008...ppp...

ppppppppppppp Universität Karlsruhe (TH)IEKP-KA/2008-3

Analysis of the InclusiveGaugino Pair Channel at

the CMS Detectorat the LHC

Sabine Reißer

Diploma Thesis

Fakultät für Physik,Universität Karlsruhe

Referent: Prof. Dr. W. de BoerInstitut für Experimentelle Kernphysik

Korreferent: Prof. Dr. G. QuastInstitut für Experimentelle Kernphysik

December 11th, 2007

Zusammenfassung

Auf der Suche nach Theorien, die die Physik vereinfachen, stellten BrunoZumino und Julius Wess im Jahre 1973 eine neue Theorie vor, die Su-persymmetrie. Diese Theorie hat die Nebenwirkung, dass sich die An-zahl der Elementarteilchen verdoppelt und jedes Teilchen des Standard-modells einen supersymmetrischen Partner erhält. Der Theorie nach sinddiese Teilchen instabil bis auf eines und sehr schwer, so dass es nichtüberraschend ist, dass sie an bisherigen Teilchenbeschleunigern nicht ent-deckt wurden. Mit dem neuen Teilchenbeschleuniger LHC am CERN inGenf in der Schweiz, soll dies erstmals möglich sein, da er eine Schwer-punktsenergie von 14 TeV erreicht. Wenn die Existenz supersymmetrischerTeilchen am CERN nachgewiesen würde, wäre sie ein idealer Kandidat fürdie Dunkle Materie, die 85% der Masse des Universums ausmacht undder bisher noch kein bekanntes Teilchen zugeordnet wurde. Das verein-fachte supersymmetrische Modell mSugra hat fünf freie Parameter, derenWerte durch Messungen des Mikrowellenhintergrundes und vergangeneBeschleunigerexperimente eingeschränkt wurden. Durch ein in den 90ernim Weltraum stationiertes Experiment, EGRET, dessen Daten kürzlich neuals Dunkle-Materie-Annihilationssignal interpretiert wurden, wurde derParameterraum weiter eingeschränkt. Der CMS Testpunkt LM9 mit denParametern m0 = 1450 Gev, m1/2 = 175 Gev, tanβ = 50, A0 = 0 undsign(µ) = +, stimmt am Besten mit diesen Ergebnissen überein.

Diese Arbeit befasst sich mit einem spezifischen supersymmetrischenKanal, wie er am CMS-Detektor am LHC nachgewiesen werden könnte,dem Gaugino-Paar-Kanal. Da die Wirkungsquerschnitte der supersym-metrischen Prozesse sehr klein im Vergleich zum Standardmodell-Hinter-grund sind, ist es das Ziel der Analyse, Eigenschaften dieses Kanals zufinden, die sich dazu eignen, das Signal vom Untergrund zu unterschei-den. Die Analyse wurde auf den CMS-Testpunkt LM9 optimiert, um die

I

II

Ergebnisse dann auf den ganzen Parameterraum anzuwenden.Der Gaugino-Paar-Kanal beinhaltet alle Prozesse der Art qiq̄j −→ χlkχnm

und hat am Punkt LM9 einen Wirkungsquerschnitt von ≈ 10 pb, währenddie Summe der betrachteten Hintergrundprozesse - Produktion von tt̄,Z+jets und W+jets - ≈ 5.2 · 105 pb beträgt. Um einen Überblick überdie wichtigsten Variablen zu bekommen, wurde ein neuronales Netz mitDatensätzen von Hintergrund und Signal trainiert. Das neuronale Netzwertete dabei die Werte folgender kinematischer Variablen aus: eta, phi,Impuls in x-, y- und transversaler Richtung, Energie und Anzahl von My-onen, Elektronen und Jets, fehlende Transversalenergie (MET) und Anzahlder Photonen. Das Netz ordnete den Variablen fehlende Transversalen-ergie, Anzahl der Jets, Tranversalimpuls des Leptons mit dem höchstenImpuls und Anzahl der Leptonen (Myonen + Elektronen), in dieser Rei-henfolge die höchste Relevanz zu. Anhand dieser Variablen und einerfünften, der effektiven Masse (Summe aus fehlender Transversalenergieund Summe der Transversalimpulse aller Jets; Meff) wurde eine Vorselek-tion getroffen, um das Verhältnis von Signal zu Hintergrund, repräsentiertdurch die Grösse σ = Signal/

√Hintergrund, zu maximieren. Anhand der

Schnitte Meff ≥ 230GeV und MET ≥ 45GeV konnte eine Signifikanz vonσ = 4.7 erzielt werden.

Mit den übriggebliebenen Ereignissen wurde erneut ein neuronalesNetz trainiert, um die Signifikanz noch zu erhöhen. Sie konnte jedochnur noch leicht erhöht werden, auf σ = 5.1.

Wenn man die Vorselektionsschnitte Meff ≥ 230GeV und MET ≥45GeV auf die ganze mSugra-Ebene anwendet, erhält man Bild 1. Dortist die Signifikanz für jeden Punkt aufgetragen. Die Signifikanz erreichtWerte über 5 im unteren m1/2-Bereich (m1/2 ≤ 300GeV) und in der soge-nannten Focus-Point-Region (m0 > 3000GeV, m1/2 > 400GeV, in der Näheder elektroschwachen Symmetriebrechungsgrenze) an Punkten, an denender Unterschied zur Brechungsgrenze kleiner als ∆m1/2 < 50GeV ist.

III

m_00 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

m_1

/2

0

200

400

600

800

1000

1200

1

10

210

Significance (30/fb)

m_03000 3200 3400 3600 3800 4000 4200 4400 4600 4800 5000

m_1

/2

400

500

600

700

800

900

1000

1100

1200

-210

-110

1

Significance (30/fb), Focus point region

Figure 1: Die Signifikanz σ. mSugra Ebene, tanβ = 50. Im unteren Bildist nur ein Auschnitt des oberen zu sehen, nämlich die sogenannte FocusPoint Region. Weitere Erläuterungen siehe Text.

Contents

Introduction 3

1 The LHC and the CMS Experiment 51.1 The Large Hadron Collider (LHC) . . . . . . . . . . . . . . . 51.2 The Compact Muon Solenoid (CMS) . . . . . . . . . . . . . . 6

1.2.1 The Silicon Tracker . . . . . . . . . . . . . . . . . . . . 71.2.2 The Electromagnetic Calorimeter (ECAL) . . . . . . . 81.2.3 The Hadronic Calorimeter (HCAL) . . . . . . . . . . . 91.2.4 The Muon System . . . . . . . . . . . . . . . . . . . . 9

2 Theoretical Framework 112.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . 112.2 Grand Unification Theory (GUT) . . . . . . . . . . . . . . . . 172.3 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.1 The Particles of the MSSM . . . . . . . . . . . . . . . . 192.3.2 SUSY Masses . . . . . . . . . . . . . . . . . . . . . . . 22

3 Dark Matter 253.1 Why Dark Matter? . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Dark Matter Candidates . . . . . . . . . . . . . . . . . . . . . 27

3.2.1 Baryonic Matter . . . . . . . . . . . . . . . . . . . . . . 273.2.2 Hot Dark Matter . . . . . . . . . . . . . . . . . . . . . 283.2.3 Cold Dark Matter . . . . . . . . . . . . . . . . . . . . . 29

3.3 The EGRET Data . . . . . . . . . . . . . . . . . . . . . . . . . 293.4 Dark Matter = χ0 . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4.1 The Relic Density . . . . . . . . . . . . . . . . . . . . . 323.4.2 Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.4.3 mSugra Parameter Space . . . . . . . . . . . . . . . . 33

1

2 CONTENTS

4 Software 374.1 CMKIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Pythia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.3 ISASUGRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.4 CMSSW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.5 Neurobayes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.6 ROOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.7 PROSPINO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5 Analysis 415.1 mSugra plane . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.2 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.3 The L1 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.4 The LM9 point . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.5 Neural Net, Part One . . . . . . . . . . . . . . . . . . . . . . . 495.6 Neural Net, Part Two . . . . . . . . . . . . . . . . . . . . . . . 545.7 mSugra plane, after precut . . . . . . . . . . . . . . . . . . . . 59

Conclusion 63

A 65

Introduction

Searching for more simplicity in physics, Julius Wess and Bruno Zuminoinvented in 1973 a new physical theory, Supersymmetry. This theory im-plied an extension of the Standard Model with which the unification of thegauge coupling constants became possible. A side product of this theoryis the existence of supersymmetric particles, which are the partners of theStandard Model particles. These particles are supposedly much heavierthan Standard model particles and are all unstable except the lightest one.If this is the case, it is not surprising that these particles have not been de-tected yet, since their masses are too high to be produced by present par-ticle accelerators. With the LHC currently being built at CERN, Geneva,this might be possible. The LHC, a ring accelerator with a circumferenceof 27 km, 100 m underground, accelerates protons to a center of mass en-ergy of 14 TeV. Since energy can be transformed into mass and vice versa,very heavy particles can be produced, with masses in the range of the su-persymmetric particles. While the LHC is still under construction, collab-orations of international physicists simulate proton-proton collisions withhigh statistics to get a realistic overview of the data that might occur. Withdetector simulations, they try to predict the future data as precisely as pos-sible. To prove wether SUSY occurs or not, the possible SUSY productionchannels have to be examined against the background. The goal is to finda channel that stays almost unchanged when applying cuts to the datathat suppress the background, i.e. the Standard Model processes almostentirely.

If Supersymmetry exists, it might also play a role for the yet unresolvedproblem of the origin of dark matter. The dark matter, which is around85% of the matter in the universe, doesn’t interact electromagnetically andis thus invisible. Its existence has only been proven by the large gravita-tional effect it has on the visible matter in the galaxies. The lightest super-

3

4 CONTENTS

symmetric particle, which is stable, might be the so-called WIMP - weaklyinteracting massive particle -, the dark matter particle.

This thesis deals with a certain supersymmetric production channel atthe LHC, the gaugino pair channel. Chapter 1 describes the LHC and theCMS experiment with its different components. The theoretical frame-work, i.e. the Standard Model and its supersymmetric extension, is de-scribed in chapter 2. Chapter 3 contains different approaches to explainthe dark matter in the universe and establishes a connection to the lightestsupersymmetric particle. Chapter 4 gives an overview of the programsthat were used in the analysis. Chapter 5, finally, contains the analysis,leading to the conclusion given in the last chapter.

