Chapter 4 Supersymmetry

Chapter 4 Supersymmetry Contents 4.1 Introduction... 68 4. Difficulties in the standard model... 68 4.3 Minimal Supersymmetric Standard Model... 69 4.3.1 SUSY... 69 4.3. Reasons to introduce SUSY... 69 4.3.3 Extra particles in the MSSM... 7 4.3.4 R-parity and the LSP... 71 4.3.5 The breaking of supersymmetry in the MSSM... 71 4.3.6 The SUGRA model... 71 4.3.7 Points in SUGRA parameter space studied by ATLAS... 73 4.4 Supersymmetry at hadron colliders... 77 4.4.1 Production of sparticles... 77 4.4. Decay of sparticles... 77 4.4.3 Standard Model background... 78 4.5 Simulation packages... 79 4.5.1 Introduction... 79 4.5. PYTHIA... 79 4.5.3 ISAJET... 8 4.5.4 PROSPINO... 8 4.5.5 ATLFAST...8 4.6 Production cross-section of SUSY events for 5 points in SUGRA parameter space. 83 4.6.1 Introduction... 83 4.6. Comparison between PYTHIA and PROSPINO... 83 4.6.3 Comparison between PYTHIA and ISAJET... 86 4.6.4 Conclusions... 86 4.7 Event characteristics of SUSY events for 5 points in SUGRA parameter space... 88 4.7.1 Introduction... 88 4.7. Background sample... 88 4.7.3 SUSY particles produced in primary process... 89 4.7.4 Missing transverse energy... 9 4.7.5 Transverse sphericity... 9 4.7.6 Jet properties... 93 4.7.7 Lepton properties... 96 4.7.8 Conclusions... 98 67

Chapter 4 Supersymmetry 4.8 Scan over SUGRA parameter space... 99 4.8.1 Two-dimensional scan over m and mò... 99 4.8. One-dimensional scan over mò... 1 4.8.3 One-dimensional scan over m... 13 4.9 Conclusions... 15 4.9.1 Discovery potential of SUSY with ATLAS... 15 4.9. Potential of ATLAS to determine sparticle masses and SUSY parameters... 15 4.1 References... 16 4.1 Introduction Supersymmetry is a possible extension of the standard model. In this chapter I present some results of production cross-section calculations of supersymmetric events and results of detector response simulations due to these events. The final goals of supersymmetry simulations performed in the ATLAS collaboration are the investigation of the observability of supersymmetry with ATLAS, the investigation of the possibility to determine the parameters of the supersymmetric model with ATLAS, the determination of search strategies and the optimisation of the design of the ATLAS detector. The existing theoretical difficulties in the standard model are described in section 4.. Supersymmetry, the reason to introduce supersymmetry, the minimal supersymmetric standard model and the SUGRA model are described in section 4.3. The production and decay of supersymmetric particles at LHC are described in section 4.4. The packages used for the simulation studies are described in section 4.5. The results of cross-section calculations are presented in section 4.6. The measured signals for the five points in the parameter space of the SUGRA model studied by the ATLAS collaboration are presented in section 4.7. The production cross-sections and the detected fractions of supersymmetric events as function of the parameters of the SUGRA model are presented in section 4.8. The current conclusions on the potential of ATLAS for supersymmetry studies are finally shortly discussed in section 4.9. 4. Difficulties in the standard model Predictions based on the standard model (chapter 1) are at the moment in excellent agreement with experimental measurements. From the theoretical viewpoint however, several aspects of the standard model are not very satisfactory. It looks like that one is seeing the low energy manifestation of a more fundamental theory. One of these aspects is the large number of adjustable parameters described in chapter 1. A more serious problem is the quadratic divergence of the Higgs mass due to loop corrections described in more detail in appendix D. A Higgs boson can temporarily split into a quark-antiquark pair resulting in a correction to the Higgs mass. These corrections are quadratically divergent [1]: m ( ~ H = m + c α / 4 ) Λ 68 (4.1) with m the bare Higgs mass, H m the observed Higgs mass, α ~ the coupling constant, describing the coupling of the Higgs boson to the quark-antiquark pair, and Λ the cut-off energy up to which loop corrections are included into the mass calculation. One can view Λ as the scale where the standard model is not valid anymore and new physics occurs.

