Search for scalar muonswith the L3 detectorat ps = 183GeVAnne PohlHumboldt University Berlin30.12.19981AbstractA search for scalar muons in a supersymmetric model with gauge mediatedsupersymmetry breaking has been performed. All possible decay channelsof the smuons have been analysed. For the analysis data collected with theL3 detector in 1997 at ps = 183GeV center of mass energy with anintegrated luminosity of L = 55:46 pb�1 has been used. No evidence forsuch particles has been found. Therefore upper limits on their productioncross section on lower bounds on their mass have been set.

1Diplomarbeit; revised version

2

Contents1 Theoretical Introduction 31.1 The Standard Model of Particle Physics . . . . . . . . . . . . 31.2 Motivation for Physics beyond the Standard Model . . . . . . 41.3 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Gauge Mediated Supersymmetry Breaking . . . . . . . . . . . 91.5 Phenomenology of GMSB Models . . . . . . . . . . . . . . . . 141.5.1 Neutralino NLSP scenario . . . . . . . . . . . . . . . . 151.5.2 Neutralino-Stau co-NLSP scenario . . . . . . . . . . . . 151.5.3 Slepton co-NLSP scenario . . . . . . . . . . . . . . . . 161.5.4 Stau NLSP scenario . . . . . . . . . . . . . . . . . . . 172 The L3 Experiment 192.1 The LEP ring . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2 The L3 detector . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.1 The Central Track Detector . . . . . . . . . . . . . . . 222.2.2 The Calorimeter System . . . . . . . . . . . . . . . . . 242.2.3 The Scintillation Counters . . . . . . . . . . . . . . . . 272.2.4 The Luminosity Monitor . . . . . . . . . . . . . . . . . 272.2.5 The Muon Filter . . . . . . . . . . . . . . . . . . . . . 272.2.6 The Muon Spectrometer . . . . . . . . . . . . . . . . . 282.3 Trigger and Data Acquisition . . . . . . . . . . . . . . . . . . 302.4 Event Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 312.4.1 Event Generators for the SM Processes . . . . . . . . . 312.4.2 SUSYGEN - The Signal Event Generator . . . . . . . . 322.4.3 Event Simulation and Reconstruction . . . . . . . . . . 323 Analysis 353.1 Signal and Background . . . . . . . . . . . . . . . . . . . . . . 353.2 Preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.3 Cut Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.3.1 Distributions and Cuts . . . . . . . . . . . . . . . . . . 471

2 CONTENTS3.3.2 Optimization . . . . . . . . . . . . . . . . . . . . . . . 503.4 Limits on the number of produced smuons . . . . . . . . . . . 574 Analysis with a Neural Net 634.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.2 A Neural Net Selection for Smuon Search . . . . . . . . . . . . 674.2.1 Analysis of scenario 1 and 2 . . . . . . . . . . . . . . . 704.2.2 Analysis of scenario 3 . . . . . . . . . . . . . . . . . . . 704.2.3 Application to the data . . . . . . . . . . . . . . . . . . 725 Results 755.1 Cross Section and Mass Limits . . . . . . . . . . . . . . . . . . 755.2 Estimation of uncertainties . . . . . . . . . . . . . . . . . . . . 825.3 Interpretation of the results . . . . . . . . . . . . . . . . . . . 835.4 Comparison with other results . . . . . . . . . . . . . . . . . . 845.5 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . 85A Listing 91

Chapter 1Theoretical Introduction1.1 The Standard Model of Particle PhysicsOur today's understanding of the fundamental constituents of matter andtheir interactions is described by a very successful theory, the so called Stan-dard Model of electroweak and strong interactions [1]. It is based on theidea, that all matter is composed of fermions, and the interactions betweenthem are mediated by bosons.In the Standard Model the fermions are structured in three families (genera-tions) which di�er only in the masses of their members. Each family containsone quark doublet and one lepton doublet, as it can be seen from table 1.1.In addition, every particle is accompanied by an antiparticle that has exactlyFERMIONS BOSONS1st 2nd 3rd charge force boson massleptons �e �� �� 0 strong g 0e � � -1 weak Z0 91 GeVquarks u c t 23 W� 80 GeVd s b -13 elmgn. 0Table 1.1: The elementary particles of the Standard Modelthe same properties but the opposite charge.Most matter of the universe is composed of the fermions of the �rst genera-tion. The other fermions can be produced with large concentration of energyin a small volume (e.g. with large particle colliders) but they decay into the�rst generation fermions within a split second (except the neutrinos whichare stable within our today's knowledge).3

4 CHAPTER 1. THEORETICAL INTRODUCTIONFour forces (the electromagnetic, weak and strong force and the gravitation)allow interactions between fermions by exchanging the corresponding bosons:the photon, the heavy Z0 andW� bosons, the gluons and the graviton (whichis not yet discovered).The Standard Model describes the interactions of the three generations ofquarks and leptons de�ned by a non-Abelian gauge theory based on thegroup SU(3)C � SU(2)L � U(1)Y . Since there is no theory at all for thegravitation which is orders of magnitude weaker than the other three forces(at least for energies small compared to the Planck scale), gravitational in-teractions are not included in the Standard Model.One of the main open questions in the Standard Model is the origin of thefermion and boson masses. In principle gauge theories can only describe theexchange of massless gauge bosons since otherwise the gauge invariance isbroken [2]. The appearance of a non-zero mass of the electroweak gaugebosons Z0 and W� therefore implies electroweak symmetry breaking.The simplest mechanism for the breaking of the electroweak symmetry isrealized in the Standard Model. To accomodate all observed phenomena, acomplex isodoublet scalar �eld is introduced which, through self-interactions,spontaneously breaks the electroweak symmetry SU(2)L�U(1)Y down to theelectromagnetic U(1)EM symmetry, by acquiring a non-vanishing vacuum ex-pectation value. After the electroweak symmetry breakdown, the interactionsof the gauge bosons and fermions with the isodoublet scalar �eld (Yukawainteractions) generate the masses of these particles. In this process (the socalled Higgs mechanism), one scalar �eld remains in the spectrum, manifest-ing itself as a new physical particle still to be discovered, the Higgs boson H.1.2 Motivation for Physics beyond the Stan-dard ModelThe precision measurements at LEP (the Large Electron Positron collider atCERN, see chapter 2) have given an extraordinary con�rmation of the valid-ity of the Standard Model up to the electroweak energy scale and there areno experimental indications for failures of this theory at energies above thatscale. Our believe that the Standard Model is a low-energy approximationof a new fundamental theory is based only on theoretical but well-motivatedarguments.First of all the electroweak symmetry breaking sector is not on �rm exper-imental grounds. The understanding of the mechanism responsible for the

1.3. SUPERSYMMETRY 5breakdown of the electroweak symmetry is one of the central problems inparticle physics. If the fundamental particles { leptons, quarks and gaugebosons { remain weakly interacting up to high energies, then the sector inwhich the electroweak symmetry is broken must contain one or more fun-damental Higgs bosons with masses of the order of the symmetry breakingscale (� 174GeV). Alternatively the symmetry breaking could be generateddynamically by novel strong forces at a scale � 1TeV.From the theoretical point of view the Higgs mechanism su�ers from the socalled hierarchy or naturalness problem [3] which leads us to believe that newphysics must take place at the TeV energy scale:If the Standard Model is embedded in a Grand Uni�ed Theory (GUT)[4] at high energies, then the natural scale of the electroweak symmetrybreaking would be close to the uni�cation scale of the gauge couplings,MGUT � 1016GeV, due to the quadratic nature of the radiative corrections tothe Higgs mass (fermion loops) of the order MP lanck which result in instablemasses in the electroweak sector. This hierarchy problem is considered to beone of the most serious drawbacks of the Standard Model and most of theattempts to build theories beyond the Standard Model have concentrated onits solution. It results from the di�culty in quantum �eld theory in keepingfundamental scalar particles much lighter than the maximum energy scaleup to which the theory remains valid.Furthermore, the complexity of the fermionic and gauge structures makesthe Standard Model look like an improbable fundamental theory: It con-tains many free parameters (e.g. the three gauge coupling constants, thenine fermion masses and the four Cabbibo-Kobayashi-Maskawa mixing pa-rameters) which correspond to important physical quantities but cannot becomputed in the context of the model. Simplifying the Standard Modelstructure and predicting its free parameters are therefore basic tasks of asuccessful theory.1.3 SupersymmetrySupersymmetry [5, 6] represents the best motivated known extension of theStandard Model. It o�ers an elegant solution to the hierarchy problem of theHiggs sector and it is consistent with present experimental data. Certainlyit predicts new particles to be discovered in this generation of collider exper-iments.Supersymmetry transforms bosons to fermions and vice versa. This meansthat bosons and fermions sit in the same supersymmetric multiplet. In thesimplest version of supersymmetry (the so called N = 1 SUSY), each Stan-