Chapter 1

The LHC and the CMSExperiment

1.1 The Large Hadron Collider (LHC)

Figure 1.1: LHC

5

6 CHAPTER 1. THE LHC AND THE CMS EXPERIMENT

The Large Hadron Collider, in short LHC is a particle accelerator atCERN, the European Organization for Nuclear Research located nearbyGeneva in Switzerland. The LHC is a ring accelerator with a circumferenceof 27 km, 100 m under the earths suface. Here proton-proton-collisionswith a center of mass energy of 14 TeV will be realized, 7 TeV for eachbeam. A heavy ion mode for lead ions and a center of mass energy of 1148GeV is also intended. Four experiments are located at the ring: two smallones, ALICE and LHCb and the two general purpose experiments ATLASand CMS, see fig. 1.1. While at the moment still under construction, thecompletion of LHC is scheduled for 2008. Two different periods, a lowand a high luminosity period are planned. The luminosity represents thenumber of transits per area and time. In the first years of LHC there willbe a luminosity of L = 2 · 1033 1

cm2s, this will be increased to a luminosity of

L = 1034 1cm2s

.

The main purpose of the LHC is the validation of the current standardmodel by finding the higgs boson and remeasuring the top and bottomquark masses. The LHC center of mass energy will be bigger than atany other particle accelerator. A big group of physicist also believes theLHC might give some answers about physical theories beyond the stan-dard model such as supersymmetry.

1.2 The Compact Muon Solenoid (CMS)

The Compact Muon Solenoid (CMS) is a cylindrical detector with a lengthof 21 meters and a diameter of 15 meters and weighs 12 500 tons. A pic-ture of the detector is given in fig. 1.2. The detector deserves its name forits compactness - it has just an eighth of the ATLAS’ volume and twice itsmass -, its optimization for tracking muons and its solenoid which is ableto generate a powerful magnetic field of 4 Tesla. In the center of the detec-tor, protons which have an energy of each 7 TeV are brought to collision.”Bunches” of about 100 billion protons are focussed by the LHC magnetsto cross every 25 ns in the detector center. Concentrically arranged aroundthe beam axis are the trackers, calorimeters and the solenoid (see fig. 1.3).

1.2. THE COMPACT MUON SOLENOID (CMS) 7

Figure 1.2: CMS detector

1.2.1 The Silicon TrackerThe purpose of a tracker is to reconstruct particle tracks and to measuretheir momentum with a high energy resolution such as to define their ver-tex of origin. The CMS tracker consists of two parts, a silicon pixel detectorand a silicon microstrip detector. The cylindrical tracker has a length of 5.8meters and a diameter of 2.6 meters.

The pixel detector consists of three barrel layers arranged concentricallyaround the beam axis and two layers in the endcap disks at front and back-side. The size of one pixel is almost square 100 · 150µm2. The pixel areareaches up to the region of pseudorapidity of |η| = 2.4. The pseudorapid-ity η represents the angle θ between the particle track and the beam axis.It is calulated by the following equation

η = −ln[tan

(θ

2

)]

If |η| = 2.4 the angle θ is 10◦ or 170◦.The pixels allow a track reconstruction resolution of 15µm. By extrap-

olation of the tracks the origin vertex of the particles can be defined.


Figure 1.3: CMS slice

The microstrip detector itself can be divided again into two parts, thetracker inner barrel (TIB) with four and the tracker outer barrel (TOB) withsix layers, which allow a two-dimensional track reconstruction.

The total area of the tracker is 1m2 and 66 million pixels for the pixeldetector and 200m2 of 9.6 million silicon strips for the microstrip detector.

1.2.2 The Electromagnetic Calorimeter (ECAL)The electromagnetic calorimeter is the next concentric layer around thesilicon tracker with the task to measure the energy of electrons, photonsand, in collaboration with the hadronic calorimeter, of jets. It is build ofabout 76 000 PbWO4 crystals. Charged particles cause light showers inthe scintillating crystals which are measured by silicon photodetectors todetermine the particle energy. 80% of the light is emitted during 25 ns,the LHC bunch crossing time. The crystals in the central region of thecalorimeter (η < 1.48) have a front face cross section of 22 · 22mm2 anda length of 230 mm. They are positioned at a distance of 1.29 m from thedetector center. The crystals in the endcaps, 3.17 m from the collision pointhave a front face cross area of 24.7 · 24.7mm2 and a length of 220 mm. Thetranverse granularity is ∆η × ∆Φ = 0.0175 × 0.0175. The ECAL covers aregion up to |η| = 3 (5.7 < θ < 174.3).

1.2. THE COMPACT MUON SOLENOID (CMS) 9

Figure 1.4: Muon System

1.2.3 The Hadronic Calorimeter (HCAL)The Hadronic Calorimeter surrounds the ECAL and measures in connec-tion with the latter the energy of hadronic particle jets and calculates themissing transverse energy. The HCAL also consists of different parts suchas the central hadron barrel part (HB, < |η| < 1.4, 30◦ < θ < 150◦) andtwo endcaps (HE, 1.4 < |η| < 3.0) placed within the solenoid, whiletwo forward calorimeters (HF) extend the calorimeter reach up to |η| = 5(0.8 < θ < 179.2). An additional layer of scintillators, the hadron outerdetector HO is arranged outside the coil with a reach of |η < 1.26 to im-prove the missing energy resolution. The granularity of HB and HO is∆η×∆Φ = 0.087×0.087 and that of the endcaps ∆η×∆Φ = 0.0175×0.0175.

1.2.4 The Muon SystemThe conceptual goal of the CMS detector is to identify and reconstructmuons very precisely . Its muon system, as can be seen in figure 1.4, con-sists of different parts. Drift tubes in the central part (|η| < 1.2), cathodestrip chambers at the endcaps (0.9 < |η| < 2.4) and resistive plate cham-bers (RPC) in the barrel and the endcap identify the muons and measuretheir charge and momentum and quickly provide the Level-1 trigger withinformation wether to select or skip an event. In the beginning the RPCswill reach up to |η| < 1.6 and will be extended to |η| < 2.1 later. With themuon system a reconstruction efficiency of 90% can be reached for muons


with a transverse momentum of > 100Gev.

Chapter 2

Theoretical Framework

2.1 The Standard ModelThe current physical model contains a set of particles and forces.

• The electromagnetic force with its interaction particle, the photon γ,affects the three generations of charged leptons e− µ− τ− and theirantipartners e+ µ+ and τ+, its reach is infinite.

• The weak force with the lowest reach of 10−18m interacts throughexchange of heavy bosons W± and Z0 and is responsible for certainradioactive decays

• The strong force holds the three generations of quarks (u, c, t withd, s, b, each one with an antipartner) in the confinement of a hadrontogether by exchange particles called gluons (→’glue’). It has a reachof 2.5 · 10−15m.

• Gravitation with the hypothetic exchange particle, the graviton, isdescribed by Einsteins General Relativity and reaches infinitely.

The so called Standard Model now is a relativistic quantum field theorythat is able to describe all of these forces supported by the algebraic rulesof Lie groups excepting gravitation. An overview of the particles of theStandard Model is given in table 2.1. Here Q stands for the electric charge

11

12 CHAPTER 2. THEORETICAL FRAMEWORK

in units of e, I3 for the z-component of the isospin and Y for the hyper-charge after the Gell-Mann-Nishijama relation:

Q = I3 +1

2Y (2.1)

Fermions Spin = 1/21. Gen. 2. Gen. 3. Gen. Q Y I3

Quarks(

ud

)

L

(cs

)

L

(tb

)

L

2/3−1/3 1/3

1/2−1/2

uR cR tR 2/3 4/3 0dR sR bR −1/3 −2/3 0

Leptons(

νee

)

L

(νµµ

)

L

(νττ

)

L

0−1 −1

1/2−1/2

eR µR τR −1 −2 0

Bosons Spin = 1Interaction Boson Q Y I3

electromagnetic γ 0 0 0weak Z0 0 0 0weak W± ±1 0 ±1strong g1 · · · g8 0 0 0

Table 2.1: The particles of the standard model. From [1].

The Lagrangian DensityIn classical mechanics a the equations of motion of a given dynamical sys-tem can be obtained through the Euler-Lagrange equation

d

dt

(∂L

∂q̇i

)− ∂L

∂q̇i= 0 (2.2)

2.1. THE STANDARD MODEL 13

where qi and q̇i are the generalized coordinates and their time derivatives.

L = T − V (2.3)whereas T is the kinetic and V the potential energy [3]. For relativistic fieldtheory the concept of particles and their dynamics is replaced by the con-cept of fields φi which depend on the space-time coordinates xµ = (t, ~x).The Lagrange function is replaced by the Lagrangian density L

L(qi, q̇i, t) → L(φi(xµ), φ̇i(xµ), xµ), L =∫

d3x L (2.4)

Thus Eq. 2.2 can be transferred to

∂

∂xµ

(∂L

∂(∂µΦα)

)− ∂L

∂Φα= 0, ∂µ =

∂

∂xµ(2.5)

• The Dirac Lagrangian of a free spin- 12

particle is given by

L = Ψ̄(iγµ∂µ − m)Ψ (2.6)

γµ are the γ-matrices

γ0 =

(1 00 −1

)and γi =

(0 σi

−σi 0

)

with the Pauli-matrices σi. If one inserts the Dirac Lagrangian intoEq. 2.5, one obtains the Dirac equation

(iγµ∂µ − m)Ψ = 0 (2.7)

• With the same procedure one obtains the Proca equation for a mas-sive vector field Aν

∂µFµν + m2Aν = 0 (2.8)

from the Proca Lagrangian

L = −14F µνFµν +

1

2m2AνAµ (2.9)

with the antisymmetric field tensor F µν = (∂µAν − ∂νAµ)


• and the Klein-Gordon equation for a scalar field Φ

(∂µ∂µ + m2)Φ = (2 + m2)Φ = 0 (2.10)

from the Lagrangian

L = 12((∂µΦ)(∂

µΦ) − m2Φ2) (2.11)

Ψ is the wave function of the particle, for example an electron. If onechanges the wave function by a gauge transformation U = exp(−iλQ)

Ψ → Ψ′ = Ψ · exp(−iλQ) (2.12)

the Lagrangian stays unchanged (this can be verified by inserting the newLagrangian into Eq. 2.7), while Q is the generator of the group i.e. theelectric charge and λ an arbitrary phase transition. The group of phasetransitions of the form U = exp(iα) with α as a real parameter is calledan Abelian group U(1). An effect of the U(1) phase invariance is the con-servation of the electric charge Q. If λ(x) is a function of space and timethe Lagrangian changes as an extra term appears because of the deriva-tive. Thats is why the derivative in Eq. 2.7 is replaced by the covariantderivative Dµ

∂µ → Dµ = ∂µ + iQAµ (2.13)with

Aµ → A′µ = Aµ + ∂µλ(xµ) (2.14)Aµ is a local vector field, the gauge field. In electrodynamics this fieldcan be regarded as the photon field which couples to Q. If one appliesall of these replacements and add the Proca Lagrangian (Eq. 2.9) for themassless photon field one obtains

L = Ψ̄(iγµ∂µ − m)Ψ − QΨ̄γµΨAµ −1

4F µνFµν (2.15)

In the theory of weak interactions the exchange particles have massesof 80 (W±) and 91 Gev (Z0, all gauge bosons have been experimentallydetected and measured at CERN in 1983), so the local gauge invarianceis obviously broken because of the additional mass terms. To solve thisproblem an additional scalar background field φ, the Higgs Field, has beenintroduced to provide the particles with their masses.