4.3 Minimal Supersymmetric Standard Model grows not only H W The cut-off energy Λ should be close to the electroweak scale O(1 TeV). The reason is that in the standard model the mass of the W ± boson m ± is related to the Higgs mass m. If Λ W H m but also m ± grows, which is in disagreement with the existing experimental data of for example LEP. The problem that the masses of the bosons in the standard model are related to each other which makes it impossible to have a very heavy Higgs boson is the so-called gauge hierarchy problem. Because the bare Higgs mass m is a fundamental input parameter of the standard model, choosing the bare Higgs mass to cancel the large loop corrections can in principle solve the gauge hierarchy problem. If the validity range of the standard model is extended to M x (GUT scale O(1 15 GeV)), the value of the bare mass has to be specified to a precision of 1-4 if the standard model is supposed to stay consistent with current measurements. This problem is the so-called fine tuning problem. If one assumes the existence of grand unification (chapter 1), additional problems are occurring. The evolution of the three coupling constants for electromagnetic, weak and strong interactions does not unify them at one energy (figure 4.1). The evolution of the coupling constants as function of the energy is also described in some more detail in appendix D. In the case of grand unification baryon number and lepton number are not absolutely conversed quantities, permitting decays such as []: p p + + e ν + µ + π + π + The proton lifetime predicted in models based on grand unification is too short. 4.3 Minimal Supersymmetric Standard Model 4.3.1 SUSY It is far from trivial to have an extension of the standard model consistent with all experimental data and predicting new physics at a scale below 1 TeV. A possible extension to the standard model is SUSY (SUperSYmmetry) [3]. Supersymmetry is a symmetry between fermions and bosons, coarsely summarised by the statement that the number of fermionic degrees of freedom must equal the number of bosonic degrees of freedom. In the simplest supersymmetric extension which is not in disagreement with current experimental results (MSSM: Minimal Supersymmetric Standard Model) each standard model particle degree of freedom has one supersymmetric partner with the same quantum numbers, forming together a multiplet [1]. It is important to note the difference between a particle and a degree of freedom. A spin particle has one degree of freedom. A spin ½ particle can be right-handed or left-handed and has two degrees of freedom 1. Also a spin 1 particle with mass (moving at speed of light) has two degrees of freedom. A massive spin 1 particle has three degrees of freedom. (4.) 4.3. Reasons to introduce SUSY There is no experimental evidence for the existence of SUSY. Also the abundance of new particles and new parameters is in itself an unpleasant feature. 1 A massless right-handed particle has spin and velocity parallel, a massless left-handed particle has spin and velocity anti-parallel. 69

Chapter 4 Supersymmetry From the theoretical viewpoint however, SUSY has several attractive properties. Additional contributions of the bosonic partners of the quarks cancel the standard model quadratic divergences mentioned in section 4.. In a supersymmetric GUT, the evolution of the three coupling constants for electromagnetic, weak and strong interactions may unify them at one energy (figure 4.). SUSY also corrects the prediction of a too small proton lifetime [4]. g 3 g 3 g g g 1 g 1 1 15 GeV E 1 16 GeV E Figure 4.1 Evolution of the three fundamental coupling constants for the electromagnetic (g 1 ), weak (g ) and strong (g 3 ) interaction without SUSY [4] (not on scale). Figure 4. Evolution of the three fundamental coupling constants for the electromagnetic (g 1 ), weak (g ) and strong (g 3 ) interaction with SUSY [4] (not on scale). 4.3.3 Extra particles in the MSSM The SUSY partners of the gluons are called gluinos (spin ½). Both a gluon and a gluino have two degrees of freedom. Like the gluons, gluinos are occurring in eight different colour configurations. The supersymmetric partners of the quarks and leptons are called squarks and sleptons. These are scalar particles with spin. To have the same number of degrees of freedom for the particles and sparticles, the left-handed and right-handed states should be treated as different particles. This is however not true for the neutrinos because in the standard model only lefthanded neutrinos are existing. The Higgs sector in the MSSM consists of two charged states (H ± ) and three neutral ones (h, H, A ) [5]. The supersymmetric partners of these particles are called Higgsinos (spin ½). The supersymmetric partners of the W ±, Z and γ bosons are called gauginos (spin ½). Between the Higgsinos and gauginos mixing occurs, giving two charginos Χ 1, Χ and four ~ ± ~ ± ~ ~ ~ ~ neutralinos Χ 1, Χ, Χ 3 and Χ 4 (spin ½). These charginos and neutralinos are linear combinations of the original Higgsinos and gauginos. The extra particles of the MSSM, consisting of the supersymmetric partners ( sparticles ) and the four extra Higgs bosons, are summarised in table 4.1. Here, ~ ~ t 1, b 1, ~ ~ t and b are mixtures of the left and right-handed squarks 3. The total number of degrees of freedom of the charginos and neutralinos (16 = 8 ) is equal to the total number of degrees of freedom of the W ±, Z, γ bosons and Higgs bosons (16 = 3 3 + 1 + 5 1). 3 In principle mixing is possible between left and right handed squarks of each flavour but is expected only to be significant for the third generation squarks. 7