6 CHAPTER 1. THEORETICAL INTRODUCTIONdard Model particle is accompanied by exactly one supersymmetric partnerwhich di�ers in spin by half a unit: scalar particles (with spin 0) are thepartners of quarks and leptons, and fermion particles (with spin 12) are thepartners of the Standard Model bosons. Similarly the spin-2 graviton has aspin-32 companion, the gravitino.Each lepton and quark has two scalar partners, one for each chirality state,'left' and 'right', which have di�erent interactions in the Standard Model.The scalar mass eigenstates are given by mixtures of the two 'left' and 'right'states. The squark and slepton mixing angles and masses are in generalfree parameters of the theory. But as mixings among the two slepton statesare assumed to be proportional to the corresponding lepton masses in theslepton mass matrix1, ~�L;R and ~eL;R are approximately mass eigenstates. Ingeneral, the right-handed sleptons are expected to be lighter than the left-handed sleptons. Since a non-trivial mixing between the two ~� states can beexpected, especially for large tan � (see below), the lighter stau is no longera pure right-handed state but a mixing state called ~�1.Supersymmetry requires two Higgs doublets, as opposed to the singleHiggs doublet of the Standard Model and therefore an extended spectrum ofphysical Higgs particles. The two doublets are necessary to generate massesfor up- and down-type fermions in a supersymmetric theory. Each Higgsdoublet has one vacuum expectation value and the ratio between the up anddown type Higgs vacuum expectation values is called tan�. Out of the eightdegrees of freedom of the two complex doublets, three are eaten in the Higgsmechanism (and give a mass to the Z0 andW� particles) and �ve correspondto physical particles. These form two real CP2-even scalars (h, H), one realCP-odd scalar (A), and two complex scalars (H�). All tree-level3 massesand gauge couplings of the �ve Higgs particles are completely described bytwo parameters (e.g. MH� and tan�).Supersymmetry provides a solution to the hierarchy problem by stabiliz-ing the Higgs mass parameter due to the cancellation of radiative correctionsfrom fermionic and bosonic loops when the masses of bosons and fermionsare of the same order. It also predicts the existence of a Higgs boson lighterthan the Z0. The mass of the lightest Higgs is bounded to bemh < MZ j cos 2� j : (1.1)1and therefore proportional to the corresponding Yukawa couplings2The CP operator transforms left (right)-handed particles to right (left)-handed an-tiparticles and vice versa.3lowest order

1.3. SUPERSYMMETRY 7Radiative corrections to mh can shift the upper limit to at most 150GeV [7]for extreme values of the parameters.The supersymmetric model is consistent with electroweak symmetry break-ing. This is obtained by the Super-Higgs mechanism. Generally, the e�ectof gauge interactions is to increase the masses as we evolve from MGUT toMW . Therefore, if all masses are equal at MGUT , one expects gluinos to beheavier than charginos and neutralinos (see below), and similarly squarksto be heavier than sleptons, because of the dominant QCD e�ects. On theother hand, Yukawa interactions decrease the masses in the renormalizationfrom high to low energies. Therefore, the stops will be the lightest amongthe squarks, since the top quark coupling gives the dominant Yukawa e�ect.After electroweak symmetry breaking, the fermionic partners of the Higgsparticles mix with the fermionic partners of the electroweak gauge bosons toproduce particles with one unit of electric charge (charginos) or no electriccharge (neutralinos).Invariance under supersymmetry implies that particles inside a supermul-tiplet are degenerate in mass. In nature, supersymmetry is obviously not anexact symmetry and must be broken. The scale, at which this happens, hasa de�nite physical meaning, since all new supersymmetric particles acquiremasses of the order of this scale. It is this energy scale at which supersym-metry has to be looked for in experiments. If supersymmetry shall solve thehierarchy problem the new particles cannot be much heavier than the TeVscale, since otherwise the cancellation mechanism for the Higgs mass due tobosonic loops cannot work.Supersymmetry ensures that the couplings of all the new particles are strictlyrelated to ordinary couplings. Therefore the supersymmetric generalizationof the Standard Model is a well de�ned theory where all new interactionsare described by the mathematical properties of the supersymmetric trans-formation in dependence on the considered parameter space.It should also be mentioned that when supersymmetry is promoted toa local symmetry, which means that the transformation parameter dependson space-time, then the theory automatically includes gravity and is calledsupergravity. Because of this characteristic supersymmetry is believed to bea necessary ingredient for the complete uni�cation of forces.Assuming that supergravity is either spontaneously or dynamically brokenin a sector of the theory that does not directly couple to ordinary particles(hidden sector), gravity communicates the supersymmetry breaking.However, since the mechanism which breaks supersymmetry is not yetknown there is no possibility to compute the soft SUSY breaking terms in

8 CHAPTER 1. THEORETICAL INTRODUCTIONthe supersymmetric lagrangian4 and therefore the mass spectrum of the newparticles. This means that the number of free parameters is quite large.The simplest model available is the Minimal Supersymmetric StandardModel (MSSM [9]). It is de�ned as the supersymmetric extension of theStandard Model which contains the minimal number of new particles and in-teractions that are consistent with the Standard Model gauge group. In theMSSM, with Grand Uni�cation assumption (constraint MSSM), the massesand couplings of the gauginos and of the SUSY particles as well as their pro-duction cross sections, are entirely described once �ve parameters are �xed:tan � (the ratio between the up (Hu) and down (Hd) type Higgs vacuum ex-pectation values), M (the gaugino mass parameter), � (the higgsino mixingparameter), m0 (the common mass for scalar fermions at the GUT scale) andA (the trilinear coupling in the Higgs sector).The most important feature of supersymmetric phenomenology is theexistence of a discrete symmetry, called R-parity:R = (�1)3(B�L)+2S : (1.2)Here B is the baryon number, L is the lepton number, and S is the spin.This symmetry distinguishes ordinary particles (R = 1) from their super-partners (R = �1) but it is not an automatic consequence of supersymmetryand gauge invariance. R-parity conservation means that B � L is conservedbut not necessarily each, B and L alone. If R-parity is indeed conserved{ which is considered in this analysis { only an even number of particlescan appear in each interaction. As a consequence, sparticles are produced inpairs and the lightest supersymmetric particle (LSP) is stable. From cosmo-logical arguments on particle relic abundance it follows that the LSP mustbe a neutral and only weakly interacting particle.In most of the models, this stable particle turns out to be the lightest neu-tralino ~�01. A stable neutral particle is allowed by present searches and evenwelcome since it might explain the presence of dark matter in the universe.From the point of view of collider experiments the LSP will behave like aheavy neutrino which escapes the detector, leaving unbalanced momentumand missing energy in the observed event.4The most general supersymmetric Lagrangian is [8]:L = Lgauge + Lkin + LY ukawa + L� + Lsoft, where the �rst three terms contain onlyStandard Model parameters, the fourth term L� contains the new parameter � explainedbelow and Lsoft contains the many new SUSY breaking parameters.

1.4. GAUGE MEDIATED SUPERSYMMETRY BREAKING 91.4 Gauge Mediated Supersymmetry BreakingIf nature is indeed supersymmetric, it is important to understand the mech-anism by which SUSY breaking occurs and is transmitted to the particles ofthe Standard Model and their superpartners. One possibility is that SUSYis broken in a hidden sector at a scale of around 1011GeV and communicatesto the observable sector only via gravitational interaction. Models with thiskind of SUSY breaking are called supergravity models (SUGRA). However,since gravity is avour blind, this scenario has a major problem involvingavour changing neutral currents [10]. This can be avoided if SUSY is bro-ken at a relatively low scale of � 105GeV and the messengers of the SUSYbreaking are the ordinary SU(3)C�SU(2)L�U(1)Y gauge interactions. Thiskind of SUSY breaking models are called Gauge Mediated SupersymmetryBreaking (GMSB) models.GMSB models can be constructed out of six parameters [11]: M;� and n,� and tan �, and pF . M is the messenger scale (104 : : : 109GeV), � is theuniversal sparticle mass scale, and n is the number of messenger pairs whichis �xed by the choice of the messenger sector. These three parameters ap-pear in the messenger sector and therefore they are relevant for the scaleand structure of the model. The parameter tan� is the ratio of the vacuumexpectation values of the two Higgs doublets and the parameter � is thecoe�cient in the bilinear (mass) term in the superpotential, �HuHd. Thesetwo parameters appear in the Higgs sector and therefore they are relevantafter the electroweak symmetry breaking. The �fth parameter, pF , is thefundamental SUSY breaking scale.Sometimes another parameter is used that can be reconstructed out of theothers: F , the SUSY breaking scale felt by the messenger particles. For thisparameter the following relation holds:pF > pF > � with F = � �M: (1.3)In a theory which is only globally supersymmetric (i.e. without gravity)the spontaneous breaking of SUSY generates a massless neutral spin-12 par-ticle, the goldstino. If gravity is introduced, so that SUSY is realized locally,the goldstino is eliminated while the gauge sparticle { the gravitino { acquiresa mass and longitudinal helicity components. This is known as the Super-Higgs mechanism. The massive gravitino has �32 as well as �12 helicity states.The interactions of the gravitino can be seen as gravitational ones. Thereforethe chances of detecting the e�ects of the gravitino in particle physics mayseem, at �rst, very remote. But it is not so if the gravitino mass is very smallsince here the gravitational type interactions transmute into weak type inter-actions. In fact, the continuous limit of local SUSY, when gravity is turned

10 CHAPTER 1. THEORETICAL INTRODUCTIONo�, is a spontaneous broken global SUSY. Then the gravitino mass vanishesand the �12 helicities of the very light gravitino behave as the goldstino ofthe globally supersymmetric theory (high energy limit) [12].Since gravity is so weak, only the longitudinal component of the gravitinointeracts5. This �12 helicity component { the goldstino { couples to matterwith strength � 1F . The resulting gravitino mass ism ~G = Fp3M (1.4)where M = (8�)�1=2 = 2:4 � 1018GeV is the reduced Planck mass and thenewtonian gravitational constant. To be relevant for GMSB the fundamentalscale of supersymmetry breaking must satisfy the relation 10TeV < pF