2.1. THE STANDARD MODEL 15

V(Φ)

Φ

Figure 2.1: Higgs potential for µ2 > 0 (upper graph) and µ2 < 0 (lowergraph) (from [1]).

Spontaneous Symmetry BreakingThe Higgs Lagrangian has the following form [3]

LHiggs = (∂µφ)(∂µφ) − V (φ) (2.16)

and is invariant under transformations of the SU(2)L ⊗ U(1)Y symmetrygroup. Here L stands for lefthanded fermions and Y for the hypercharge(see Eq. 2.1). V (φ) is

V (φ) =1

2µ2φ2 +

1

4λφ4 (2.17)

with λ like before a positiv real constant and µ the Higgs boson mass para-mater. V has, depending on the sign of µ2, one or three extrema appear (seefig. 2.1):

dV

dφ= 0 ⇒ φ0 = 0, φ2,3 = ±

√−µ

2

λ(2.18)

If µ2 > 0 one gets back to the Klein-Gordon Lagrangian (Eq. 2.11) withan additive self-interacting φ4-term and µ is just the mass of the scalarparticle µ = m. Applying perturbation theory one describes the field as afluctuation around the ground state, i.e. the minima v = ±

√−µ2/λ by

φ(x) = v + ηx (2.19)


and insert this into the Lagrangian (Eq. 2.16) with µ2 = −v2λ to obtain

L′ = 12(∂µη)(∂µη) − λv2η2 − λvη3 −

1

4λη4 +

1

4λv4 (2.20)

[3]. According to Eq. 2.11 the second order term λv2η represents the massterm

mη =√

2λv2 =√

−2µ2 (2.21)and the higher order terms in η the self-interaction terms. By this methodone created a mass for the particle of our scalar field by choosing a par-ticular vacuum state v =

√µ2/λ. But the Lagrangian L′’s symmetry is

broken, since it is not invariant to an exchange of η to −η. This is calledspontaneous symmetry breaking.

The Higgs MechanismThe Lagrangian for a complex scalar field of the form

φ =1√2(φ1 + iφ2) (2.22)

isL = (∂µφ)∗(∂µφ) − µ2φ∗φ − λ(φ∗φ)2, (2.23)

compare Eq. 2.16. For a complex field the fluctuations from Eq. 2.19 looklike this:

φ(x) =1√2(v + η(x) + iξ(x)) (2.24)

and yield the Lagrangian [3]

L′ = 12(∂µξ)

2 +1

2(∂µη)

2 + µ2η2 + const. + higher order terms (2.25)

As in Eq. 2.21 the third term represents the mass term for the η-field. Theξ-field, on the other hand, is massless, represented by the Goldstone bo-son.

For a vector field Aµ the gauge invariant Lagrangian becomes with theusual substitutions

Dµ = ∂µ + iQAµ, Aµ → Aµ −1

Q∂µα (2.26)

2.2. GRAND UNIFICATION THEORY (GUT) 17

L = (∂µ − iQAµ)φ∗(∂µ + iQAµ)φ + µ2φ∗φ − λ(φ∗φ)2 −1

4FµνF

µν (2.27)

If one applies pertubation theory according to Eq. 2.25 one obtains theLagrangian for a massive vector field Aµ with mass mA = qv, a massivescalar field η with mass mη =

√2λv2 and a massless Goldstone boson field

ξ [3]:

L′ = 12(∂µξ)

2 +1

2(∂µη)

2 − v2λη2 + 12q2v2AµA

µ+

qvAµ∂µξ − 1

4FµνF

µν + higher order terms(2.28)

2.2 Grand Unification Theory (GUT)Unifiying forces have been one of the main motivation for developing newtheories beyound the Standard Model. In 1864 Maxwell unified electricityand magnetism in his Maxwell equations. In 1950, Einstein described inhis ’Unified Field Thory’ his attempts to unify gravitation and electromag-netism.

In the early universe of the Planck era - this means at scales of 10−35m,a temperature of about 1032K and a universe age of about 10−43s - the fourforces were unified in one force. When the universe started to expand thegravitation separated, and this was the time of the Grand Unified Theo-ries.

2.3 SupersymmetryA theory that is very popular and that gives the possibility to unify thecoupling constants, as shown in fig. 2.2, is Supersymmetry. The couplingconstant is a dimensionless factor describing the strength of the interactionbetween the exchange particles or gauge bosons. The coupling constantsat low energies are [5]

strong force αS 1electromagnetic force α 1/137weak force αW 10−6gravity αg 6 · 10−39


0

10

20

30

40

50

60

0 5 10 15log10 [Q/GeV]

1/α i

1/α1

1/α2

1/α30

10

20

30

40

50

60

0 5 10 15log10 [Q/GeV]

1/α i

1/α1

1/α2

1/α3

SM MSSM

Figure 2.2: Unification of the coupling constants of the strong force α1, theelectromagnetic force α2 and the weak force α3 in the Standard Model (left)and in the Minimal Supersymmetric Standard Model (MSSM; right)

Due to quantum fluctuations the coupling constant is not constant but en-ergy dependent. The coupling constants αi in the picture accord to theU(1)Y , the SU(2)L and the SU(3)C symmetry groups. As one can see inthe picture in the MSSM, the coupling constants are unified in one point.

The theory bases on a symmetry between bosons and fermions. Sincenone of the hitherto known particles are each others superpartners thenumber of elementary particles is doubled. Each fermion gets a super-partner whose name differs from its own by the letter ’s’, e.g. electron andselectron, while each boson gets a partner with the name suffix ’ino’ suchas W and Wino.

The supersymmetric algebra has generators Q that change the particlespin by 1

2[2]:

Q|boson〉 ∝ |fermion〉 and Q|fermion〉 ∝ |boson〉 (2.29)

2.3. SUPERSYMMETRY 19

Since Q can change a particle’s spin, they must have a Spinor componentthemselves and therefore anticommutate:

{Qα, Qβ} = 0 and {Qα, Q̄β} = 2σµαβPµ (2.30)

with the four-momentum vector Pµ and the Pauli spin matrices σµ. TheMinimal Supersymmetric Standard Model (MSSM) requires only one gen-erator Q and is thus a N = 1 supersymmetry. The SUSY-particles differfrom their Standard Model partner only by their mass. All other quantumnumbers stay the same. Since their mass is much higher, the symmetryis broken. Until now no supersymmetric particle has been detected. It isassumed that none of the present particle accelerators have been able toproduce energies high enough to generate their high masses.

2.3.1 The Particles of the MSSMIn the MSSM a second Higgs multiplet is required. Left-handed leptons ofone generation are grouped together with their superpartners into multi-plets, just like left-handed quarks. Right-handed leptons and quarks formdoublets with their superpartners. The gauge bosons of one group formmultiplets with their partners just like the Higgs doublets. The wholespectrum is shown in table 2.2.

The Lagrangian is split into two parts; one part implies the supersym-metric generalization of the Standard Model and the other one is for theSUSY breaking [2]:

L = LSUSY + LSUSY −breakLSUSY = Lgauge + LY ukawa

while the SUSY Lagrangian again is split into two parts, the gauge termthat represents the kinetic energy and the interaction of fermions with thegauge fields and the Yukawa term that represents the interaction of theparticles with each other. The superpotential WR implied by the Yukawaterm is

WR = εij(habU Q

jaU

Cb H

i2 + h

abD Q

jaD

Cb H

i1 + h

abL L

jaE

Cb H

i1 + µH

i1H

j2) , (2.31)

with the Yukawa couplings hU,D,L, the indices of the lepton/quark genera-tions a, b = 1, 2, 3, the total antisymmetric tensor εij and the SU(2)-indices


Superfield Bosons Fermions SU(3)C SU(2)L U(1)YGauge F.

Ga ga g̃a 8 0 0Vk W k (W±, Z0) w̃k (w̃±, z̃0) 1 3 0V′ B/γ b̃ / γ̃ 1 1 0

Matter F.LiEi

L̃i = (ν̃, ẽ)LẼi = ẽR

Li = (ν, e)LEi = eR

11

21

−12

QiUiDi

Q̃i = (ũ, d̃)LŨi = ũRD̃i = d̃R

Qi = (u, d)LUi = uRDi = dR

333

211

1/3−4/32/3

Higgs F.H1H2

H1H2

H̃1H̃2

11

22

−11

Table 2.2: The particles of the MSSM. The SM particles are grouped withtheir SUSY partners into multiplets. a = 1 . . . 8 is the index of SU(3)c andk = 1 . . . 3 the index of SU(2)L. i = 1 . . . 3 is the generation index. Thelast three columns give the quantum numbers in the according symmetrygroup [2].

i, j = 1, 2. The fields with index C are charge-conjugated; all of them aresuperfields.

Due to the fact that proton decay does not occur or is at least stronglysupressed, the MSSM Yukawa term does not have a term that allows lepton-quark transitions. To prevent proton decay a new symmetry has been in-troduced, the R-parity; the fields have to be invariant under phase transi-tions of the kind Φ → e±iRπΦ. R is a quantum number that is 1 for particlesof the Standard Model and −1 for SUSY-particles. It is defined as:

R = (−1)3(B−L)+2S (2.32)

For example, the baryon number B of an electron equals 0, the lepton num-ber L = 1 and the spin S = 1

2. Thus R = 1. For a selectron on the other

hand the spin is S = 0 and R = −1. R-parity conservation implies thatSUSY particles are always produced in pairs. The lightest supersymmet-


ric particle therefore has to be stable and might be - in case it is neutral -the elusive of Dark Matter.

The SUSY-breaking termsThe SUSY-breaking term in the Lagrangian looks generally like this [2]:

VSUSY-break = m2H1H

†1H1 + m

2H2H

†2H2 + Bµ

(HT2 iτ2H1 + h.c.

)

+∑

i

(m̃2QiQ̃

†i Q̃i + m̃

2Li

L̃†i L̃i + m̃2Ui

Ũ †i Ũi + m̃2Di

D̃†i D̃i + m̃2Ei

Ẽ†i Ẽi + h.c.)