4.3 Minimal Supersymmetric Standard Model Table 4.1 Extra particles of the MSSM. name spin particles squarks ~ ~ ~ ~ d ~ ~ ~ ~ ~ ~ ~ ~ L, ul, sl, cl, b1, t1, d R, ur, sr, cr, b, t sleptons ~ e, ~ ν ~, ~, ~ ~ ~ ~ ~ el, µ L ν µ L τ1, ντl, R, µ R, τ L e charginos ½ ~ ± ~ ± Χ 1, Χ neutralinos ½ ~ ~ ~ ~ Χ 1, Χ, Χ 3, Χ 4 gluino ½ g ~ Higgs bosons 4 h, H, A, H ± 4.3.4 R-parity and the LSP In the SUSY model a new quantum number called R-parity is introduced. This number is 1 for all the standard model particles and -1 for all the supersymmetric partners 5. If R-parity is multiplicatively conserved, sparticles can only be produced in pairs and the LSP (Lightest SParticle) is necessarily stable. It is very unlikely that the LSP is coloured or electrically charged. In this case heavy isotopes should exist, because the LSP could bind to nuclei or atoms. These isotopes have however not been found experimentally. The LSP, which is the end product of each decay of sparticles, thus escapes experimental detection, resulting in apparent non-conservation of transverse energy/momentum in SUSY events (missing transverse energy). The most probable LSP candidate is one of the neutralinos ( Χ ~ ). 4.3.5 The breaking of supersymmetry in the MSSM In an unbroken supersymmetric theory the super-partners would be mass degenerate with the standard model partners. This is obviously not the case, otherwise these particles would have been observed. Therefore some mechanism has to break SUSY. One of the nicest properties of SUSY, the cancellation of the quadratic divergences in the Higgs mass, must however be maintained. The complete cancellation can not be maintained in a broken supersymmetric model, but the remaining divergence is not quadratic (like (4.1)) but logarithmic in the cut-off scale Λ and proportional to the mass difference between the particles of a SUSY multiplet. This means that the masses of the squarks should not significantly exceed 1 TeV and therefore be observable at the LHC. Several terms can parameterise the breaking process. In the MSSM only the so-called soft breaking terms are included. These terms are called soft because they preserve the remedy to the quadratic divergences of the Higgs mass. These are terms describing the masses of the scalar particles and gauginos and the couplings of the scalar particles. Even with this restriction, 14 independent parameters are necessary to describe all sparticles masses and couplings, making systematic studies very difficult [6]. 4.3.6 The SUGRA model A reduction of the number of free parameters is possible if one assumes that the parameters are not all independent but are related by higher symmetries, which are only defined at ultra- 1 4 The Higgs boson H exists also in the standard model. 5 The extra Higgs bosons in the MSSM h, A and H ±, are not super partners but normal particles with R-parity 1. 71

Chapter 4 Supersymmetry high energy. In a supergravity model the gravitational field is made supersymmetric. The partner of the graviton is called gravitino [7]. A very attractive class of models is based on supergravity combined with grand unification. In these models it is assumed that SUSY symmetry breaking in the effective theory defined at M x (GUT energy scale) is due to gravitational interactions. The SUGRA model combines the MSSM extension with supergravity and grand unification. Only five parameters are necessary to describe this model: m, m 1/, A, tanβ and sign(µ) = ±. A detailed description of these SUGRA parameters is beyond the scope of this thesis. Parameter m is the common mass of the scalar spin particles (squarks and sleptons) at energy scale M x. Parameter m 1/ is the common mass of the gauginos at energy scale M x. Parameter A is the common coupling term of two scalar particles (e.g. two sleptons) to a Higgs boson at energy scale M x. Parameter µ is a common mass parameter of the Higgsinos at energy scale M x. Parameter tanβ relates the masses of the Higgs bosons A m and m [5] 6 : masses of the massive vector bosons ± W m m m H h ± H = ½ m + m A = ½ m + m A = m + m ± W A Z Z + ( m + m ) ( m + m ) A A Z Z 4m 4m A Z A m m Z Z m, m, m and m ± with the cos β cos β From (4.3), it follows that the mass of the lightest Higgs boson m is strongly restricted: h m m h Z h H H (4.3) (4.4) However the masses mentioned above can receive large loop corrections, dominated by the exchange of virtual top and bottom quarks and squarks. These corrections can push the upper h mass limit above the Z mass. If the SUGRA model is correct, the maximum possible value for the h mass is about 135 GeV [8]. The various MSSM masses and couplings have to evolve from the common value at M x to that at the electroweak scale. This evolution of masses and couplings is described in some more detail in appendix D and based on the so-called renormalisation group equations [1]. In the simplest SUGRA model the first two generations of squarks are degenerate. The SUGRA parameters m and m ½ mainly determine the masses of the sparticles, see section 4.8. Experimental test of the SUGRA model The SUGRA model provides an economic and elegant framework. The assumptions about physics at ultra-high energy on which it is based, are however not necessarily correct. The attractive point is that in the SUGRA model the various sparticle masses and couplings can be calculated from the five parameters. There is a rather strict correlation between the sparticle masses and the cross-sections, see section 4.6. These predictions can serve as a test of the underlying assumptions at ultra-high energy. If sparticles are discovered and their properties can be determined, the five SUGRA parameters can be calculated via a fit from the sparticle 6 This parameter is not specific for SUSY but general for each model with a similar set of Higgs bosons. 7