1.4. GAUGE MEDIATED SUPERSYMMETRY BREAKING 11For searches at LEP2 only masses of the NLSP less than 100GeV are relevant.For the neutralino NLSP the decay mode into photon and gravitino (see�gure 1.5) is always dominant. (Even if the decay modes into the Z0 bosonor the neutral Higgs boson are kinematically allowed, they are suppressed bya phase-space factor.) The width of the neutralino decay is given by�(~�01 ! ~G) = � m5~�0116�F2 = � �( ~f ! f ~G); (1.7)where � is a factor which depends on the neutralino contents. Since theratio �=M is typically larger than one the neutralino NLSP has a dominantBino6 component [14], which will be assumed in the following.Since the decay length L = c� scales with F2 a measurement of L is a directmeasurement of SUSY breaking in the hidden sector. The determination ofsuperpartner decay chains depends crucially on the di�erences between m~�01 ,m~�1 and m~lR , with l = e or �, as explained in the next section.In general, if m ~G could be arbitrary small compared to the superpartnermasses, then all decays of supersymmetric particles could proceed directly tothe corresponding Standard Model particle and a gravitino. However, takinginto account the lower bounds on the gravitino mass as mentioned before,the decay width for non-NLSP sparticles should be quite small and thereforenegligible.In the following the gravitino is always assumed to be light enough that thedecay length of the NLSP is of the order O(�m) and smaller (prompt decay).Otherwise the NLSP decay could be seen as a kink or not at all, if the NLSPdecays outside the detector, but these cases shall not be studied within thiswork.Since the sleptons can be quite light in GMSB models (especially asNLSP) their production could be possible at present center of mass energies.In addition the cross section for ~�+R ~��R production at LEP2 (see chapter2) as a function of the ~�R mass is model independent, since this processhappens through s-channel exchange of or Z0 (see �gure 1.1). Identicalarguments hold for the ~�R, in the limit of vanishing left-right mixing. For~e+R ~e�R pair production there is a destructive interference of s-channel andt-channel (with ~�0 exchange, see �gure 1.2) so that the cross section can besigni�cantly smaller than the one for smuon pair production. In the worstcase (and if m~lR < ps� 20GeV) the ~eR cross section is much lower.The dependence of the smuon pair production cross section on the smuon6The Bino is the supersymmetric partner �eld of the Standard Model vector �eld B�.

12 CHAPTER 1. THEORETICAL INTRODUCTION

�

e�

e+

~l�R

~l+R

Figure 1.1: Slepton pair production in the s-channel for ~�R , ~�R and ~eR. ThisFeynman graph is also possible with Z0 exchange.

�~�0

e�

e+

~e�R

~e+R

Figure 1.2: Pair production of ~eR in the t-channel

1.4. GAUGE MEDIATED SUPERSYMMETRY BREAKING 13mass as well as on the center of mass energy can be seen in �gure 1.3. Takinginto account the better detection e�ciency for muons than for taus smuonpair production would be the discovery process for sleptons and thereforeshall be studied in this thesis.

Figure 1.3: Smuon pair production cross section as a function of m~�R fore+e� collisions at (from left to right) ps = 130,136,161,172 (solid lines)and 185,190,195,200GeV (dashed lines) (from [15])

14 CHAPTER 1. THEORETICAL INTRODUCTION'

&

$

%

GMSB Phenomenology: Scenarios ! MessengersNecessary conditions on GMSB parameter space for di�erent scenarios:Nm = 1 Nm = 2 Nm = 3 Nm = 42 5 10 50

tan β

10

100

Λ [

TeV

]

(A) neutralino NLSP

2 5 10 50tan β

10

100

Λ [

TeV

]

(B) stau NLSP

2 5 10 50tan β

10

100

Λ [

TeV

]

(C) slepton co−NLSP

2 5 10 50tan β

10

100

Λ [

TeV

]

(D) neutralino−stau co−NLSP

(A) Neutralino NLSP (B) Stau NLSP(C) Slepton co-NLSP (D) Neutralino-Stau co-NLSP

? Figures refer to light superpartners (w/in LEP2 reach):present limits � 70-80 GeV

1.5. PHENOMENOLOGY OF GMSB MODELS 15� ~�1 ! � ~Gis dominant. In the following each scenario will be described in more detail.1.5.1 Neutralino NLSP scenario�

~�01

~��

~G

Figure 1.5: Feynman graph for the decay of a scalar muon ~�R in the neu-tralino NLSP scenarioIt is found (see �gure 1.4 (A)), that for models with one to three pairs ofmessenger �elds n and for small to intermediate values of tan � (tan � < 25),the lightest neutralino ~�01 is the NLSP. Here the mass ordering ism~�01 < m~�1 +m� : (1.8)In the neutralino NLSP scenario all sparticle decays will terminate in ~�01 ! ~G.For the decay of pair produced scalar muons (see �gure 1.5) this leads tothe signature �+��

E= 7, since the gravitinos escape undetected, carryingaway energy and momentum. Here the branching fractions of ~�! �~�01 and~�01 ! ~G are always 100% and the lifetime of the neutralino is short enoughthat the decay happens at the vertex (prompt decay, see above).1.5.2 Neutralino-Stau co-NLSP scenarioIf the neutralino and the stau are nearly degenerate in mass (that meanstheir mass di�erence is less than m� ) and if the neutralino is lighter thanselectron and smuon, ~�01 and ~�1 act as co-NLSP's. The parameter space forthis scenario can be seen from �gure 1.4 (D).7E= = missing energy

16 CHAPTER 1. THEORETICAL INTRODUCTIONFor scalar muon searches no di�erence to the signatures of the neutralinoNLSP scenario can be seen. Therefore for the analysis both scenarios will betreated as one.1.5.3 Slepton co-NLSP scenario

�~�

~G

�

Figure 1.6: Smuon decay in the slepton co-NLSP scenarioFor larger multiplicities of messenger �elds (n � 2) and if tan� is not toolarge (tan � � 8) (see �gure 1.4 (C)) the ~� mixing is small and the ~�R � ~�1is the NLSP.In the case that ~�1, ~�R and ~eR are lighter than all other sparticles and nearlydegenerate in mass, m~eR � m~�R < m~�1 +m� ; (1.9)the three sleptons act as co-NLSP's, all decaying directly into a gravitino andthe corresponding Standard Model partner lepton. The branching fraction ofthis decay is 100% (at least if the decay takes place inside the detector [16] {an assumption which is made in this analysis) and the resulting leptons arehighly energetic.There can also be competing three body decays ~lR ! �l��� ~�1 through o�-shellcharginos (~��i ) but the width is always less than about 10�7 eV for ~�R (and~�1) decays and more than four orders of magnitude smaller for the ~eR decays,corresponding to a physical decay length of (at least) a few meters [14]. Sothese decays do not play a role in collider phenomenology in slepton co-NLSPmodels.The signature of pair produced smuons ~�R decaying in this model is �+�� E=(see �gure 1.6).

1.5. PHENOMENOLOGY OF GMSB MODELS 171.5.4 Stau NLSP scenario

�~�01

~�~��

~G��

Figure 1.7: Feynman graph for the ~�R decay in the stau NLSP scenarioThis scenario can be constructed if n = 1 and tan � > 25. For highermultiplicities of messenger pairs (n > 2), ~�1 becomes the NLSP for most ofthe parameter space (see �gure 1.4 (B)).Since tan� exceeds 4 : : : 8 the ~� mixing becomes large and the ~�1 mass smallenough that the decay ~lR ! ~�1� l through o�-shell neutralinos is kinematicallyallowed. The physical decay length for the three body decay of ~lR can oftenbe quite large if �m = m~lR � m~� � m� is less than a few GeV and/or theratio m~�01=m~lR is large [16] (see also �gure 1.8). If the three body decays of~�R and ~eR dominate, which is the case when the Bino contents of ~�01 is high8[15], the l and � emitted in the decay can be quite soft, if �m is small.It is also important to realize that the dominant decay for ~lR is dependenton the parameter space, since the three body decays have to compete withthe two body decays into a gravitino with the width given in formula 1.5.As a consequence the search for smuons should concentrate on the signature�+���+���+�� E= (see �gure 1.7).8this is assumed here, as already mentioned

18 CHAPTER 1. THEORETICAL INTRODUCTION

Figure 1.8: The decay width in meV for ~eR ! ~�1�e (solid lines) and ~�R !~�1�� (dashed lines) as a function of �m = m~lR�m~��m� with m~lR = 90GeVand m~�01=m~lR = 1.1, 1.5, 2.0 and 3.0 (from top to bottom) and a Bino-like(see former footnote) neutralino (from [16]). For comparison: the two bodydecay width is �(~�R ! � ~G) � 10�3meV.