+∑

i,j

(Aiju h

iju

˜̄UiH2Q̃j + Aijd h

ijd

˜̄DiH1Q̃j + Aije h

ije

˜̄LiH1L̃j + h.c.)

+1

2

3∑

l=1

Mlλ̃lλ̃l + h.c.,

while B is the bilinear coupling and Aiju,d,e the trilinear couplings withthe generation indices i, j = 1, 2, 3, H1,2 are the Higgs doublets and µ theHiggs mass parameter. The gauginos, which are the partners of the gaugebosons, are the λ̃l while their masses are the Ml with indices l = 1, 2, 3.

This looks and is indeed complicated since 48 parameters are neededto break Supersymmetry. With the minimal supergravity model mSUGRAone is able to make relations between parameters such that their numberis broken down to only 5 at the GUT-scale:

• The unified gaugino mass m1/2M1(MGUT) = M2(MGUT) = M3(MGUT) ≡ m1/2 (2.33)

• The unified scalar mass m0m̃E,L,U i,Di,Qi(MGUT) = mH1,2(MGUT) ≡ m0 (2.34)

• The unified trilinear coupling A0At(MGUT) = Ab(MGUT) = Aτ (MGUT) ≡ A0. (2.35)

• The Higgs mass parameter µ which connects both multiplets• The bilinear coupling B which is equivalent to tanβ = v1/v2, v1 and

v2 are the vacuum expectation values of the two Higgs doublets.


2.3.2 SUSY MassesFrom the scalar part of the Lagrangian

V = VF + VD + VSUSY-break (2.36)

the masses of the SUSY particles can be obtained. Here VF contains thederivatives of the superpotential with respect to the scalar fields Ai =H1, H2, Ũ , Q̃, . . .

VF =∑

i

∣∣∣∣∂W

∂Ai

∣∣∣∣2

= |hU Ũ †Q̃ + µH1|2 + |hDD̃†Q̃ + hEẼ†L̃ + µH2|2+ |hUQ̃H2|2 + |hDQ̃H1|2 + |hEL̃H1|2+ |hU Ũ †H2 + hDD̃†H1|2 + |hEẼ†H1|2 .

while VD is

VD =g′

2

(1

6Q̃†i Q̃i −

2

3Ũ †i Ũi +

1

3D̃†i D̃i −

1

2L̃†i L̃i + Ẽ

†i Ẽi +

1

2H†1H1 +

1

2H†2H2

)2

+g2

8

(Q̃†i~τQ̃i + L̃

†i~τL̃i + H̃

†1~τH̃1 + H̃

†2~τH̃2

)2

+g2s8

(D̃†i

~λD̃i − Ũ †i ~λ?Ũi − D̃†i~λ?D̃i)2

,

[2] with the eight SU(3)C Gell-Mann matrices ~λ and the SU(2)L Pauli-matrices ~τ .

Quarks and LeptonsThe masses of quarks and leptons can be obtained by the following equa-tion [1]:

m2q = h2q|Hi|2 = hqv2i mit

{i = 2 for up-quarksi = 1 for down-quarks

m2l = h2l |H1|2 = hlv21

with the vacuum expectation value of the Higgs field v and the corre-sponding Yukawa term h.


Squarks and SleptonsThe mass equations for squarks and sleptons are given explicitly for everyright- and lefthanded quark. The superpartners aren’t handed.

m̃2eL = m̃2Li

+ m2Ei + M2Z cos(2β)

(−1

2+ sin2 θW

)

m̃2νL = m̃2Li

+ M2Z cos(2β)

(1

2

)

m̃2eR = m̃2Ei

+ m2Ei − M2Z cos(2β)(sin2 θW

)

m̃2uL = m̃2Qi

+ m2Ui + M2Z cos(2β)

(+

1

2+ sin2 θW

)

m̃2dL = m̃2Qi

+ m2Di + M2Z cos(2β)

(−1

2+

1

3sin2 θW

)

m̃2uR = m̃2Ui

+ m2Ui + M2Z cos(2β)

(2

3sin2 θW

)

m̃2dR = m̃2Di

+ m2Di − M2Z cos(2β)(

1

3sin2 θW

)

The terms on the right side which have a tilde derive from the VSUSY −breakterm. Being the same for fermions at the GUT-scale, they can be obtainedwith help of the renormalization group equations [4] at lower energies.i = 1, 2, 3 again marks the different generations.

The squark and slepton mass states are mixed states of the partnerstates of the right- and lefthanded quarks and leptons. Since the mixingfor the two first generations, proportional to their mass, is relatively small,one considers only the third generation mixing:

Mt̃ =(

m̃2tL mt(At − µ cotβ)mt(At − µ cotβ) m̃2tR

)

Mb̃ =(

m̃2bL mb(Ab − µ tanβ)mb(Ab − µ tanβ) m̃2bR

)

Mτ̃ =(

m̃2τL mτ (Aτ − µ tanβ)mτ (Aτ − µ tanβ) m̃2τR

).

To obtain their mass eigenstates these matrices have to be diagonalized:


m2t̃1,2 =1

2

(m̃2tL + m̃

2tR

)±√

1

4

(m̃2tL − m̃2tR

)2+ m2t (At − µ cotβ)2

m2b̃1,2

=1

2

(m̃2bL + m̃

2bR

)±√

1

4

(m̃2bL − m̃2bR

)2+ m2b (Ab − µ tanβ)2

m2τ̃1,2 =1

2

(m̃2τL + m̃

2τR

)±√

1

4

(m̃2τL − m̃2τR

)2+ m2τ (Aτ − µ tanβ)2.

Gauge BosonsThe gauge boson masses are derived analogue to the Standard Model withtwo Higgs doublets instead of one:

M2W± =g2

2(|H1|2 + |H2|2) =

g2

2(v21 + v

22) and

M2Z =g′2 + g2

2(|H1|2 + |H2|2) =

g′2 + g2

2(v21 + v

22)

Gauginos and HiggsinosThe neutral gauginos and the neutral higgsinos mix to the so-called neu-tralinos. The 4 × 4 mixing matrix looks like:

M (0) =

(M1 0 −MZ cos β sin θW MZ sin β sin θW0 M2 MZ cos β cos θW −MZ sinβ cos θW

−MZ cos β sin θW MZ cos β cos θW 0 −µMZ sin β sin θW −MZ sin β cos θW −µ 0

)

(2.37)Analogously, the charged gauginos and higgsinos mix to charginos:

M (c) =

(M2

√2MW sin β√

2MW cos β µ

)(2.38)

whose mass eigenstates after diagonalization are

m2χ±1,2

=1

2M22 +

1

2µ2 + M2W

∓ 12

√(M22 − µ2)2 + 4M4W cos2 2β + 4M2W (M22 + µ2 + 2M2µ sin 2β)

(2.39)

Chapter 3

Dark Matter

3.1 Why Dark Matter?The assumption that there is Dark Matter, that means matter that one can-not see in space is founded by different facts. If one starts in the solarsystem, measurements of the planets which have been made for centurieswith growing precision confirm a relation between the radial velocity ofthe planets moving around the sun and their distance to the latter. If oneneglects the gravitational attraction between the planets - which is reason-able because the heaviest planet, Jupiter already has a mass that is a 1000times smaller than that of the sun (Msun ≈ 2·1030kg) the centrifugal force ofa planet traveling around the sun equals the gravitational force attractingit towards the sun:

mP lanetv2

r=

GM�mP lanetr2

⇒ v =√

GM�r

(3.1)

Here M� is the mass of the sun, G the gravitational constant, v the velocityand r the distance to the sun, the result of this equation is fig. 3.1.

Now it’s a legitimate assumption that one has the same rotation curvefor the stars in our galaxy which rotate around the black hole in the galacticcenter. Instead, the rotation curve stays almost constant v = const., seefigure 3.2. If one calculates back the responsible mass distribution, onegets

M(r) =v2

G2r (3.2)

25

26 CHAPTER 3. DARK MATTER

Figure 3.1: The rotation curve of our solar system

and the density distribution

M(r) = δ(r) · V δ(r) = v2

43πG2

1

r2→ δ(r) ∝ 1

r2(3.3)

This means there must be mass in our galaxy with the given density dis-tribution that one cannot see i.e. which does not interact with light and isthus neutral.

Another hint for Dark Matter is given by gravitational lenses. Accord-ing to Einstein big masses can influence the way of light and attract it insuch away that light rays are bent around massive objects. If the observer,a massive object and a galaxy are perfectly aligned the observer can seea ring of light because the light which is coming from the galaxy is bentaround the object from each side and forms a ring. These rings have al-ready been oberved and are called Einstein rings. If one knows how faraway the galaxy is one can calculate the mass of the object in between.

3.2. DARK MATTER CANDIDATES 27

Figure 3.2: The rotation curve of the galaxy NGC 1398. From [1]

3.2 Dark Matter Candidates3.2.1 Baryonic MatterThe missing mass has been tried to explain by other massive compact haloobjects, the MACHOs, like black holes, neutron stars brown, red or whitedwarfs, i.e. baryonic dark matter. From Cosmic Background Radiationmeasurements it is known that they cannot make up for the amount ofmass that is missing.

Cosmic Microwave Background (CMB)In the beginning of the universe photons were coupled to free electronsand positrons by electromagnetic interaction. 380 000 years after the bigbang, the universe became transparent. This means the reactions

γ −→ e+e− and e+e− −→ γweren’t in equilibrium any more, the temperature fell down to 3000K andcharged particles began to form atoms, the light could pass without ob-


stacles. In the plasma, there were density fluctuation due to gravitationalattraction, thus potential wells. Photons that escape from these potentialwells are Doppler shifted, i.e. they lose energy by escaping from the po-tential well and thus change their wavelength. The photons that escapedat decoupling time have been predicted and finally detected in 1964 ascosmic microwave background. Having a temperature of 3000 K at timeof decoupling they cooled down to 2.7K until now due to the expansion ofthe universe.

Acoustic OscillationsThe baryonic plasma before decoupling tried to collapse under gravita-tion. But the hot photons in between pushed against with their radia-tion pressure. This caused oscillations of the plasma that contracted undergravitation and extended under radiation pressure alternately. The infor-mation about these acoustic oscillations is also stored in the backgroundphotons. The WMAP satellite was launched in 2001 to measure the Cos-mic Background Radiation with high precision. From the data taken theuniverse composition could be determined as follows [6]:

total density Ωtot = 1.02 ± 0.02baryon density Ωb = 0.044 ± 0.04matter density Ωm = 0.27 ± 0.04

The Dark Matter is responsible for 85 % of the mass of the universe, only15 % of the matter is baryonic like us, the stars, the visible matter. Therehave been different approaches to explain the role of Dark Matter in theformation of the universe, the top-down and the bottom-up scenario.