4.3 Minimal Supersymmetric Standard Model masses and couplings. The quality of the fit can serve as an experimental test of the correctness of the SUGRA model, and it yields information about physics at ultra-high energy. 4.3.7 Points in SUGRA parameter space studied by ATLAS The ATLAS collaboration has decided to study five points in the SUGRA parameter space, which are given in table 4. 7. The five points in SUGRA parameter space together with the lines of constant squark and gluino mass are given in figure 4.3, together with the lines of ~ ~ constant l R and W 1 (gaugino) mass in figure 4.4. Theoretical constraints exclude the bricked regions. Experimental data excludes the cross-hatched regions. From these figures it follows that the five points are distributed in the range with squark and gluino masses up to ~ ~ 1 TeV, a l R mass up to 8 GeV and a W 1 mass up to 3 GeV. Table 4. Points in SUGRA parameter space studied by ATLAS. parameter point 1 point point 3 point 4 point 5 m (GeV) 4 4 8 1 m ½ (GeV) 4 4 1 3 A (GeV) 3 sign(µ) + + - + + tan(β). 1.. 1..1 7 The order for the five sets of parameters used in this note agrees with [9]. This differs from the order used in some older studies. Especially the order used in [1] is different. 73

Chapter 4 Supersymmetry Figure 4.3 The five points (marked as large dots) in SUGRA parameter space, together with the lines of constant q ~ and g ~ mass. Theoretical constraints exclude the bricked regions. Experimental data excludes the cross-hatched regions. Taken from [11]. 74

4.3 Minimal Supersymmetric Standard Model Figure 4.4 The five points in SUGRA parameter space, together with the lines of constant ~ ~ l R and W 1 mass. Taken from [11]. Mass spectrum of the sparticles The mass spectrum of the sparticles for the five SUGRA points studied is given in table 4.3 (based on calculations with PYTHIA, see section 4.5.). The first two generations of squarks ~ and sleptons are degenerate. The lightest neutralino Χ 1 is always the LSP. For point 1 [1, 13], the gluino g ~ is the heaviest sparticle. Compared to the other points the charginos and neutralinos are relatively heavy. The difference in mass for the squarks of different flavour is mostly within 5%, only the ~ t 1 squark is significantly lighter. The difference is mass for the sleptons is always within 1%. The charginos and neutralinos ~ have a much larger difference in mass. The heaviest neutralino ( Χ 4 ) is more than four times ~ heavier than the lightest one ( Χ 1 ). The mass spectrum of point [1, 13] is very close to ~ ~ ~ ± point 1, only the neutralinos Χ 3, Χ 4 and chargino Χ are significantly lighter. Point 3 [14, 15] has the lightest sparticles and is relatively easy to detect (see section 4.6). The ~ t squark is the heaviest sparticle. For point 4 [15, 16], the sleptons are very heavy and have almost the same mass as the squarks. The neutralinos and charginos however are rather light. The d ~ squark is the heaviest sparticle and significantly heavier than the gluino. Point 5 L 75

Chapter 4 Supersymmetry [13, 17] is consistent with a reasonable amount of dark matter 8 coming from the LSP. The sleptons are relatively light. The gluino is the heaviest sparticle. For all five points studied, the mass of the lightest Higgs boson is below 115 GeV. As expected from equation (4.3), the mass of H ± lies always slightly above the mass of A. Also the mass of H lies always slightly above the mass of A. Table 4.3 Mass spectrum of the SUGRA particles. squarks particle mass [GeV] point 1 point point 3 point 4 point 5 u ~ L, c ~ L 958 96 318 9 686 u ~ R, c ~ R 93 96 31 911 661 d ~ L, s~ 96 964 34 93 689 L d ~ R, s~ 94 97 314 91 66 R ~ t 1 659 719 57 6 51 ~ t 93 97 35 814 71 ~ b 86 876 81 788 636 1 ~ b 9 91 313 94 661 gluino g ~ 15 19 3 586 767 sleptons e~ L, ~ µ L, ~τ 49 491 16 814 39 e~ R, ~ µ R, ~ τ1 43 431 7 85 157 ~ ν el, ~ ν µ L, ~ ν τl 486 485 7 81 3 neutralinos charginos ~ Χ 168 168 45 7 11 ~ Χ 35 319 97 13 31 ~ Χ 77 493 45 18 481 ~ Χ 744 514 6 39 56 1 3 4 ~ Χ 34 318 97 115 3 ~ Χ 741 514 61 39 53 ± 1 ± Higgs sector A 117 71 36 839 615 h 9 113 68 11 9 H ± 13 75 368 843 6 H 14 71 368 84 6 8 The dark matter is matter observed in the universe that can not be explained by current models. 76