Chapter 2The L3 Experiment2.1 The LEP ringThe Large Electron Positron ring LEP (see �gure 2.1), situated at the euro-pean laboratory for particle physics (CERN), is located in a 26:7 km circum-ference tunnel underneath the Swiss-French border near Geneva. The tunnelconsists of eight circle segments and eight straight sections.At a depth between 50 and 150m up to eight bunches of electrons andpositrons circulate, in opposite directions, in the same vacuum vessel keptin the orbit by dipole magnets. In addition the bunches are steered ontotheir required trajectories with focusing quadrupole and sextupole magnets.The beams collide at four interaction points in the straight sections wherethe vertical extension of the beam is � 20�m and the horizontal extension� 200�m. Four experiments ALEPH [17], DELPHI [18], L3 [19] and OPAL[20] are placed around the interaction points. To forestall a beam collision atthe remaining four possible interaction points electrostatic separators dividethe beams in the other four straight sections.The LEP ring was designed to study e+e� collisions in an energy range be-tween the Z0 mass (LEP1) and 200GeV (LEP2). Since there is no possibilityto accelerate particles from zero up to those energies in one ring a complexpreaccelerator system consisting of linear accelerators and smaller accelera-tor rings is necessary before the electrons and positrons are injected into theLEP ring and accelerated to their nominal energy. Due to the curvature ofthe electron and positron trajectories the particles loose energy. This syn-chrotron radiation is proportional to the fourth power of the particle energyand inversely proportional to the fourth power of the particle mass. The lat-ter dependence is the reason for the high energy loss of electron acceleratorsin contradiction to a proton accelerator. The lost energy has to be replaced19

20 CHAPTER 2. THE L3 EXPERIMENTPOINT 4.

LAKE GENEVA GENEVA

CERN Prévessin

POINT 6.

POINT 8.

POINT 2.

CERN

SPS

ALEPH

DELPHI

OPAL

L3

LEP

e Electron -

+e Positron

R. Le

wi

jan. 1

990

sFigure 2.1: The LEP ring at CERNto preserve the desired beam energy. Both, the compensation and the accel-eration is done by cavities which were made of copper but are now replacedby more powerful super-conducting ones which are needed because of thehigher energy losses resulting from the higher center of mass energies. Inthat way the center of mass energy of e+e� annihilations has been increasedfrom the Z resonance in 1995 (LEP1) up to 183GeV in 1997 and will beincreased further up to � 200GeV at the end of the LEP program in theyear 2000 (LEP2). At these high energies it is possible to study not onlystandard model physics but also to search for new phenomena beyond thestandard model.2.2 The L3 detectorThe L3 experiment [21] is one of the four detectors at the LEP ring that allhave a cylindrical structure but use di�erent technologies for particle detec-tion.

2.2. THE L3 DETECTOR 21

e-

e+

Outer Cooling Circuit

Muon Detector

Silicon Det

ector

Vertex Det

ectorHadron C

alorimeter

DoorCro

wn

Barrel Yo

ke

Main Coil

Inner Cooling Circuit

BGO Calo

rimeter

Figure 2.2: View of the L3 detectorA perspective view of the L3 detector is shown in �gure 2.2.The L3 coordinate system is de�ned as follows: Its origin lies at the inter-action point in the center of the detector. The electron direction is signedas the z axis within the L3 coordinate system, the x direction points to thecenter of the LEP ring and the y direction points vertically upwards. Oftenspherical polar coordinates are used: then the x�y plane corresponds to ther � � plane and z is given by the polar angle �.The design of the L3 detector has been optimized towards a very accurateenergy and position measurement of muons, electrons and photons. Verticesand hadron jets are also studied. To achieve this L3 is divided into severalsubdetectors which surround the interaction point. All detector elements areinstalled inside a 12m inner diameter solenoid coil which is surrounded by aniron yoke and provides a magnetic �eld of 0:5Tesla along the beam axis. The�eld is relatively low but the volume is large and therefore the muon momen-tum resolution, which improves linearly with the �eld but quadratically withthe track length, has been optimized. In this magnetic �eld charged particles

22 CHAPTER 2. THE L3 EXPERIMENTmove on helicoidal trajectories along the symmetry axis of the beam direc-tion. From the helix curvature the particle momentum can be determined aswell as the charge (see section 2.2.6).Except for the muon system all subdetectors are installed in a steel supporttube of 32m length and 4:45m diameter. This tube is concentric with theLEP beam and symmetric with respect to the interaction point. Coming fromthere a particle crosses the following subdetectors which will be described inmore detail in the following subsections:� a silicon microvertex detector� a time expansion chamber� a Z chamber� an electromagnetic calorimeter� scintillation counters� a hadron calorimeter� a muon spectrometerMost of the L3 subdetectors consist of barrel elements around the beam pipeand endcap elements in the forward and backward direction to cover thepolar angle range as much as possible.2.2.1 The Central Track DetectorThe L3 central track detector is designed with the following goals:� detection of charged particles and precise measurement of the locationand direction of their tracks� determination of the momentum and the sign of the charge� reconstruction of the interaction point and of secondary verticesThese goals and the limited radially available space for the inner detectorwithin the electromagnetic calorimeter have determined its design (�gure2.3).

2.2. THE L3 DETECTOR 23The Silicon Microvertex Detector (SMD)The cylindrical SMD is directly surrounding the beam pipe. At a distance of6 cm and 8 cm from the interaction point two concentric layers of double sidedsilicon strip sensors measure the position of charged particles in cylindricalcoordinates r,� (at one side) and z (at the other side). The extension of theSMD in z direction is 30 cm and therefore it covers a polar angle range of22� < � < 158�. Traversing the SMD a charged particle produces electron-hole pairs along its path which create a short current pulse in the strips nearthe crossing path. The position measurement must be very precise for thedetermination of momenta and production vertices. The spatial resolution isin the order of 10�m in the r�� projection and of 25�m in the z projection.The Time Expansion Chamber (TEC)To extend the charged particle tracking over a lever arm a time extensionchamber (TEC) surrounds the SMD. It is a precise wire chamber for the posi-tion measurement which is made up of two concentric cylinders in a commongas �lled volume with a sensitive length of roughly 1m. The anode wireplanes are arranged at radial extensions from 9 cm to 46 cm forming 12 innerand 24 outer sectors. Following the TEC principle, the high �eld ampli�-cation region at the sense wire plane is separated from the low �eld driftregion by an additional grid wire plane. There are two types of sense wires:standard wires to measure precisely the r � � coordinates of the tracks andcharge division (CD) wires, which are read out on both sides, to determinethe z coordinates. Additionally, for a part of the standard wires in the outerTEC, groups of �ve grid wires on each side of the ampli�cation region areread out. Comparing the induced signals, the left-right ambiguity for theseanodes (LR wires) can be solved. These ambiguities occur because only thedrift distance, but not its direction can be determined. Each sector of theinner TEC includes six standard and two CD wires, the outer sectors include31 standard, 14 LR and 9 CD wires.The time between the beam crossing and the arrival time of the anode signalis converted into the distance at which the particle passed the anode wire.A precise calibration of the drift velocity is necessary to transform the timemeasurement into a position measurement. With 50 coordinate measure-ments a single wire resolution of � 50�m in the r � � plane is obtained.The Z ChamberThe z chamber measures the charged particle trajectories in the z directionadditionally to the SMD measurement at a radial distance of 47 to 49 cm over

24 CHAPTER 2. THE L3 EXPERIMENT{

GridAnodesGrid

CathodesZ chamber

Chargedparticletrack

SMD

InnerTEC

OuterTEC

Y

X

B

Figure 2.3: The L3 inner tracking systema length of 107 cm. The z chamber consists of two thin cylindrical multiwireproportional chambers. A traversing particle induces a mirror charge oneach of the four cathode strips at the chamber surfaces which is read out.The two cathode strip layers perpendicular to the beam axis measure the zposition with a resolution of 450�m. For the matching of TEC hits with thez chamber information a � measurement is performed with the remainingtwo layers of strips. For that purpose these are arranged in a helix form.2.2.2 The Calorimeter SystemThe energy of particles emerging from e+e� collisions is measured in L3 bythe total absorption technique (calorimetry) with BGO crystals and a ura-nium hadron calorimeter (�gure 2.4). Combining the information from BGOand hadron calorimeter a resolution of 10% in the total energy and 40mradin the direction of 45GeV jets has been obtained.

2.2. THE L3 DETECTOR 25Hadron Calorimeter Barrel

Hadron CalorimeterEndcaps

LuminosityMonitor

FTC

BGO

BGO

SMD

HC1

HC3 HC2 Z chamber

TEC

Active lead rings

SLUM

RB24 Figure 2.4: The inner detector and calorimeter systemThe Electromagnetic CalorimeterTo identify electrons and photons an electromagnetic calorimeter is placedaround the z chamber. It uses Bismuth Germanate Bi4Ge3O12 (BGO) asboth the showering and detecting medium.The electromagnetic calorimeter consists of a barrel and two endcaps all madeof BGO crystals which transform the electromagnetic energy depositions intoa scintillation light signal. The 7680 crystals of the barrel are arranged in twosymmetric half barrels, giving a polar angle coverage 42� < � < 138�. Theendcaps with 1536 BGO crystals each are split into two halves for installationaround the beam tube. They extend the polar angle range to 12� < � < 168�.Each crystal in the barrel is 24 cm long and is shaped like a truncated pyramidabout 2 � 2 cm2 at the inner end and 3 � 3 cm2 at the outer end. Twosilicon photo diodes and associated electronics detect the light. The energyresolution obtained for electrons and photons with energies above 2GeV isabout 2% and the spatial resolution better than 2mm.