3.2.2 Hot Dark MatterIn this scenario one assumes that the role of the Dark Matter is played bythe neutrino, a particle which is already known to exist. Neutrinos arevery light and so there would have to be incredible amounts of neutrinosin the universe. Unitil now it is known that 50 trillion neutrinos originat-ing from the sun pass through our bodies every second. Since neutrinosare so light they travel with almost speed of light and would be in thiscontext the Hot Dark Matter. If at the time of structure formation (380 000

3.3. THE EGRET DATA 29

years after Big Bang) there were huge amounts of fast traveling neutrinosaround, any structure would have been washed out immediately. Thismeans the universe of today would have evolved from big scales to smallscales. First the galaxy clusters would have collapsed down to galaxies, tostars. Space observations with the modern telescopes such as the Hubbletelescope have shown that this is not the case. Really old galaxies havebeen observed and galaxy clusters that are still in a forming process.

3.2.3 Cold Dark MatterThe bottom-up scenario assumes that structures have been formed fromsmall to big. This means that when the universe became transparent theslowly moving Cold Dark Matter particles amplified the structure build-ing of the baryonic matter by falling into their potential well, thus strength-ening the attractive potential. The structures grew and built stars, galax-ies, that form galaxy clusters. As a consequence the Cold Dark Mattermust consist of neutral particles that weakly interact and that are slow andheavy. They are called Weakly Interacting Massive Particles or WIMPs.

3.3 The EGRET Data

Figure 3.3: The Compton Gamma Ray Observatory. From NASA [8].


In 1991 the Compton Gamma Ray Observatory (CGRO) was deployedin the low earth orbit in a distance of 450 km from earth. Its missionwas to measure the gamma radiation in the range from 20 keV to 30 GeVin all sky directions. A picture of the CGRO is given in fig. 3.3. TheCGRO took data for nine years. On board were four different instruments.The Burst and Transient Source Experiment (BATSE) searched for shortgammy ray bursts which were observed detailly by the Oriented Scintil-lation Spectrometer Experiment (OSSE). The Imaging Compton Telescope(COMPTEL) determined the angle and energy of arriving photons. TheEnergetic Gamma Ray Experiment Telescope (EGRET) measured high en-ergetic gamma radiation from 20 MeV to 30 Gev, determined their originangle to a fraction of a degree, and its energy with an accuracy of 15%.EGRET measured an excess of diffuse gamma radiation in all sky direc-tions.

Figure 3.4: Annihilation signals of monoenergetic quarks/bosons.

After [2], the excess of gamma rays measured by EGRET can be ex-plained by Dark Matter annihilation. Annihilation signals of monoen-ergetic quarks or bosons are shown in fig. 3.4. While the shape of the

3.3. THE EGRET DATA 31

Figure 3.5: Gamma radiation measured by EGRET (blue dots). The shapemarked with ’WIMPs’ is what is left when all known backgrounds arereduced from the signal. The yellow area is the sum for the whole back-ground while the red part represents what is added because of WIMP an-nihilation. The light blue area is the uncertainty.

signals stays the same with exception of τ+τ−-signal, only the strengthvaries. If one now subtracts the shapes of the known backgrounds suchas bremsstrahlung, π0-decay, inverse compton radiation etc., from the sig-nal shape, the reamining signal can be fitted to the shapes in fig. 3.4, seefig. 3.5. If Dark Matter particles are identical with the supersymmetricneutralinos, they are Majorana particles, thus their own antipartner. Theyannihilate into Standard Model particles, which decay into positrons andelectrons, antiprotons and protons, neutrinos, photons. For example

χ0 + χ0 −→ f + f̄χ0 + χ0 −→ Z0 + W0χ0 + χ0 −→ W + + W−

The further decay products are lots of hadronic jets which decay over theneutral pion into two gammas. There are 30-40 gammas produced in each


annihilation. The WIMP temperature after [2] is 0.9 K, which means theycan be considered monoenergetic. Thus the gamma ray excess measuredby EGRET might result from Dark Matter annihilation. More about theEGRET-data interpretation as Dark Matter annihilation is given in refer-ence [2].

3.4 Dark Matter = χ0If the WIMP is identical to the supersymmetric neutralino χ0, some con-straints for the mSugra parameter space, namely the parameters m0, m 1

2,

tanβ, A0 and sign(µ) (compare section 2.3.1) can be made; these are dis-cussed in the following subsections.

3.4.1 The Relic DensityThe relic density is constant density of WIMPs after freeze-out, i.e. spacebecame so big and the particles where so far away from each other thatthey practically didn’t meet and annihilate any more. The relic density ofthe dark matter has been calculated by WMAP to

ΩDM = 0.224 (3.4)

If the neutralino is Dark Matter, of course the relic density has to be iden-tical.

3.4.2 MassesFrom collider experiments, mainly the Large Electron Positron collider(LEP), the precessor of the LHC, there have been found limits for themasses of supersymmetric particles. See also [7]. The most important li-mits for the neutralino, the chargino and the Higgs boson, are (from [2]):

m(χ0) > 36GeV

m(χ±) > 103GeV

m(h)) > 114.4GeV

3.4. DARK MATTER = χ0 33

Figure 3.6: The mSugra parameter plane with A0 = 0.5m0, µ > 0 andtanβ = 51. The light blue line is the region allowd by WMAP. The coloreddot regions are indicated. The favored region, where EGRET, WMAP andelectroweak data are fullfilled, is at m0 ≈ 1400 and m 1

2≈ 180. From [9]

3.4.3 mSugra Parameter Space

In fig. 3.6 the mSugra plane is shown, with the values of A0 = 0.5m0, µ > 0and tanβ = 51 and the constraints that include WMAP and EGRET data.The light blue line is the allowed region from WMAP, if one considersthe Dark Matter to be the lightest neutralino with a specific annihilationcross section which is dependent on the mSugra parameters. In the yellowdotted region the Higgs boson mass is below 114.4 Gev, which is the lowerlimit measured by LEP [10] . In the bottom right corner the gauginos areso light that their radiative corrections are to small to cause electroweaksymmetry breaking. In the top left corner, the red region, the LSP wouldbe a chargino. Since the Dark Matter particle is neutral in this case, itcouldn’t be the LSP, thus this region is excluded. The regions with green


dots are excluded because their boost factor is higher than 100. The boostfactor is explained in [2] and is connected with the density distribution ofdark matter clumps. After all exclusions only the not-dotted regions inagreement with the WMAP-line are allowed, namely the region aroundm0 = 600Gev, m 1

2= 400GeV and the region around m0 = 1400GeV and

m 12

= 180GeV, which is preferred by the EGRET data. The latter regioncorresponds to the LM9 point of the CMS collaboration.

3.4. DARK MATTER = χ0 35

Chapter 4

Software

4.1 CMKINCMKIN [12] is a software package that provides an interface between par-ticle events generators like PYTHIA[11], HERWIG[17], or ISAJET[16] andCMS detector simulation. CMKIN version 6.2.0 has been used in this anal-ysis. The generators are accessed via datacards that set variables like kine-matic cuts, center of mass energy or switching discrete decay channels.The generator data are transformed into the standard HEPEVT format andstored in HBOOK-ntuples. Via H2ROOT these ntuples can be convertedinto root-files, which can be furtherly processed.

4.2 PythiaPYTHIA [11] is a program to describe high energy particle collisions be-tween elementary particles like e−, e+, p and p̄. It contains possibilitiesto consider many physical aspects like hard and soft interactions, partondistributions, initial- and final state parton showers, multiple interactions,fragmentation and decay. In this analysis PYTHIA 6.325 has been usedwith the CMKIN 6.2.0 interface.

ParametersThe parameters for the events generation have been chosen in the follow-ing way. Parameters which are not noted have been left at their default

37

38 CHAPTER 4. SOFTWARE

value.

• ECMS=14000. : The CMS center of mass energy is set to 14 TeV.

• PMAS 6,1=175.: mass of the top quark

• PMAS 23,1=91.187: mass of the Z boson

• PMAS 24,1=80.22: mass of the W boson

• MSTP 51=4046 : pdf function CTEQ5L from pdflib804

• MSTP 52=2 : choose pdf from pdflib

4.3 ISASUGRAThe Monte Carlo generator ISAJET [16] simulates high energy particle col-lisions, with the modul ISASUGRA it calculates cross sections and branch-ing ratios of supersymmetric processes. The mSugra parameters m0, m1/2,tanβ, A0 and sign(µ) are passed to the program via datacard. In this anal-ysis ISAJET version 7.71 has been used.

4.4 CMSSWThe currently growing CMSSW [13] framework is supposed to fulfill all re-quirements to proceed CMS data on generator, detector, digitization andreconstruction level. The version used is CMSSW 1 5 0, only for proces-sion of Monte Carlo data.

4.5 NeurobayesNeurobayes [14] is a neural net software package from Karlsruhe. Version20060626 has been used. The program consists in two parts: the trainerand the expert, the latter applies the learned information to the data. Bothhave been used in connection with ROOT.

4.6. ROOT 39

4.6 ROOTROOT [15] is a program with command line interpreter that is specifiedon dealing with high events numbers, stored in root-files or trees. In theformat the single variables for each event, e.g. the momentum or energyof a jet, can be accessed easily. The program, based on c++, contains manyclasses that simplify the creation of histograms and graphs and is thus animportant tool for the creation of publication papers. Version 5.16 and 4.04have been used.

4.7 PROSPINOProspino [19] is a program which calculates next-to-leading order crosssections of supersymmetric production channels at hadron colliders, i.e.for the LHC or the Tevatron. Version 2.0 has been used in this analysis.

40 CHAPTER 4. SOFTWARE

Chapter 5

Analysis

This part contains an analysis of the gaugino-pair production in the mSugraplane as it is expected from the CMS experiment at the LHC. Consideredare the processes

qiq̄j −→ χlkχnm while

k, m = 1, 2, 3, 4 andl, n = 0 or (if k = 1, 2) +, −

This gives 4 + 3 + 2 + 1 = 10 processes with only neutralinos χ01,2,3,4involved, 4 processes with only charginos χ+,−1,2 involved and 4 · 4 = 16mixed processes with χ01,2,3,4χ

+,−1,2 , in total 30 processes. The analysis has

been tuned to the CMS test point LM9, with the purpose to apply the samecuts on the whole plane afterwards. The total cross section of all processesfor the LM9 point is

σΣχlkχnm = 9.2pb [LO, Prospino2]so for a LHC luminosity of

L = 301

fb

(see Appendix A) in three yearsNΣχlkχnm = 276 000 events are expected.

This study is on generator level, i.e. no detector simulation has been in-cluded.