4.4 Supersymmetry at hadron colliders 4.4 Supersymmetry at hadron colliders 4.4.1 Production of sparticles At hadron colliders (like the LHC) sparticles can be produced via the following lowest order reactions [1]: Strong production: qq, gg gg ~~, q~~ q qq qq ~~ qg qg ~~ 77 (4.5) In the first reaction, the produced squark and antisquark are of the same flavour. Also the incoming quark and antisquark are of the same flavour. In the second and third reaction, the flavour of the incoming quark(s) determines the flavour of the produced squark(s). Associated production: ± qg q~ ~ ~ Χ i, q~ Χ i ± qq g~ ~ Χ g~ ~ (4.6), Χ i i with i = 1, 4 in the case of neutralinos and i = 1, in the case of charginos. The flavour of the incoming quark determines the flavour of the produced squark. Production of ~ Χ pairs: qq ~ Χ ± i ~ Χ m j ~, Χ ± i ~ Χ ~ ~ j, Χ i Χ j (4.7) with i = 1, 4 and j = 1, 4 in the case of neutralinos and i = 1, and j = 1, in the case of charginos. In principle any combination of i and j is allowed. Production of slepton pairs: qq ~ l ~ ~ + ~ ~ l l ~ +, ν l, l l ν, ~ ν ~ ν l l (4.8) In the expressions (4.5) to (4.8) the left- and right-handed states are not noted explicitly: q ~ = ( q~ L, q~ R ). 4.4. Decay of sparticles In general production of sparticle pairs is followed by sparticle decays through a cascade until ~ the LSP ( Χ 1 ) state is reached. In each step of the cascade a standard model particle is produced leading to a jet or a (charged isolated) lepton in the event. Jets are for example produced via the decay: ± g ~ qqχ ~ (4.9) i followed by fragmentation/hadronisation of the produced quark and antiquark. Isolated leptons are for example produced via the decay: ~ ~ Χ ± ± i W Χ j (4.1) ± with the W decaying into a l ± ν l pair. The jets are in general produced in the first steps of the cascade decay via the strong interaction where the masses between the sparticles vary most. The leptons are in general produced in the last steps of the cascade decay. This means that the spectrum of the produced jets will be harder than of the produced leptons. Hence

Chapter 4 Supersymmetry events with n jets plus m isolated leptons plus missing transverse energy signal the production of sparticles. The events can be divided in classes based on the number of isolated leptons that are produced: Events with no isolated leptons. Vetoing on isolated leptons can identify these events. Events with one isolated lepton. These events are difficult to identify, due to the huge standard model background, especially the decay W ± l ± ν l. The standard model background is described in more detail in the following section. Events with two isolated leptons. These events can be divided into decays to two opposite charge-sign isolated leptons and decays to two same charge-sign isolated leptons. The opposite charge-sign events are difficult to identify, due to background from t t, W + W and τ + τ decays. Decays to two same sign leptons are specific for SUSY events with a much smaller standard model background. These decays are possible because in all existing supersymmetric models the gluinos are at the same time particle and antiparticle. Such fermions are also referred to as majorana fermions. The consequence of this is that for each allowed decay mode the corresponding charge conjugate decay mode is also possible. The gluino g ~, being a majorana particle, is produced mostly in a q ~ g ~ pair or g ~ g ~ pair due to the conservation of R-parity. If a g ~ g ~ pair is produced, both g ~ s can decay via the same or similar decay channel and create final states with two high-p T isolated leptons of the same charge sign and produced in the same interaction. Events with three isolated leptons. These events have a low cross-section, but also a low standard model background. Events with four isolated leptons. These events have a very low cross-section, but also a very low standard model background. Events with five or more isolated leptons. These events can only be produced by multistep cascades of very heavy sparticles or in R-parity violating models where the LSP decays further into leptons [1]. 4.4.3 Standard Model background Standard model processes leading to missing transverse energy, hard jets and hard isolated leptons give a background to the SUSY signal. The missing transverse energy in this case is coming from high-p T neutrinos and high-p T particles outside the detector acceptance. The most important standard model processes are [9]: tt -production with, most often, at least one semi-leptonic decay. The W produced decays via W ± l ± ν l, leading to missing transverse energy from the neutrino and one detected hard isolated lepton (if the lepton is a muon or electron and inside the detector acceptance). Z + + jet production, followed by a Z ν lν l or Z τ τ decay. The hard neutrinos produced cause missing transverse energy. The τ + τ pair produced decays further into leptons and neutrinos. ± W + jet production, followed by a W ± l ± ν l decay. 78