26 CHAPTER 2. THE L3 EXPERIMENT

ElectromagneticBarrel

Hadron end cap

Hadro

n Barr

el

Electromagneticend cap

TECB

GO

HC1

HC2

HC3

HC1

Figure 2.5: The L3 hadron calorimeterThe Hadron CalorimeterTo get an optimum energy measurement for hadrons and jets a hadroncalorimeter is placed around the electromagnetic one. The uranium hadroncalorimeter is divided in a barrel and a forward-backward part.The hadron calorimeter barrel is 470 cm long, has an outer radius of 180 cmand an inner radius of 90 cm. It covers the central region (35� < � < 145�)and consists of 9 rings of 16 modules each.The endcaps of the hadron calorimeter cover the polar angle region 5:5�

2.2. THE L3 DETECTOR 27energy. It consists of uranium absorbers interspersed with proportional wirechambers, which act as the sampling medium. Since only non-showering par-ticles (like muons) can reach the outer detector the hadron calorimeter actsas a �lter for muons, too.2.2.3 The Scintillation CountersThe scintillation counters are located in the region between the two calorime-ters at a radial distance of 88:5 cm. In this position the scintillator can beused in the trigger on hadronic events and muons.In total there are 30 barrel scintillation counters which are bent to followthe shape of the hadron calorimeter barrel. The angular coverage of the bar-rel counters is 34� < � < 146�. Therefore they cover the acceptance of themiddle muon chamber (MM). The endcap counters extend the coverage to11:5� < � < 168:5�, since they are located in front of the hadron calorimeterendcaps. There are 16 endcap counters on each side of the detector. In theazimuthal angle 93% of the solid angle is covered by scintillators.The good time resolution (< 1 ns for the barrel and < ns for the endcaps[22]) in the time-of-ight measurement for muons is used to discriminatedimuon events from cosmic muons. A single cosmic muon which passes nearthe interaction point resembles a muon pair event produced in e+e� interac-tion, but the time-of-ight di�erence between opposite scintillation countersis � 5 ns for cosmics and zero for muon pairs.2.2.4 The Luminosity MonitorTo measure the luminosity by counting small angle Bhabha events a lumi-nosity monitor was installed in the forward and backward regions. It consistsof two BGO calorimeters which are situated symmetrically on each side ofthe interaction region at z = �2:7m. The luminosity monitor accepts anangular region of 1.7 to 3:6� with full e�ciency. In order to improve theangular resolution a silicon detector (SLUM) was installed in front of eachof the calorimeters (see �g.2.4). Since the cross section of Bhabha events iswell known in the limit of small angles, the number of observed events canbe converted into a luminosity value with a precision of 0:2%.2.2.5 The Muon FilterThe muon �lter is mounted on the inside wall of the L3 support tube andadds 1.03 absorption lengths to the hadron calorimeter. It consists of eightidentical octants, each made of six 1 cm thick brass (65% Cu and 35% Zn)

28 CHAPTER 2. THE L3 EXPERIMENTabsorber plates, interleaved with �ve layers of proportional chambers andfollowed by �ve 1:5 cm thick absorber plates matching the circular shape ofthe support tube. The main purpose of the muon �lter is to reduce thepenetration of strongly interacting particles to the muon spectrometer, butit also gives an additional measurement of traversing particle trajectories.2.2.6 The Muon Spectrometer2.9 m

Outer Chamber (MO)

16 wires

Middle (MM)

24 wires

Inner (MI)

16 wires

xxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxx

OV

46 cm

5 cm

10 cm

24 Sense Wires

HV MESH

FIELD SHAPING

1 cm

Honeycomb

Alum

xxxxx

29 Field Wiresxxxxxxxxxxxxxxxxxxxx

µ

Receiver

Lens

LED

Figure 2.6: The muon spectrometer of the L3 detectorThe outer detector is a large muon spectrometer, mounted outside of thesupport tube. It has been designed for very accurate measurements of the

2.2. THE L3 DETECTOR 29momentum of high energy muons. This is achieved using a con�guration ofthree layers of drift chambers which measure the curvature of the muon tra-jectory very precisely in the region between the support tube and the magnetcoil.The barrel muon system is complemented by forward backward muon cham-bers (FBMU). Here a toroidal magnetic �eld of 1:2Tesla is applied in additionto the solenoidal �eld of 0:5Tesla. The polar angle acceptance of both muondetectors covers the range from 36� to 158�.The spectrometer consists of two ferris wheels, each of them having eightS

L=2.9 m

MI : 16 wires MM : 24 wires MO : 16 wires

µ- TrackB

s1

s2s3

Figure 2.7: Momentum measurement with the L3 muon spectrometerindependent units called octants. Each octant consists of �ve precision driftchambers in three layers: two chambers (MO) in the outer layer, two cham-bers (MM) in the middle layer and one chamber (MI) in the inner layer.These chambers (called p chambers) are used to determine the muon momen-tum by measuring the track in the r�� plane. For this a precise alignmentof the chambers is crucial. The inner and outer chambers are closed on thetop and bottom by additional drift chambers (called z chambers) to measurethe z coordinate, so that there are in total six z chambers per octant. Themiddle chambers are closed by honeycomb panels to avoid degradation of themomentum resolution due to multiple scattering.Each p chamber consists of drift cells with signal wires in beam direction. Ifa particle traverses one of these drift cells, a track segment is reconstructedin this cell. The most important information of the track segment are its

30 CHAPTER 2. THE L3 EXPERIMENTposition and the track inclination relative to the wire plane.The momentum measurement relies on the fact, that a moving charged par-ticle is deected in a magnetic �eld due to the Lorentz force. The result-ing bending of the muon track can be measured over the deviation from astraight line, the sagitta S, see �gure 2.7. Using a small angle approximationthe sagitta can be calculated byS = 126:4 (L=m)2 B=TpT=GeV : (2.1)Here B is the magnetic �eld and pT is the transverse momentum.Since with the middle layer of p chambers the sagitta is measured and there-fore its position error has a big inuence on the momentum measurementeach of these chambers has 24 signal wires instead of 16. Because of thelarge distance L between inner and outer muon chamber of 2:9m a momen-tum precision of 2:5% is reached for 45GeV muon tracks when they aremeasured in all three layers. For tracks with hits in only two layers a circulararc can be adjusted with the help of the track gradient, but the momentumprecision decreases to about � 20% [23].2.3 Trigger and Data AcquisitionIn contradiction to the beam crossing rate of 90:4 kHz (for eight bunches)the collision rate is much lower (� 0:1Hz. The trigger system has the taskto decide whether an e+e� interaction took place and whether it should berecorded. This decision is performed at three levels of increasing complexityand must be �nished after less than 10�s to start the readout sequence ateach bunch crossing. The complete detector readout takes 500�s to com-plete unless it is aborted. While a readout sequence is active no new input isaccepted. All the subdetectors provide, in addition to the main data, triggerdata in digitized form within a few �s. The level 1 trigger analyses the triggerdata of the subdetectors and initiates either the digitalisation of the maindata when at least one of the subdetectors contains a signal or the reset ofthe readout time before the next beam crossing. The trigger data are furtheranalysed by the level 2 trigger with the aim to reject background events ac-cepted by the level 1 trigger. The level 3 trigger has access to the completedigitized data and requires correlations between detector components. Onlyif this last scrutiny arrives at a positive decision the event is transmitted tothe main data acquisition computer to be written on tape and disk.In addition to the normal triggered events a detector readout is performed

2.4. EVENT SIMULATION 31from time to time independent on the trigger decision. These so called beam-gate events are used to analyse the detector noise. To determine the triggere�ciency of level 2 and level 3 trigger some events 1 are accepted in spite ofthe presence of a negative trigger decision.2.4 Event Simulation2.4.1 Event Generators for the SM ProcessesKORALWThe program KORALW [24] generates all W decay channels into pairs ofleptons or quarks, taking into account the kinematics of massive particleswith exact four momentum conservation for the entire W+W� productionand decay processes. KORALW includes not only QED e�ects in the initialstate but also in the leptonic decays of the W and secondary decays, i.e. inthe � lepton decays. Hadronization of quarks is also performed. The e�ectsof spin are included in combined W -pair production and decay and the �polarization is also taken into account in its decays. KORALW is used forthe simulation of the e+e� ! W+W� ! f �ff �f background in this analysis.KORALZThe Monte Carlo program KORALZ [25] simulates the process of lepton andquark pair production, including multiple QED hard bremsstrahlung fromthe initial state fermions and single photon bremsstrahlung from the �nalstate fermions. Radiative corrections of the �rst order in � are taken intoaccount as well as longitudinal spin polarizations of the beams and spin po-larization e�ects in the � decay process.KORALZ is used for the simulation of dileptonic background processes e+e� !f �f .PYTHIAPYTHIA / JETSET [26] is a general purpose MC event generator for a multi-tude of processes in high energy physics. Any �nal state allowed for a processis included in the generation, initial state radiation and �nal state radiationare implemented. Finite fermion masses are included in the phase space fac-tors for partial widths. The emphasis is on the detailed modeling of hadronic�nal states, i.e. QCD parton showers, string fragmentation and secondary1prescaled events: every 10th event at level 2, every 100th event at level 3