41

42 CHAPTER 5. ANALYSIS

5.1 mSugra planeThe total SUSY cross sections in the mSugra plane are shown in fig. 5.2.The main SUSY-production channels at the LHC are

pp −→ g̃g̃pp −→ q̃g̃pp −→ q̃q̃pp −→ χ̃χ̃

The fractions of these channels of the total SUSY cross section are shown infig. 5.1, the cross section for the inclusive gaugino channel is given in fig.5.2. The plot on the right at the bottom shows that the gaugino channelcontributes most to the total SUSY cross section. While the gluinos areproduced mostly around the LM9 point in a region around m0 ≈ 1400 andm1/2 ≈ 200, the gaugino fraction stays almost constant when m1/2 risesand exceeds with m0. The gluino channel, which is interesting because ithas the highest cross section at the preferred LM9 point, is studied by EvaZiebarth in her diploma thesis. Therefore this analysis will focus on thegaugino channel.

5.2 BackgroundsAs background processes there have been considered tt̄, W+jets, W with-out jets, Z+jets, Z without jets, and QCD. The decay modes for Z0 and W±have been shown in Appendix, table A.3. The top quark decays to nearlyhundred percent into a b-quark and a W± boson. The jets in the channelsW+jets and Z+jets derive from initial or final state radiation.

The backgrounds have been simulated with Pythia, using the chan-nels given in table 5.1. They have been generated without any cuts andstored as ntuples of 10 000 events each. The process numbers for eachbackground are shown in the same table. The background and the signaldata have been processed through the CMSSW framework written by [21].The framework made the following requirements:

• jetpt ≥ 20 GeV

5.2. BACKGROUNDS 43

m00 1000 2000 3000 4000

1/2

m

200

400

600

800

1000

1200

00.10.20.30.40.50.60.70.80.91

squarks/cstot

m00 1000 2000 3000 4000

1/2

m

200

400

600

800

1000

1200

00.10.20.30.40.50.60.70.80.91

gluino+squarks/cstot

m00 1000 2000 3000 4000

1/2

m

200

400

600

800

1000

1200

00.10.20.30.40.50.60.70.80.91

gluino/cstot

m00 1000 2000 3000 4000

1/2

m

200

400

600

800

1000

1200

00.10.20.30.40.50.60.70.80.91

gaugino/cstot

Figure 5.1: Fractions of the different channels of the total SUSY cross sec-tions. tanβ = 50.


m_00 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

m_1

/2

0

200

400

600

800

1000

1200

1

10

210

310

410

gaugino cross section

Figure 5.2: Gaugino pair production cross section in the mSugra plane,tanβ = 50.

5.3. THE L1 TRIGGER 45

cs[pb] generated [1/fb]tt̄ (Toprex) inclusive gg/qq̄ → tt̄ 488 890 000 1.82Zjets MSEL 13 ISUB=15 fif̄i → gZ0 1.1 · 105 2.5 · 106 0.02

ISUB=30 fig → fiZ0Wjets MSEL 14 ISUB=16 fif̄j → gW± 3.5 · 105 2.5 · 106 0.007

ISUB=31 fig → fkW±QCD MSEL 1 ISUB=11 fifj → fifj 5.4 · 1010 8.5 · 106 1.6 · 10−7

ISUB=12 fif̄i → fkf̄kISUB=13 fif̄i → ggISUB=28 fig → figISUB=53 gg → fkf̄kISUB=68 gg → gg

Table 5.1: Processes used in Pythia to generate backgrounds. Cross sec-tions are from [18].

• jeteta ≤ 4

• electronpt ≥ 3 GeV

• electroneta ≤ 2.4

• muonpt ≥ 3 GeV

• muoneta ≤ 2.4

5.3 The L1 TriggerThe L1 hardware trigger allows only a part of the events to be proceededand stored. The conditions for a L1 acception are given in Appendix, tableA.6. For the signal at the LM9 point 50.5% of the events are accepted. Thevalues of cross sections of the signal and some background processes, thetrigger efficiency and the cross sections after passing the trigger are givenin table 5.2. The effect of the trigger on the particle numbers is shown inAppendix, table A.7. Due to their high remaining cross sections the fol-lowing channels have been considered in this analysis: tt̄, W+jets, Z+jets,and QCD.


m_00 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

m_1

/2

0

200

400

600

800

1000

1200

1

10

210

310

cross section after L1 trigger

m_00 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

m_1

/2

0

200

400

600

800

1000

1200

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

L1 trigger efficiency

Figure 5.3: The gaugino cross sections after the L1 trigger in the mSugraplane. Below, the trigger efficiency is shown. The most important triggercriteria is the MET threshold. In the lower plot the red area is the onewith the best trigger acceptance, since the MET is high. Almost all eventshere are accepted via the MET threshold of MET > 61. In the blue regionthe acceptance is very low, since most events have a MET which does notexceed the threshold. The white area at the top, including the triangle atvalues around m0 = 3500, m1/2, has not been generated.

5.4. THE LM9 POINT 47

channel cross section trigger remaining csBackground/csSignalPYTHIA efficiency cross section

gauginos 10.55 pb 0.51 5.38pb 1tt̄ 488pb 0.93 453.8pb 91Z+jets 1.1 · 105pb 0.065 7190pb 1336W+jets 3.5 · 105pb 0.12 42620pb 7922QCD 5.4 · 1010pb 5.8 · 10−5 3.1 · 106pb 5.8 · 105

Table 5.2: Cross sections given by Pythia. All cross sections have beencalculated in leading order.

After trigger only a few QCD events have been left over. The fur-ther analysis thus considers only the three remaining backgrounds W+jets,Z+jets and tt̄.

In fig. 5.3 the cross section after the L1 trigger and the trigger selectionefficiency, beneath, is shown for the gaugino signal in the whole mSugraplane. The efficiency is around 90% at m1/2 > 400 and small in the lowm1/2 and in the focus point region, which is roughly above m0 = 3000,close to the electroweak symmetry breaking border.

5.4 The LM9 pointTo tune the analysis it has been optimized for a specific point, the LM9point. The cuts found here are lateron applied for the whole mSugra plane.The LM9 point has the following coordinates in the mSugra space:

m0 = 1450 Gev,m 1

2= 175 Gev,

tanβ = 50

A0 = 0

sign(µ) = +.

At this point the gaugino cross sections for the single pair processes areshown in Appendix, table A.1. They have been calculated by Prospino2.The cross sections aren’t much different from the ones given by Pythia.Both programs give a total gaugino decay cross section of around 10 pb.


part of nJets nLep mean MET main part of mean METsignal background this bg of bg0.131 2j 1l 57 WJets 0.169 350.130 2j 0l 82 QCD 0.262 10.123 3j 0l 84 QCD 0.189 00.101 3j 1l 72 WJets 0.063 340.086 1j 1l 53 WJets 0.517 350.074 1j 0l 85 QCD 0.0348 00.074 4j 0l 86 QCD 0.143 00.055 4j 1l 79 WJets 0.023 320.045 5j 0l 87 QCD 0.0635 00.026 3j 2l 71 ZJets 0.048 10.026 2j 2l 44 ZJets 0.216 00.021 5j 1l 80 WJets 0.006 380.016 6j 0l 71 QCD 0.0349 00.015 4j 2l 72 ZJets 0.021 00.013 1j 2l 53 ZJets 0.054 20.011 0j 1l 29 WJets 0.128 24

Table 5.3: The main signatures. Triggered events, with precuts ptjets > 30,ptelectrons > 10, ptmuons > 70.

Pythia also gives the branching ratios of the supersymmetric Gauginos.They are shown in Appendix, table A.2. From that the decay products foreach particle have been calculated, shown in Appendix, table A.4. Dealingwith combinations of gauginos, also the pair decay products are shown inAppendix, table A.5.

There have been generated 50 000 signal events, which is about 5fb.These events had to run through the same CMSSW framework as the back-ground, compare section 5.2. The main signatures for the gaugino channelat the LM9 point are shown in table 5.3. The number in the left columnshows the fraction af the signal. The mean missing transverse energy foreach signature is shown in the 4th column, while the last three columnsshow the main background for this signature, the fraction of this back-ground and again the mean missing transverse energy. In this tabel the500 remaining QCD events have still been considered.

5.5. NEURAL NET, PART ONE 49

particle mass [ISAJET] mass [SOFTSUSY]top 175 174.3Z0 91.187 91.187W± 80.22 80.41

χ01 66.91 69.89χ02 123.70 130.32χ±1 124.37 130.51χ03 234.0 285.47χ±2 259.83 300.03χ04 260.16 300.46

Table 5.4: The masses of the gauginos at LM9 in [GeV], calculated byISAJETv7.71 [16] used by Pythia and SOFTSUSYv2.0.11 [22]

MassesThe masses of the considered particles are given in table 5.4. In the tablevalues calculated by two different programs are given, SOFTSUSY andISAJET. As one can see, there is quite a difference between the values,but the general relationships are the same. The lightest particle is the χ10,followed by the χ20 and the χ1±, which have almost same masses and areonly a few GeV from double the mass of the χ10. The next heavier gauginois the χ30, and the heaviest are χ2± and χ40 which are only hundreds of MeVapart.

5.5 Neural Net, Part OneThe triggered events have been used to train a neural net, NEUROBAYES,with all available variables such as eta, phi, momentum in x, y and z di-rection and energy of the three highest pt leptons and jets, the particlenumbers for electrons, muons, leptons (electrons+muons), jets, photons,and the missing transerve energy. The backgrounds have been weightedby their cross section, while a signal number one to one to the total back-ground was used. The network output is shown in fig. 5.4. The red curverepresents the signal and the black curve the total background. The neu-ral network uses all variables to determine as precisely as possible if an


Figure 5.4: Neurobayes output. The red curve is the signal, while the blackcurve is the total background, weighted by the cross section for each pro-cess. The x-axis is the propability for each event to be signal (positivevalues) or background (negative values).