4.5 Simulation packages 4.5 Simulation packages 4.5.1 Introduction This section describes the simulation packages that I have used for the simulations described in section 4.6, section 4.7 and section 4.8. The event generator PYTHIA is described in section 4.5., the event generator ISAJET is described in section 4.5.3. An event generator is a Monte Carlo computer program used for the simulation of interactions between beam particles at LHC, giving rise to a signal in the detector. These programs can also be used to calculate production cross-section of SUSY events. The program PROSPINO is described in section 4.5.4. This program is not a complete event generator and can only be used to calculate production cross-sections of SUSY events. The events generated with PYTHIA have been combined with detector simulation based on ATLFAST. The package ATLFAST is described in section 4.5.5. 4.5. PYTHIA The FORTRAN package PYTHIA is a commonly used event generator. Both version 5.7 and version 6.1 have been used to calculate the results presented in the following sections. Version 5.7 of PYTHIA [19] does not include SUSY events and needs the extension SPYTHIA (version.8) []. In the remaining part of this chapter this extension is not mentioned explicitly. In version 6.1 [1] the SUSY extension is fully integrated. PYTHIA calculates the production and full cascade decay of SUSY events including QED 9 /QCD 1 initial and final state radiation 11, fragmentation, hadronisation and decays of unstable particles. Strong production processes, associated production processes, the production of ~ Χ pairs and the production of slepton pairs are included. In version 6.1 all calculations are done in double precision. Version 6.1 contains several changes compared to version 5.7 [1]. The calculation of sparticle masses has been improved. The strategy for the selection of slepton family and squark flavour, in processes with several families or flavours allowed, has also been changed. The parton distribution functions have been updated. Particle data information has been updated to the particle data group 1996 edition []. PYTHIA calculates for each generated event an event record that is implemented as a FORTRAN common block. Each jet or particle that appears at some stage of the fragmentation or decay chain is stored in the event record. From the stored information it can be reconstructed which jet or particle it is, from which it originates, its present status (fragmented/decayed or not), its momentum, energy and mass, and the space and time position of its production vertex. PYTHIA can be used both for SUGRA and for more general MSSM simulations. This makes it possible to study a much richer phenomenology than that possible in SUGRA inspired models only. In the case of SUGRA simulations, the masses and couplings of the sparticles are not calculated by numerically solving the renormalisation group equations starting 9 QED (Quantum ElectroDynamics) describes the electromagnetic interaction 1 QCD (Quantum ChromoDynamics) describes the strong interaction between quarks and gluons. 11 Initial stage radiation can for example be the process where a gluon splits off a quarkantiquark pair before going into the hard interaction. 79

Chapter 4 Supersymmetry from the five SUGRA parameters, but are calculated via approximate analytic formulae, using the five SUGRA parameters as input []. The effect of pile-up events can be included in PYTHIA by generating several events at the same time and putting one after the other in the event record, to simulate the full amount of particle production a detector might be facing. The included minimum bias events are due to low-p T processes, double diffractive processes (AB XY), single diffractive processes (AB XB or AB AX) and elastic processes (AB AB). In the current implementation of PYTHIA all events are supposed to be produced at the same vertex (the origin), the length of the LHC interaction region along the beam line is not taken into account. 4.5.3 ISAJET ISAJET (version 7.31) is another frequently used Monte Carlo program for simulation of pp and p p interactions at high energies [3]. It also generates e + e - scattering events, although this is less developed. This program is also written in FORTRAN. QCD describes the hard scattering process. Phenomenological models for the fragmentation and hadronisation of the partons and the creation of jets are used. Events are generated in four distinct steps: A primary hard interaction is generated according to the appropriate QCD cross-section. Corrections due to QCD initial and final state radiation are added. Partons are fragmented into hadrons, and the decay of particles with a lifetime less than about 1-1 seconds is described. Additional jets are added due to the remaining partons that do not participate in the hard interaction. It is assumed that these jets are identical to jets due to a minimum bias event at the remaining energy. The strong production, the associated production, the production of ~ Χ pairs and the production of slepton pairs are included in ISAJET. For each event ISAJET generates a common block in which parton and particle information about the momentum, decay products and origin (the particle by which it was created) is stored for each generated jet. A serious restriction of ISAJET compared to PYTHIA is that ISAJET is basically developed for analysis studies at the level of partons (without detector response simulation). ISAJET does not provide information about the production vertex of particles. All particles are always produced at the origin and decay at the origin. This makes it much more difficult to incorporate ISAJET into detector simulation programs. 4.5.4 PROSPINO With the FORTRAN package PROSPINO [4], the production cross-section of squarks and gluinos at hadron colliders can be calculated (strong production only). Next-to-leading order SUSY QCD corrections to all possible final states ( q ~ q~, qq ~~, qg ~~, gg ~ ~ ) are included (see below). Both the total cross-section as well as the differential distribution in the transverse momentum p T and the rapidity y of one of the outgoing particles can be calculated, with the rapidity given by 1 : E + p z y = ln (4.11) E pz The cross-sections are summed over all squark flavours (except the top squark). The calculation is based on a SUSY model in which all squarks have one common mass. The squark 1 For massless particles the rapidity y is equal to the pseudorapidity η. 8