32 CHAPTER 2. THE L3 EXPERIMENTdecays. The electroweak description is not competitive for high precisionstudies since it is restricted to improved Born level formulae. PYTHIA isalso used for 4-fermion physics (

physics). In this analysis PYTHIA is usedfor the simulation of the background processes e+e� ! ZZ, e+e� ! Zeeand e+e� ! q�q.DIAG36DIAG36 [27] is an event generator for the full set of QED diagrams fore+e� ! e+e�f �f , including all fermion masses. Phase space generation cancover the whole kinematically allowed phase space. DIAG36 is used as MCgenerator for leptonic 4-fermion background.PHOJETPHOJET [28] is a minimum bias event generator for hadronic pp, p and

interactions. In the program the complete lepton-photon vertex for transveralpolarized photons is simulated. Only photons with very low virtualities areconsidered in the model. The extension to virtual (and longitudinally polar-ized) photons is in progress. PHOJET is used as MC generator for hadronic4-fermion background e+e� ! e+e�q�q.2.4.2 SUSYGEN - The Signal Event GeneratorThe production and decay of sleptons has been simulated using the generatorSUSYGEN [29] by the authors S.Katsanevas and P.Morawitz. SUSYGEN isa Monte Carlo generator for the production and decay of all (R-parity odd)MSSM sparticles in e+e� colliders. It is exible enough that the user canassume or relax di�erent theoretical constraints, and it is easily generalizableto extensions of the MSSM due to the choice of the input parameters spec-ifying the SUSY model. Initial state radiation and an interface to JETSETare included. Cascade decays are also taken into account.2.4.3 Event Simulation and ReconstructionTo understand the detector response, events are generated with a MonteCarlo program, which simulates a multiparticle con�guration from the initiale+e� annihilation up to a time of order c� � 1cm. Afterwards the particlesare passed through the L3 detector simulation, based on the GEANT [30]program, which is responsible for the propagation of particles through a geo-metrical description of the L3 detector, taking into account the interactions

2.4. EVENT SIMULATION 33of the particles with the detector material. GEANT includes the e�ects ofenergy loss, multiple scattering and showering in the detector material and inthe beam pipe. Additional time dependent detector ine�ciencies are takeninto account. When it turns out that the degeneration in detector perfor-mance leads to unrecoverable systematic biases (which is tested with MCstudies), the corresponding real data is declared as bad ('bad runs') anddropped from the analysis.In a last step the MC events are reconstructed by converting the informationof several subdetectors into values of kinematical variables of �nal particles.This last step is done in the same way for MC events and real data.Particle Identi�cation� Hadronic events are reconstructed using information from all subde-tectors. The energy of the event is obtained from the energy deposi-tions in the electromagnetic and hadronic calorimeters and the particlemomenta as measured in the central tracking system and the muonchambers. Jets are reconstructed with the DURHAM algorithm [32].� Taus are de�ned as isolated hadronic narrow jets with energy largerthan 2GeV and one to three associated tracks 2. This includes theleptonic decaus of the tau. The energy of the tau is de�ned as theenergy contained in a cone of 10� half opening angle around the taudirection. Its isolation is assured by requiring that there are no addi-tional tracks and no more than two additional calorimetric clusters ina cone of 30� half opening angle and that the ratio of the energies inthe two mentioned cones is less than 2.� A narrow electromagnetic shower matched with a track is identi�ed asan electron. A narrow electromagnetic shower not matched with atrack is identi�ed as a photon. The energy measured in the electro-magnetic calorimeter has to be larger than 1GeV and is assigned tothe identi�ed electron or photon.� Amuon is identi�ed by a track in the muon chamber which is matchedwith a track in the central tracking chamber. To reconstruct a muontrack in the muon chamber hits in at least two of the three layersof drift chambers of the muon spectrometer are necessary. Then thereconstruction is successfull in 90%. Muon tracks are accepted onlywhen the transversal distance to the vertex is less than 500mm [23].2Tracks are reconstructed out of hits in the central tracking chamber. A track is de�nedby at least 25 hits in the TEC [31].

34 CHAPTER 2. THE L3 EXPERIMENTOnce the lepton or photon identi�cation has been performed the energy mea-sured in the BGO is assigned to electrons or photons and the momentummeasured in the muon detector is assigned to the muons, adding the averageenergy loss in the calorimeters and any contribution of collinear �nal stateradiation measured in the BGO.

Chapter 3AnalysisIn this analysis the data collected by the L3 detector in 1997 at a center ofmass energy ps = 183GeV are used. These data correspond to an integratedluminosity of L = 55:46 pb�1.3.1 Signal and BackgroundThere are three di�erent signal topologies in dependence on the parameterspace which have to be taken into account in this analysis (as described insection 1.5). For that reason the analysis is split into three subanalyses whichwill be described below:� SCENARIO 1The slepton co-NLSP scenario leads to the decay channel ~�! � ~G,the signature is therefore two muons + E=.� SCENARIO 2In the neutralino NLSP scenario the smuon decay terminates in~�! � ~G, the signature to search for is two muons + two photons+ E=. In the case of very soft and therefore undetected photons thesignature is like above.� SCENARIO 3For the stau NLSP scenario the smuon decays via ~� ! ��� ~G re-sulting in two muons + four taus + E=. Here the muons and onetau pair can be quite soft and therefore missing.Signal events have been generated with the MC program SUSYGEN [29] (see2.4.2) for di�erent masses of the smuons up to the kinematic limit and for eachdecay scenario. Here the gravitino mass was assumed to be m ~G = 60 eV. For35

36 CHAPTER 3. ANALYSISthe generated mass points the scenario independent cross section for smuonpair production (see also section 1.4 and �gure 1.3) and the expected numberof smuon events are given in table 3.1.In the case of scenario 1 the produced smuons act as NLSP's and no addi-tional assumptions have to be made.In scenario 2 the mass of the neutralino NLSP must be taken into account.Three representative values for the mass were chosen: m~�01 = 5GeV (lightneutralino), m~�01 = 25GeV (medium neutralino), and m~�01 = 45GeV (heavyneutralino).For the analysis of scenario 3 the stau mass must be known. To have thestau as heavy as possible m~�1 was always set 3GeV lighter than the smuonmass 1. Hereby a wide range of stau masses could be covered.It should be remarked that in this work only prompt decays are analysedand the branching fractions for each of the decays are 100 %. Searches forsleptons decaying in ight (displaced vertices searches, kink searches) andstable heavy particles have been performed by the LEP experiments [42].

�

e�

e+

e��ff

e+

Figure 3.1: One Feynman diagram for the 4-fermion backgroundSince the signal signature always consists of two muons and missing energy,possibly with additional photons and taus, the main background consists of:1For technical reason the neutralino had to be real and therefore its mass was set tom~� � 1GeV. To allow the neutralino to decay into tau and stau the stau mass had to be� 2GeV lighter than the neutralino.

3.1. SIGNAL AND BACKGROUND 37� 4-fermion processesThese are two photon interactions with two electrons and two otherfermions (e.g. muons, taus or quarks) in the �nal state: e+e� !e+e�f �f (see �gure 3.1). The electrons normally disappear in the beampipe and manifest themselves in form of missing energy. Since thecross section for this process at these center of mass energies is ordersof magnitude larger than any SUSY signal at LEP this process is themost copious source of background (see also table 3.2).

�

W�W+

e�

e+

l+�ll�

��l

Figure 3.2: One possible Feynman graph for the background from W -pairproduction� W -pair productionAt center of mass energies ps > 160GeV W -pair production is kine-matically allowed. One possible Feynman graph is shown in �gure 3.2.In the case that bothW bosons decay into muon (tau) and neutrino thesignature is indistinguishable from the signal in scenario 1, because theneutrinos escape the detector without interaction and manifest them-selves only in form of missing energy and imbalanced momentum. Eventhough the cross section is quite small compared to the 4-fermion pro-cess (see table 3.2) this background is the dominant one after the se-lection cuts (at least in scenario 1) because of the signal-like topology.� dileptonic eventsThe s-channel production process for lepton pair production - espe-cially muon and tau production - is another important background.

38 CHAPTER 3. ANALYSIS�

e�

e+

l+

l�

Figure 3.3: One Feynman diagram for dileptonic background and 2 jet eventsThe Feynman graph for the reaction e+e� ! f �f via Z0/� exchangeis shown in �gure 3.3. The 'radiative return' to the Z resonance byemission of hard initial state radiation photons which may be lost inthe beam pipe is included into the MC simulation of this kind of back-ground.� 2-jet eventsFor scenario 3 quark pair production e+e� ! q�q is an important back-ground. The Feynman graph is shown in �gure 3.3.� other processesOther electroweak processes with cross sections small compared to theprevious ones, namely e+e� ! ZZ, and e+e� ! Zee are also takeninto account.� cosmicsCosmic muons are also a possible background and therefore have to betaken into account. This background has to be reduced by some specialcuts since no Monte Carlo simulation exists.The background MC samples were used with a number of simulated eventsequivalent to at least 50 times the statistics of the collected data sample. Thishas been done for all speci�ed processes except for the 4-fermion processese+e� ! e+e�f �f . For these only a factor of three of statistics was availablefor leptons in the �nal state (f = l), requiring at least 3GeV invariant massfor the f �f system and a deection angle of at least 10� for the �nal fermions.For quarks in the �nal state (f = q) only two times the expected statisticswas generated requiring at least 3GeV energy for the q�q system.