1

1.5

2

2.5

3

3.5

4

4.5

Meff0 100 200 300 400 500 600

MET

0

50

100

150

200

250

300

350Significance of Meff_METSignificance of Meff_MET

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

MET0 50 100 150 200 250 300 350

nJet

s

0

2

4

6

8

10

12

14

Significance of MET_nJetsSignificance of MET_nJets

Figure 5.5: On the x and y axis cuts on Meff and MET towards highervalues are applied. On the z-axis the significance σ is plotted for everycut. Below, the significance σ of cuts on nJets and MET.


nLeptons0 1 2 3 4 5 6 7 8 9 10

MET

050

100150200250300350

00.511.522.533.54

Significance of nLeptons_MET

nLeptons0 1 2 3 4 5 6 7 8 9 10

Mef

f

0100200300400500600

00.511.522.53

Significance of nLeptons_Meff

nLeptons0 1 2 3 4 5 6 7 8 9 10

nJet

s

02468

101214

00.20.40.60.811.21.41.61.82

Significance of nLeptons_nJets

pt1jet0 50 100 150 200 250 300

nJet

s

02468

101214

00.511.522.53

Significance of pt1jet_nJets

pt1jet0 50 100 150 200 250 300

MET

050

100150200250300350

11.522.533.544.5

Significance of pt1jet_MET

pt1lepton0 100 200 300 400 500 600

MET

050

100150200250300350

00.511.522.533.54

Significance of pt1lepton_MET

Meff0 100 200 300 400 500 600

nJet

s

02468

101214

00.511.522.53

Significance of Meff_nJets

pt1jet0 50 100 150 200 250 300

Mef

f

0100200300400500600

1

1.5

2

2.5

3

Significance of pt1jet_Meff

Figure 5.6: Compare fig. 5.5; Significance of combinations of the mostrelevant variables. The histograms which imply cuts on MET yield thehighest significance (> 4).


event is signal or background. In the plot the number of events is plot-ted over the propability for these events to be signal (positive values) orbackground (negative values). It can be seen that most of the backgroundevents can be matched to a good propability - around 90% to their origin.The signal events could be matched even more precisely.

The most relevant variables, i.e. the ones from which the network getsmost information wether the event is signal or background, are the follow-ing:

variable Neurobayes significance nbMET 68nJets 25pt of highest pt lepton 14nLeptons 11MET(y) 7MET(x) 6

To avoid confusion with the lateron used significance defined by σ =signal/

√background, the significance given by Neurobayes which is in

some complex unit is written like significance nb. Although the way tocalculate it won’t be discussed here, the values still give a good overviewof the importance of the variables.

The last two variables are the missing transverse energy in x, respec-tively in y direction. Since their significance nb is almost the same, theyare assumed to be redundant when using the total MET. Thus there are 4variables which are most important. As fifth variable the effective massMeff = MET + Σjetspt has been considered , because it turned out to bea good variable in other analyses, e.g. the one made by E. Ziebarth. Todefine a precut, two variables are picked to optimize a cut on them forthe best significance σ. For each variable there have been defined cuts inreasonable steps and combined with the others to find the two variablesand cuts that yield the best significance. In fig. 5.5, top, the significanceis shown when applying Meff and MET cuts on the data. The best signifi-cance is reached when Meff ≥ 230GeV and MET ≥ 45GeV.

Meff ≥ 230GeV and MET ≥ 45GeV ⇒ σ = 4.74(for 5/fb)

In fig. 5.5, bottom, the significance when applying nJets and MET cutson the data is shown. Here the best significance value is reached at

MET ≥ 55GeV and nJets ≥ 2 ⇒ σ = 4.64 (5/fb)


Figure 5.7: Neural net, part 2; Neurobayes output. The red curve is thesignal, while the black curve is the total background, weighted by the crosssection for each process. On x-axis there is the propability for each eventto be signal (positive values) or background (negative values). The eventsample used in the training has been preselected by the precuts found insection 5.5. As can be seen, hardly any seperation can be made after theprecut.

In the following the Meff+MET cut has been applied on the data fedinto the neural net.

These cuts reduce background an signal by the following:process cross section [pb] trig eff trig+cut eff remaining cs [pb]Signal 10.55 0.51 0.22 2.32tt̄ 488 0.93 0.35 170.80Zjets 1.1 · 105 0.06 1.4 · 10−3 154.81Wjets 3.55 · 105 0.12 2.3 · 10−3 816.85

5.6 Neural Net, Part TwoIf all events with Meff ≥ 230GeV and MET ≥ 45GeV are taken into theneural net, again weighted by their cross sections and one to one with thesignal, the neural network output looks like fig. 5.7. Obviously it is hardly

5.6. NEURAL NET, PART TWO 55

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

10

210

310

410

510

Network Output

Figure 5.8: Network output given by Neurobayes. The red curve rep-resents the signal and the black curve the total background. The x-axisshows the propability for these events to be signal. This plot can be di-rectly compared to fig. 5.7. The difference is that in fig. 5.7 the amountof signal and background events is equal in the training, while in this plotthe number of events is weighted by the real cross section.

possible to seperate background and signal after the cut. There’s only aslight excess into each direction.

The most relevant variables are nowvariable Neurobayes significance nb now and beforenPhotons 20 4nLeptons 17 11pt of highest pt lepton 11 13nJets 9 25MET 7 68

If one now compares the siginificance nb of the variables with the onesbefore the cut, the variable quality has dropped almost 50 significance nb


units for the most relevant variable. So far the network has only beentrained. By this one can get an impression of how well events can beassigned to their origin. All of this information is stored in a file calledexpertise.nb.

The second step is now to take different data and run the NeurobayesExpert on them, which uses the expertise.nb -file. The Expert gives a propa-bility for each event to be signal or background. Thus the neural net out-put can be interpreted as a variable. Just like on any other variable one cancut on this one and optimize the significance σ. In fig. 5.8 the total back-ground, weighted by cross section and cut at the precut values, is plottedin black, while the signal, also weighted by cross section, is shown in red.They are plotted over the output variable, which in this case is zero forbackground and one for signal. In fig.5.9 the three background shapes areshown seperately in comparison with the signal. The tt̄ background shapeis hardly different from the signal, while the differences in the shapes ofZjets and Wjets grow with their cross section. A cut on the network outputyields fig. 5.10. Here the significance σ = signal/

√background is plotted

over the cut. The value at x = 0 represents a cut at zero, thus takes allevents. The significance here is the same as after the precut. The signifi-cance rises slightly to its maximum at 0.52, here

σ = 5.09

Furtheron, the significance drops while more and more signal events arecut off.

This yields the following cut efficiency:process cross section [pb] trig eff trig+cut eff rem. cs [pb]Signal 10.55 0.51 0.17 1.79tt̄ 488 0.93 0.27 131.76Zjets 1.1 · 105 0.06 9.0 · 10−4 99.52Wjets 3.55 · 105 0.12 9.1 · 10−4 323.19

5.7 mSugra plane, after precutA scan of the whole mSugra-plane at tanβ = 50 has been made to see howthe cut selection made at LM9 would work in other regions of the param-eter space. For this purpose only the precuts Meff ≥ 230 and MET ≥ 45

5.7. MSUGRA PLANE, AFTER PRECUT 57

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.005

0.01

0.015

0.02

0.025

ttbar

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.005

0.01

0.015

0.02

0.025

0.03

ZJets

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.005

0.01

0.015

0.02

0.025

Wjets

Figure 5.9: The network output seperated for each background in black,red the signal. Both curves have been normalized to one. The top plotshows the tt̄ part of the background. It is almost not seperated from thesignal because the number of events in the training sample was very lowcompared to the other two backgrounds, due to its low cross section. Sincethe Wjets background has the highest cross section, the training was op-timized for this background. This is why it has been seperated compare-tively well.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

Significance

Figure 5.10: The significance for 5/fb. This plot results from cutting onthe plot in fig. 5.8 towards higher x-values. Note that in this case 0 isequivalent to -1 in fig. 5.8 and 0.5 equivalent to 0 before. The highestsignificance is reached with a cut 0.52, the significance reached here is σ =5.09.


have been considered. If one would like to gain the same selection preci-sion as on the LM9 point, it would be necessary to train the neural net forevery single point for a little gain of significance. Thus only the precutswere applied.

In fig. 5.11, the selection efficiency of trigger and precut are shown.The mean values of the main variables, MET, Meff and nJets, are plottedin fig. 5.12. The plot in fig. 5.13 at the top now shows the significancescaled to 30/fb, i.e. in three years of LHC. The plot below shows a moredetailed picture of the focus point region. The significance σ within thisarea is between 10−1 and 1.

m_00 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

m_1

/2

0

200

400

600

800

1000

1200

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Trigger+cut efficiency

Figure 5.11: mSugra plane. tanβ = 50. Compared to fig. 5.3, the picturehas not changed much. The efficiency has dropped in all points nearlyhomogeneously.


m_00 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

m_1

/2

0

200

400

600

800

1000

1200

0

50

100

150

200

250

300

mean MET

m_00 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

m_1

/2

0

200

400

600

800

1000

1200

0

200

400

600

800

1000

1200

mean Meff

m_00 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

m_1

/2

0

200

400

600

800

1000

1200

0

0.5

1

1.5

2

2.5

3

3.5

4

mean nJets

Figure 5.12: The mean values of the most important variables. tanβ = 50.Just like their production cross section, the values of the variables rise withhigh m0.


m_00 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

m_1

/2

0

200

400

600

800

1000

1200

1

10

210

Significance (30/fb)

m_03000 3200 3400 3600 3800 4000 4200 4400 4600 4800 5000

m_1

/2

400

500

600

700

800

900

1000

1100

1200

-210

-110

1

Significance (30/fb), Focus point region

Figure 5.13: The significance σ. mSugra plane. tanβ = 50. In the upperplot the whole plane is shown, the lower plot shows the focus point regionmore detailedly. Both plots are logarithmic. The highest significances arereached in the regions with the highest production cross sections, comparefig. 5.2. See text for further description.

Conclusion

In this thesis the inclusive supersymmetric channel Σqiq̄j −→ χlkχnm, as itmight be detected at the CMS detector at the LHC, is studied on generatorlevel. As background tt̄, W+jets and Z+jets production have been consid-ered. For the analysis the high energy events generator Pythia with ISAS-UGRA for the supersymmetric processes, the CMSSW framework and theneural network Neurobayes have been used. The study has been tunedto the CMS test point LM9, which agrees with the EGRET data. The crosssection for this point is ≈10 pb. The total cross section of the backgroundprocesses is ≈ 5.2 · 105pb. To find the small signal between the large back-ground selective features of the signal had to be found. In principle SUSYsignatures distinguish themselves by the missing energy of the escapingneutralinos.

In the analysis a neural net has been used twice. First, to find the mostimportant variables in order make a preselection. Second, to take the pre-selected sample and to improve the selection by taking into account allvariables.

To get an overview of all possible distinctive features, the followingvariables were fed into the Neurobayes neural net: eta, phi, momentumin x, y and z direction and energy of the three highest pt leptons and jets,the particle numbers for electrons, muons, leptons (electrons+muons), jets,photons, and the missing transerve energy. The neural net returned themost relevant variables to be MET, number of jets, pt of the highest ptlepton and number of leptons (in order of relevance). These variableshave been used to determine a precut on the events. As fifth variablethe effective mass Meff = MET + Σjetspt has been introduced , sinceit showed up frequently in similar analyses. The best significance σ =signal/

√background was reached with a cut at Meff ≥ 230GeV and MET ≥

45GeV, the significance for this cut is σ = 4.7 for 5/fb. The events which

63


fulfilled the cut requirements have been fed into the neural net again tooptimize the significance.