4.5 Simulation packages mass and gluino mass should be specified as parameters. The five lightest quarks are regarded as massless. The mass of the top quark should be specified as parameter. The total hadronic cross-section of the q ~ q ~ final state is calculated in the following way: σ pt, max ( pp q~ + q~ + X ) = dpt pt, min ymax ymin d dy σ ( q ~ + q~ + X ) dp dy T (4.1) A similar expression is valid for the q ~ q ~, q ~ g ~ and g ~ g ~ final states. The double differential cross-section is given by: d 1 1 σ h h = pt s x1 f ( x1, Q )dx1 x f p dy i j T i, j= g, q, q d ( x, Q d σ ij ( x1x, s, Q ) dtdu ) d 1 x (4.13) In these expressions p T and y are the transverse momentum and rapidity of the second particle. The indices i and j indicate the initial state partons. Expression (4.13) contains a sum over all possible initial states (quarks, antiquarks and gluons). The centre-of-mass energy is given by s. The terms x 1 and x indicate the fraction of the total momentum carried by the partons that enter the hard collision. The invariants t and u are the so-called Mandelstam variables, related to the momentum transfer from the initial-state partons to the detected final state particle. A two-body reaction (e.g. qq q ~ q~ ) is given by: k + 1 + k = p1 p (4.14) with k 1 and k the momenta of the two partons in the initial state, and p 1 and p the momenta of the two partons in the final state. In this case s, t, and u are given by: s = t = u = ( k1 + k ) = ( p1 + p ) ( k1 p1 ) = ( k p ) ( k p ) = ( k p ) 1 1 a (4.15) The parton distribution function fi ( x, Q ) parameterises the probability to find a parton i with a fraction x of the beam energy when the beam particle a undergoes a hard scattering at energy scale Q, with the energy-scale defined as the square root of the four momentum transferred between the scattering particles [19]. Two options are available for the energy scale Q in PROSPINO. The first one is the average mass of the outgoing massive particles. The second one is the so-called transverse mass of the detected particle with mass m and momentum p T : Q = m + p T (4.16) All calculations made with PROSPINO are based on the second energy scale (4.16). The double differential cross-section is calculated by numerically solving (4.1) and (4.13) in leading order and next-to-leading order approximation [5]. In leading order only the terms with α s are included, with α s the strong coupling constant (lowest order Feynman diagrams, 4 see appendix D). In next-to-leading order also the terms with α s (like loop corrections) are included. 81

Chapter 4 Supersymmetry 4.5.5 ATLFAST To calculate the global response of the ATLAS detector for the events generated with PYTHIA, I have used the FORTRAN package ATLFAST [6] (version 1. and.). The program ATLFAST provides a fast simulation based on parameterisation of the response of the ATLAS detector on particles produced (see also chapter 3). It contains the most important detector aspects: jet reconstruction in the calorimeters, momentum and energy smearing for leptons and photons, reconstruction of muons in the muon spectrometer, reconstruction of charged tracks in the inner detector (version. only), magnetic field effects and missing transverse energy. ATLFAST only analyses the stable, final particles. ATLFAST reconstructs the expected missing transverse energy, calorimeter clusters, selects and stores reconstructed isolated leptons and photons, tracks reconstructed in the inner detector, hadronic jets and tagged b jets and c jets. Calorimeter The transverse energies of all stable particles, except neutrinos, muons and the SUSY LSP are summed in calorimeter cells over the full calorimeter coverage ( η < 5). The used granularity is.1.1 (bins of pseudorapidity and azimuth η φ) for η 3, and.. for 3 < η < 5. Smearing the φ-position according to a Gaussian distribution parameterises the effect of the solenoid magnetic field on the φ-position of charged particles. No detailed model for showering is implemented in the current ATLFAST program. All calorimeter cells with transverse energy E T greater than 1.5 GeV are taken as possible initiators of a cluster. If the total transverse energy E T = E x E y summed over all cells in a cone R =.4, with R = η φ, around the initiator cell (including the initiator cell) exceeds a threshold of 1 GeV, the cluster is accepted and stored separately. The PYTHIA output is checked for isolated photon and isolated electron candidates. The photon momentum, polar angle of the electron/photon and electron transverse momentum p T are smeared according to a Gaussian distribution. The default cut for isolation is separation by R >.4 from other clusters, and a deposited transverse energy E T < 1 GeV in a cone R =. around the electron. The photons and electrons passing the selection criteria for p T and η and isolation cuts are stored. The associated clusters are identified. The clustered cells that are not associated with isolated electrons or photons are used for jet reconstruction. The energy of those clusters is smeared with a Gaussian energy resolution. The energy of non-isolated muons that fall inside the cluster cone is added to the smeared cluster energy. The resulting jet clusters with E T above threshold are labelled as reconstructed jets. If a b quark or c quark of p T > 5 GeV is found in a cone around the reconstructed jet axis, the jet is flagged as b jet or c jet. 8