3.2. PRESELECTION 393.2 PreselectionIn the beginning of each analysis a preselection is done to reduce the bigdata samples to a limited amount. Normally this is done by rejecting thebackground which topologically di�ers very much from the signal as well asnon-physics background (beam-gas interactions, detector noise, ...). Further-more the aim of the preselection is to use only data for the analysis whichwere taken in a period when the detector was fully working (or at least theparts necessary for the analysis) so that the data quality is good (no 'badruns', see section 2.4).In this preselection the 3.6 millions data events taken in 1997 were reducedto � 1800 by rejecting hadronic and purely electromagnetic events. The cutsused to reach this are listed below. The preselection is used for the analysisof all three di�erent channels and contains the following cuts:1. fully functional electromagnetic and muon detector systems:� no 'bad run' in the electromagnetic system,that means: faultless functioning of the luminosity monitor, thescintillators, the electromagnetic calorimeter and other (very for-ward) components which are important to see the 4-fermion back-ground;� no 'bad run' in the muon system,that means: perfect modus operandi of muon trigger and muonchamber to ensure the best possible muon detection;2. to reduce the cosmic background it is required:� at least one scintillator hit to be 'in time' ,that means the scintillator time corrected for the time-of-ighthas to be in the time window of the beam crossing for at least onescintillator hit: tscintillator � tTOF � 5 ns;� the best DCA to be less than 1mm,that means the minimum distance between muon track and vertexposition (distance of closest approach = DCA) measured in r��with the TEC must not exceed 1mm;� the maximum DCA to be less than 1 cm,that means the maximum distance between muon track and vertexposition measured with the muon chambers in r � � must notexceed 1 cm;

40 CHAPTER 3. ANALYSISm~�R �~�R ~�R Nexpectedin GeV in pb events10 1.72 95.420 1.45 80.430 1.11 61.640 0.73 40.550 0.49 27.260 0.34 18.970 0.20 11.180 0.07 3.990 0.002 0.1Table 3.1: Cross section and number of expected smuon pair production eventsfor several smuon masses (ps = 183GeV, 1997 data set)

background 4-fermion W -pairs dileptonsprocess (MC) e+e� ! e+e�l+l� e+e� !W+W� e+e� ! l+l�generator DIAG36 KORALW KORALZcross section > 1 nb 15 pb 9 pbNpreselected 1504 7 235background 4-fermion 2 jets W -pairsprocess (MC) e+e� ! e+e�q�q e+e� ! q�q e+e� !W+W�generator PHOJET PYTHIA KORALWcross section > 15 nb 107 pb 15 pbNpreselected 5250 92 21Table 3.2: Generators, cross sections and number of preselected events forthe main background in scenario 1 and 2 (up) and in scenario 3 (down)

3.2. PRESELECTION 41� in % BACKGROUND MC DATAafter cut eell W -pairs dileptons ps = 183GeV1 99:8 100 100 1002 56:7 84:3 78:3 25:33 10:6 22:8 46:0 0:74 3:6 1:6 23:9 < 0:1Npreselected 1747 1772� in % BACKGROUND MC DATAafter cut eeqq 2 jets W -pairs ps = 183GeV1 100 100 100 1002 56:1 82:8 82:8 19:43 55:6 73:1 70:2 19:34 0:5 2:8 2:5 < 0:1Npreselected 5368 1867Table 3.3: Preselection cut e�ciencies � and number of preselected events forbackground in scenario 1 and 2 (up) and in scenario 3 (down). For the datathe remaining percentage is given as well as the number of preselected events.

� in % SIGNAL 60GeVafter cut scenario 1 scenario 2 scenario 31 99:0 99:0 99:02 93:2 92:1 71:13 88:7 80:0 68:84 60:4 51:0 54:4Table 3.4: Preselection cut e�ciencies � for a 60GeV signal in the di�erentscenarios

42 CHAPTER 3. ANALYSIS3. only events with muons, photons and taus are accepted 2Since electrons can be decay products of the taus they are allowed inthe stau NLSP scenario. Their number is requested to be four at most.This cut reduces the hadronic background as well as Bhabha scatteringand 4-fermion processes.4. to obtain the requested signatures it is required:� between two and eight tracks are found in the event (for scenario 3between 6 and 14 tracks are allowed to permit also 3-prong decaysof the tau)� only for scenario 3: the number of jets is four to eight, whereisolated leptons are counted as jets� the number of identi�ed leptons and photons is two to six 3� exactly two identi�ed muons (for scenario 3 the number of muonsis required to be at most six because of possible tau decays intomuons or misidenti�ed muons)� at most four identi�ed taus� at most four identi�ed photons (two photons and four electronsfor scenario 3)The de�nition of leptons and photons can be found in section 2.4.3.In table 3.2 the number of expected events (from MC), the generators usedfor the MC simulation and the cross sections for the main background pro-cesses are shown. The negligible background (less than 1 event expectedafter the preselection) is not listed. The e�ciencies after the preselectioncan be found in table 3.3 and 3.4 for the main background, data and signal(60GeV), respectively, as well as the expected background and preselecteddata events.For scenarios 1 and 2 the good agreement between the expected (MC) andobserved (DATA) number of events (table 3.3, up) shows that no impor-tant background is missing. In �gure 3.4 distributions after the preselectionare shown for some variables which are described in section 3.3.1. A goodagreement between data and Monte Carlo can be seen again, except forone variable: The distribution in the polar angle of the missing momentum(�miss) shows a discrepancy for missing momenta pointing into the beam pipe2MIP's (Minimal Ionizing Particles) are not included in the analysis, because theirrelative amount is small (� 2%) and therefore would not improve the analysis.3For scenario 1 only two leptons which have to be muons are accepted for the selection.

3.2. PRESELECTION 434-fermiondileptonW pairsothersignal 60GeV

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0 20 40 60 80 100 120 140 160 180Figure 3.4: Distributions in scenario 1 and 2 after the preselection for theacolinearity angle of the two muons, the product of charge and cos ��1 (where�1 is the more energetic muon of the two and ��1 is the polar angle of thismuon), the polar angle of missing momentum, and the missing energy. Data(points) are compared to Standard Model background processes (colored his-tograms; additive) and to the expected signal (for scenario 1, 60GeV smuonmass; open histogram).

44 CHAPTER 3. ANALYSIS(�miss = 0� and �miss = 180�, respectively). This can be explained by thefact that for the 4-fermion background a cut on generator level has beenperformed (as described in 3.1) with the result that events with a deectionangle for the �nal fermions of less than 10� are not generated but of courseexist in the data. This implies that a cut on this variable has to be appliedin the following analysis.From the distribution of the product of charge and cos ��1 one can see a gapat � = 90�. Its location is exactly where the two hemispheres of the muonchambers (ferry wheels, see section 2.2.6) are composed. In �gure 3.7 furtherdistributions for the two scenarios are shown. Here the conformity of MCwith data can be seen again. The discrepancy in the scintillator time is dueto cosmics which are not simulated in the MC. Therefore a cut has to beapplied here, too.For scenario 3 a major problem with the MC simulation of e+e� ! e+e�q�qcan be seen from tables 3.2 and 3.3. Here the expectation for this backgroundis much larger than the number of preselected data events (see also �gure3.5). In �gure 3.6 the ratio between background and data is plotted. For theangular distribution a factor of three is found comparing the MC expectationto the data. The energy distribution shows not only a larger discrepancy butalso an energy dependence. Since the entries are concentrated in the �rstbins the energy dependence has no large inuence, resulting in a factor ofthree of discrepancy also for this variable.The e+e�q�q background was produced with the MC generator PHOJET.But the problems which arise here are not only of technical nature: theyare based on the fact that hadronic 4-fermion processes are not very wellunderstood theoretically. Therefore the Monte Carlo is generated with some'trivial' assumptions and the distributions are adapted to the data by handafterwards. This procedure seems not to work very well as one can see fromthe distributions in �gure 3.5.From the fact that the data are not well described by the Monte Carlo itfollows that another generator for this kind of background should have beenused. But since no other generator for e+e�q�q exists this could not be done.Nevertheless, to continue the analysis three di�erent strategies were used:� The problem was ignored and the analysis procedure was done as forscenario 1 and 2 (strategy 'no scaling').� The background from e+e�q�q was scaled down with a factor of threeand the analysis procedure was done afterwards. This strategy seems tobe correct for angular distributions (�gure 3.6, top) but is questionablefor energies (�gure 3.6, bottom) (strategy 'rescaled').

3.2. PRESELECTION 454-fermion

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0 10 20 30 40 50 60 70 80 90 100Figure 3.5: Distributions in scenario 3 after the preselection for the acopla-narity of the event, the azimuthal angle between the two most energetic lep-tons, the time for the scintillator nearest to the most energetic track, and theenergy of the most energetic lepton. Data (points) are compared to StandardModel background processes (colored histograms; additive). A large discrep-ancy is found. The expected signal (60GeV smuon mass) is indicated asopen histogram.

46 CHAPTER 3. ANALYSIS� The neural net analysis described in chapter 4 was used to separatesignal-like events from e+e�q�q-like events. After that the analysis pro-cedure was continued as described below (strategy 'neural net').The results of the di�erent strategies will be compared later.

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0 10 20 30 40 50 60 70 80 90 100Figure 3.6: Ratio between the expected number of events after preselectionfrom Monte Carlo and preselected data. The distribution is shown for theacolinearity of the event (up) and the energy of the most energetic lepton(down) in scenario 3.