The improvement gained by cutting on the network output containingall variables from the second neural net enlarged the significance fromσ = 4.7 (cut on two variables) to σ = 5.1 for 5/fb.

The precuts have been applied on the whole mSugra plane at tan β =50 to find out how the significance changes. It turned out that the signif-icance is dependent mostly on the cross section for each point. Discoveryreach for this channel, i.e. σ > 5 is fulfilled in regions with m1/2 ≤ 300GeVand in the focus point region (m0 > 3000GeV, m1/2 > 400GeV, close toelectroweak symmetry breaking) at points were the difference to the elec-troweak symmetry breaking border is ∆m1/2 < 50GeV.

Appendix A

barnBarn is a unit for a cross section.

1b = 10−28m2 = 10−24cm2

1pb = 10−36cm2

65

66 APPENDIX A.

process crosssection [pb]qiq̄j −→ χ01χ01 0.202 · 10−2qiq̄j −→ χ01χ02 0.193 · 10−2qiq̄j −→ χ01χ03 0.668 · 10−2qiq̄j −→ χ01χ04 0.811 · 10−3qiq̄j −→ χ02χ02 0.362 · 10−2qiq̄j −→ χ02χ03 0.189 · 10−1qiq̄j −→ χ02χ04 0.843 · 10−3qiq̄j −→ χ03χ03 0.119 · 10−4qiq̄j −→ χ03χ04 0.429 · 10−1qiq̄j −→ χ04χ04 0.692 · 10−4qiq̄j −→ χ01χ+1 0.880 · 10−1qiq̄j −→ χ01χ−1 0.540 · 10−1qiq̄j −→ χ01χ+2 0.413 · 10−2qiq̄j −→ χ01χ−2 0.218 · 10−2qiq̄j −→ χ02χ+1 3.60

process crosssection [pb]qiq̄j −→ χ02χ−1 2.11qiq̄j −→ χ02χ+2 0.144 · 10−1qiq̄j −→ χ02χ−2 0.764 · 10−2qiq̄j −→ χ03χ+1 0.267 · 10−1qiq̄j −→ χ03χ−1 0.141 · 10−1qiq̄j −→ χ03χ+2 0.587 · 10−1qiq̄j −→ χ03χ−2 0.283 · 10−1qiq̄j −→ χ04χ+1 0.156 · 10−1qiq̄j −→ χ04χ−1 0.823 · 10−2qiq̄j −→ χ04χ+2 0.696 · 10−1qiq̄j −→ χ04χ−2 0.333 · 10−1qiq̄j −→ χ+1 χ−1 2.90qiq̄j −→ χ+1 χ−2 0.113 · 10−1qiq̄j −→ χ−1 χ+2 0.113 · 10−1qiq̄j −→ χ−2 χ+2 0.571 · 10−1

Table A.1: Cross-sections of gaugino pair production at LM9. FromProspino [19].

67

Decays of χ02 [br]0.033 χ01 e− e+0.033 χ01 µ− µ+0.032 χ01 τ− τ+0.066 χ01 νe ν̄e0.066 χ01 νµ ν̄µ0.066 χ01 ντ ν̄τ0.154 χ01 d d̄0.154 χ01 s s̄0.157 χ01 b b̄0.119 χ01 u ū0.119 χ01 c c̄

Decays of χ+(−)1 [br]0.111 χ01 e+ νe0.111 χ01 µ+ νµ0.111 χ01 τ+ ντ0.334 χ01 d̄ u0.334 χ01 s̄ c

Decays of χ03 [br]0.223 χ01 Z00.033 χ01 h00.108 χ02 Z00.318 χ+1 W−0.318 χ−1 W+

Decays of χ04 [br]0.050 χ01 Z00.085 χ01 h00.027 χ02 Z00.080 χ02 h010−6 χ03 νe ν̄e10−6 χ03 νµ ν̄µ10−6 χ03 ντ ν̄τ10−6 χ03 d d̄10−6 χ03 s s̄10−6 χ03 b b̄10−6 χ03 u ū10−6 χ03 c c̄0.378 χ+1 W−0.378 χ−1 W+

Decays of χ+2 (χ−2 ) [br]0.284 χ+1 Z00.117 χ+1 h00.096 χ01 W+0.503 χ02 W+10−6 χ03 e

+ νe10−6 χ03 µ

+ νµ10−6 χ03 τ

+ ντ10−6 χ03 d̄ u10−6 χ03 s̄ c

Table A.2: Decays of gauginos, branching ratios.

68 APPENDIX A.

Decays of Z0 [br]0.154 d d̄0.119 u ū0.154 s s̄0.119 c c̄0.152 b b̄0.034 e− e+0.067 νe ν̄e0.034 µ− µ+0.067 νµ ν̄µ0.034 τ− τ+0.067 ντ ν̄τ

Decays of W +(−) [br]0.321 d̄ u0.017 d̄ c0.017 s̄ u0.321 s̄ c0.000 b̄ u0.001 b̄ c0.108 e+ νe0.108 µ+ νµ0.108 τ+ ντ

Decays of h0 [br]10−6 d d̄0.000 s s̄0.036 c c̄0.721 b b̄0.000 µ− µ+0.087 τ− τ+0.050 g g0.006 γ γ0.001 γ Z00.009 Z0 Z00.089 W + W−

Table A.3: Decays of Z0, W± and h0, branching ratios.

69

branching ratios χ040.402086 χ04 −→ χ01 4 q 0 l 0 ν0.112415 χ04 −→ χ01 2 q 1 l 1 ν0.112319 χ04 −→ χ01 2 q 0 l 1 ν0.111477 χ04 −→ χ01 2 q 1 l 3 ν

0.111 χ04 −→ χ01 2 q 0 l 0 ν

branching ratios χ030.341491 χ03 −→ χ01 4 q 0 l 0 ν0.186306 χ03 −→ χ01 2 q 0 l 0 ν

0.0939097 χ03 −→ χ01 2 q 1 l 1 ν0.0938293 χ03 −→ χ01 2 q 0 l 1 ν0.0934741 χ03 −→ χ01 2 q 1 l 3 ν

branching ratios χ020.703854 χ02 −→ χ01 2 q 0 l 0 ν0.197837 χ02 −→ χ01 0 q 0 l 2 ν0.032981 χ02 −→ χ01 0 q 2 l 4 ν0.032981 χ02 −→ χ01 0 q 2 l 0 ν

branching ratios χ+,−10.668284 χ+,−1 −→ χ01 2 q 0 l 0 ν0.110608 χ+,−1 −→ χ01 0 q 1 l 3 ν0.110608 χ+,−1 −→ χ01 0 q 1 l 1 ν0.110499 χ+,−1 −→ χ01 0 q 0 l 1 ν

branching ratios χ±20.431609 χ±2 −→ χ01 4 q 0 l 0 ν0.105677 χ±2 −→ χ01 2 q 0 l 2 ν

0.0933937 χ±2 −→ χ01 2 q 0 l 0 ν0.0701438 χ±2 −→ χ01 2 q 1 l 3 ν0.0701438 χ±2 −→ χ01 2 q 1 l 1 ν

Table A.4: branching ratios of the main decay channels for each gaugino.q includes all quarks and their antipartner excepting t and t̄. l incudes allleptons and their antpartners excepting τ and τ̄ . ν includes all 6 neutrinos.

70 APPENDIX A.

branching ratios χ±1 χ±10.45 χ±1 χ±1 −→ 2 χ01 4 q 0 l0.30 χ±1 χ±1 −→ 2 χ01 2 q 1 l

branching ratios χ±2 χ±20.23 χ±2 χ±2 −→ 2 χ01 6 q 0 l0.19 χ±2 χ±2 −→ 2 χ01 8 q 0 l

branching ratios χ04χ040.20 χ04χ04 −→ 2 χ01 6 q 0 l0.18 χ04χ04 −→ 2 χ01 6 q 1 l



branching ratios χ±1 χ010.67 χ±1 χ01 −→ 2 χ01 2 q 0 l0.22 χ±1 χ01 −→ 2 χ01 0 q 1 l











branching ratios χ±2 χ±10.29 χ±2 χ±1 −→ 2 χ01 6 q 00.23 χ±2 χ±1 −→ 2 χ01 4 q 0




Table A.5: branching ratios of the main decay channels for each gaugino-pair. q includes all quarks and their antipartner excepting t and t̄. l incudesall leptons and their antpartners excepting τ and τ̄ .

71

pt(Muon) [di-muon] > 3[single muon] > 14

pt(Electron) [di-electron] > 12[single electron] > 23

pt(Photon) [di-photon] > 12[single photon] > 23

pt(Jet) [4 jets] > 51[3 jets] > 71[2 jets] > 101[1 jets] > 151

MET > 61HT [Σpt(j(pt> 30), e, µ)+MET] > 301HT, MET > 201, > 41pt(Jet), MET > 101, > 41pt(Muon), MET > 5, > 31pt(Electron), MET > 16, > 31pt(Photon), MET > 16, > 31pt(Muon), pt(Jet) > 7, > 101pt(Electron), pt(Jet) > 16, > 101pt(Photon), pt(Jet) > 16, > 101pt(Electron), pt(Muon) > 16, > 7pt(Photon), pt(Muon) > 16, > 7

Table A.6: L1 trigger values, all in [GeV]. From [20]

72 APPENDIX A.

nEvents nJets nElectrons nMuons nPhotonsSIGNAL 50005 156020 11651 11251 128989triggered 25314 88041 8880 10040 88803Efficiency 0.51 0.56 0.76 0.89 0.69Effev/Effpart 1 1.10 1.49 1.75 1.35tt̄ 890088 5027984 503258 476209 6438133triggered 828452 4702142 485832 466459 6155701Efficiency 0.93 0.94 0.97 0.98 0.96Effev/Effpart 1 1.01 1.04 1.05 1.03Zjets 1320132 2248277 124367 120940 1064389triggered 83346 203230 40592 77944 99211Efficiency 0.06 0.09 0.33 0.64 0.09Effev/Effpart 1 1.5 5.5 10.67 1.5W+jets 1338455 2765565 116151 111539 1226401triggered 167256 333892 68991 85798 140076Efficiency 0.13 0.12 0.59 0.77 0.11Effev/Effpart 1 0.92 4.54 5.92 0.85

Table A.7: Trigger efficiency on the particle numbers for signal and back-ground.

Bibliography

[1] Martin Niegel, diploma thesis: Untersuchung der 3-Lepto

analysis of the inclusive gaugino pair channel at the cms ...thesis/data/iekp-ka2008...ppp...

Documents