3.3. CUT SELECTION 473.3 Cut SelectionA cut selection is a conventional method for the separation of a certain signalsignature out of the data. The aim is to isolate a signal with low cross sectionfrom the background with high cross section. With the help of selectioncuts on various variables in which signal and background di�er signi�cantlyfrom each other a signal enriched subset is separated. In this section such aselection is described.The �rst step in a cut selection is to �nd variables in which signal andbackground can clearly be distinguished. The choice of these variables ismade with Monte Carlo studies. After that the selection is applied to thedata to pick out signal-like events.3.3.1 Distributions and CutsIn the case of the smuon search this means to isolate the signal from thebackground which is at least a hundred times bigger. Since for each of thethree smuon decay channels explained above two undetected gravitinos areexpected in the �nal state, the main characteristics of supersymmetric pro-cesses under study are large missing transverse momentum, large missingenergy, and large acoplanarity angle (for explanation of the variables see be-low). The distributions shown in the last section illustrate how the selectionof signal events has to be done, since in the shown variables signal and back-ground di�er from each other and can easily be separated by cuts. Thereforethe following set of variables was chosen for the selection (the distributionsof the described variables can be seen in �gures 3.4, 3.5, 3.6, and 3.7):� VARIABLE 1 (ACOL): angle between the muons in spaceThis angle is also called acolinearity angle. It is de�ned such thatthe event is forced into two jets and the angle between these jets iscalculated. The acolinearity angle is 0� when the jets point into thesame direction and 180� when the jets are back-to-back. In the case ofscenario 1 where only two muons are required to be in the event thisangle corresponds to the angle between the muons.Since dileptons are produced back-to-back this cut is mainly to reducedileptonic background.� VARIABLE 2 (PHI): azimuthal angle between the two muonsThis variable is used to reduce background from W -pair and dileptonsas well as 4-fermion background. For scenario 1 and 2 this variable ismainly the acoplanarity angle.

48 CHAPTER 3. ANALYSIS4-fermiondilepton

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0 20 40 60 80 100 120 140Figure 3.7: Distributions in scenario 1 and 2 after the preselection for theacoplanarity angle of the two muons, the scintillator time for the scintillatornearest to the more energetic muon track, and the energy of the most andnext-to-most energetic muon. Data (points) are compared to Standard Modelbackground processes (colored histograms; additive) and to the expected signal(scenario 1, 60GeV smuon mass; open histogram).

3.3. CUT SELECTION 49� VARIABLE 3 (TMM): polar angle of the missing momentumTo reduce 4-fermion background (where the scattered electrons escapein the beam pipe) it is required that the missing momentum vectorshould point far away from the beam pipe.� VARIABLE 4 (QCOS): product of muon charge and cosine of the polarangle between the muonsThis cut reduces W -pair background due to the asymmetric distribu-tion for this kind of events. All other processes are uniform distributedwith respect to this variable.� VARIABLE 5/6 (E1, E2): energies of the two muonsThis cut was used since the muons resulting from the decay of a smuonhave energies in a well de�ned interval: Emin;max = 14(ps�ps� 4m~�R).For scenario 3 the two most-energetic particles were used instead of themuons.� VARIABLE 7 (ACOP): angle between the muons in the r � � planeThis angle is also called acoplanarity angle. In analogy to the acolin-earity angle this angle is de�ned as the angle between two jets but inthe r�� plane instead of in space. In the case of scenario 1 this anglecorresponds to the azimuthal angle between the muons.Since the missing momentum vector of 4-fermion events points mainlyinto the beam pipe perpendicular to the r� � plane they are back-to-back in this plane and the acoplanarity angle is around 180�. Thereforea cut high acoplanarity reduces 4-fermion background.� VARIABLE 8 (EMIS): missing energy of the eventTo determine this variable the event is forced into two jets. From theirenergies and the angle between them the missing energy is calculated.For processes with no unseen particles the missing energy is expectedto be low. In the Standard Model only processes with neutrinos inthe �nal state show missing energy. In reality processes with particleslost in the beam pipe (e.g. 4-fermion events) also have to be takeninto account. In the case of 4-fermions the missing energy is espe-cially high. Consequently this variable mainly reduces dileptons and4-fermion events.� VARIABLE 9 (TIME): time of the nearest scintillatorThis variable contains the time of the scintillator nearest to the muontrack which has a hit. The time is corrected for the time of ight fromvertex to scintillator and therefore should be zero for muons coming

50 CHAPTER 3. ANALYSISfrom the vertex. Since the time resolution of the scintillators (0:9 nsfor the barrel scintillators and 0:9 ns for the endcap scintillators) has tobe taken into account and in addition the calibration seems not to bevery good particles from the vertex have tscintillator � 3 ns.) Thereforetscintillator is used to reject cosmics which passed the preselection cuts.Here one single set of cut variables is used for all possible �nal states. Fromthat it follows that the analysis procedure for each of the three scenarios isthe same.For scenario 1 it was found that better results can be obtained requiringevents with exactly two muons and nothing else. This is one additional con-straint but simpli�es some variables as already mentioned in the variabledescription.3.3.2 OptimizationIn general the searching procedure for new physics consists of two steps: inthe �rst step a signal is searched for by applying the cuts in a way that themaximal sensitivity is reached. For big numbers of events the statistical sig-ni�cance has to be optimized, for a few events the Poisson statistic is valid.If the number of selected data is in good agreement with the number of ex-pected background events and therefore no signal is found the cuts used areoptimized in a second step to reach the best possible limit on the numberof produced new particles at a certain con�dence level. The optimization isbased on MC distributions and is done without looking at the data.Since for the Poisson statistics the sensitivity function s is directly related tothe limit on the number of produced events N expmax by s = 1Nexpmax here the twosteps were combined.For small numbers n0 of events expected to be selected the distribution of n0follows a Poisson distribution with the true value n as average [33]:Pn(n0) = e�n nn0n0! : (3.1)For a given n an upper limit N can be de�ned so that with a certain prob-ability (usually 95%) random observations of n would give values not largerthan n0: 0:95 = 1Xn=n0+1PN(n) 0:05 = n0Xn=0PN(n) (3.2)

3.3. CUT SELECTION 51Let Nn0 be the 95% con�dence level Poisson upper limit set on the expec-tation value of a signal when n0 events are observed and no background issubtracted (that means, the expected number of background events is b < 1).Then� in a fraction Pn(0) of several experiments no event will be found andthe 95% con�dence level upper limit N on the number of signal eventsto be expected within the acceptance of this analysis will be set at N0;� in a fraction Pn(1) of the experiments one event will be observed, fromwhich N will be set at N1;� ...Ni is adjusted until the relation 3.2 obtains and one �nds:Nn0 = 3:00; 4:74; 6:30; :::; for n0 = 0; 1; 2; :::; respectively: (3.3)The average value of N is N95 = n0Xi=0NiPN(i): (3.4)In the case that the number of expected background events is not zero andthe number of observed events has two components, signal and background,estimating a limit on the signal is more complicated [34]. Assuming thenumber of expected background events b to be known with negligible erroran upper limit can be de�ned by extension of formula 3.1 and 3.4:N95 = e�(b+N)Pn0i=0 (b+N)ii!e�bPn0i=0 bii! : (3.5)In this analysis the cut values are optimized for every generated smuon masspoint using MC signal and background. The optimization procedure varies allthe cuts simultaneously, minimizing the ratio between the average Poissonupper limit on the signal with background subtraction N95 and the signale�ciency �, N expmax = N95� : (3.6)This corresponds to the maximization of the sensitivity function s = 1Nexpmax(see above).Practically this was done using the program MINUIT [35] which is conceivedas a tool to �nd the minimum value of a multi-parameter function and to

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3.3. CUT SELECTION 53analyse the shape of the function around the minimum. As minimizer SIM-PLEX was used, a multidimensional minimization routine. The program wasused iteratively, that means, the output parameters of run i (the optimizedcut values) were given as start values for run i + 1 until output and inputparameters were equal. This normally was the case after 5-10 iterations.To avoid an inuence due to statistical uctuations (especially for the 4-fermion channel, where the available statistics is quite low) the dependenceof the cut position on the smuon mass was analysed and two �ts were done,assuming no mass dependence or a linear dependence on the smuon mass,respectively. This strategy also avoids a bias on the signal e�ciency as wellas on the position of the cut value. An example for such a �t is given in�gure 3.8. Since the errors of the optimized cut positions were not correctlyestimated by MINUIT the �2 of the �ts was not meaningful. Therefore theby eye better �t of the two was taken. The result of the �t { a value forthe cut position { was used for the calculation of the limit by applying theresulting (�nal) cut to the MC and data samples, respectively. These cutvalues are shown in table 1.5.Figure 3.9 shows the distributions of some variables after applying the �nalcuts on all other variables except the plotted one (so called N � 1 plots).These plots show that a cut on this variable (the cut position is indicated byan arrow) is still necessary for additional background rejection. In additiona good agreement between data and MC can be seen.

54 CHAPTER 3. ANALYSIS4-fermionW pairsdileptonothersignal 60GeV

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0 10 20 30 40 50 60 70 80 90 100Figure 3.9: Distributions for the acolinearity angle (scenario 1), the time ofthe scintillator nearest to the most energetic muon track (scenario 2, lightneutralino), the azimuthal angle di�erence of the two muons (scenario 2,medium neutralino), and the energy of the most energetic muon (scenario 2,heavy neutralino). Data (points) are compared to Standard Model backgroundprocesses (colored histograms; additive) and to the expected signal (60GeVsmuon; open histogram). The cut position is indicated by an arrow. All