4.6 Production cross-section of SUSY events for 5 points in SUGRA parameter space Inner detector (version.) The PYTHIA output is checked for stable charged particles. The track parameters are reconstructed from the true vertex position, stored in the event record of PYTHIA. The five track parameters (a, z, φ, cotθ, Q/p T ) are smeared according to a Gaussian distribution. The covariance matrix of the track parameters is taken into account. The matrix elements depend on η and on p T. In the program several tables of matrix elements for different sets of η and p T -values are stored. A two-dimensional interpolation is used to calculate the matrix elements for a given set of η and p T -values. The interpolation is linear in η and p T. The inner detector parameterisation implemented in ATLFAST is described in more detail in chapter 3. Muon spectrometer and combined muon spectrometer/inner detector The PYTHIA output is checked for isolated muon candidates. The muon momentum is smeared according to a Gaussian momentum resolution. The momentum resolution is based on the muon spectrometer alone, or the muon spectrometer combined with the inner detector 13. The muon momentum resolution implemented in ATLFAST as function of p T, η and φ is described in more detail in chapter 3. All muons passing the selection criteria in p T and η are stored. Isolated muons passing isolation cuts, in terms of distance from calorimeter clusters, are stored separately. The default cut is a separation by R >.4 from other clusters and a deposited energy E T < 1 GeV in a cone R =. around the muon. 4.6 Production cross-section of SUSY events for 5 points in SUGRA parameter space 4.6.1 Introduction I have calculated the cross-section of SUSY events with PYTHIA and PROSPINO. I have studied the effect of next-to-leading order effects with PROSPINO. I have compared the calculated cross-sections with the cross-sections given in literature, using ISAJET as event generator. Comparison between the different simulation packages is difficult, because they are all based on somewhat different physics models. Also the model used for the parton density a fi ( x, Q ) has important consequences for the cross-section. 4.6. Comparison between PYTHIA and PROSPINO The fact that PROSPINO is based on a somewhat different MSSM model, where the u ~, d ~, c ~, ~ s and b ~ squarks have the same mass, complicates the comparison between PYTHIA and PROSPINO. From table 4.3 it follows that for the SUGRA model the squarks u ~ R, d ~ ~ R, b are slightly lighter than u ~ L and d ~ ~ L. The lightest bottom squark b 1 however is always significantly lighter. The mean value of the five squarks is used as input for PROSPINO. These numbers are summarised in table 4.4. 13 The inner detector parameterisation differs from the parameterisation used to smear the five track parameters. This means that in version. of ATLFAST two different parameterisations for the inner detector momentum resolution are implemented. 83

Chapter 4 Supersymmetry Table 4.4 The squark/gluino masses used in PROSPINO. point 1 point point 3 point 4 point 5 m squark (GeV) 931 935 313 9 669 m gluino (GeV) 15 19 3 586 767 The results of comparing PYTHIA with PROSPINO are presented in table 4.5. The PYTHIA results are based on 1 4 events. Five different values are given in this table: PROSPINO in leading order (LO), using a parton density function from the PDFLIB [7] library (set 9 of group 4, CTEQ 3L LO). PROSPINO in leading order (LO), using the parton density function internally implemented in PROSPINO (GRV94 [4]). PROSPINO in next-to-leading order (NLO), using the internal GRV94 parton density function. The PROSPINO next-to-leading order results include the sum of leading and next-to-leading order contributions. PYTHIA version 5.7 using the same CTEQ 3L LO parton density function from the PDFLIB library as PROSPINO. PYTHIA version 6.1 using the same CTEQ 3L LO parton density function from the PDFLIB library. For each SUGRA point studied, the total production cross-section of squark pairs is given, splitted in the contribution from the production of squark-antisquark pairs and the production of squark-squark pairs. The production cross-section of squark-gluino pairs and the production cross-section of gluino pairs are also given. The production of top squarks is always excluded. The total SUSY production cross-section is also given (PYTHIA only). This number also includes top squark production and production of charginos and neutralinos (associated production). These processes are not included in PROSPINO. From the table it follows that the cross-section increases significantly when the next-toleading order corrections are included. The next-to-leading order cross-sections are up to a factor two higher than the leading-order cross-sections, e.g..38 against.1 for pp g ~ g~ production in the case of SUGRA point. The model used for the parton distribution function has important consequences for the cross-section. The lowest-order parton distribution function from the PDFLIB library (CTEQ 3L) gives significantly higher results than the internal PROSPINO GRV94 parton distribution function. Sometimes the leading-order CTEQ 3L results are even larger than the next-to-leading order GRV94 results. PYTHIA version 5.7 gives in general higher cross-section values than PROSPINO, even if the same CTEQ 3L parton distribution function is used. There is also no exact agreement between version 5.7 and version 6.1 of PYTHIA, differences of more than 1% are occurring. For the same model and program, the cross-sections of point 1 and point do not differ very much. Point 3 has a cross-section value of at least a factor 1 higher than the other points. For SUGRA points 1,, 3 and 5 the most important contribution comes from squarkgluino production. Except for point 3 the contribution from gluino-gluino is only a relatively small fraction (about 1%). For point 4 the most important contribution comes from gluinogluino production. The production of squark-gluino pairs is about 5% smaller for this point. The production of squark-squark or squark-antisquark pairs is only a relative small fraction for this point (about 1%). 84

4.6 Production cross-section of SUSY events for 5 points in SUGRA parameter space Table 4.5 Production cross-sections of SUSY final states calculated with PROSPINO and PYTHIA [pb]. PROSPINO LO (CTEQ 3L) PROSPINO LO (GRV94) PROSPINO NLO (GRV94) PYTHIA version 5.7 (CTEQ 3L) PYTHIA version 6.1 (CTEQ 3L) point 1 pp qq ~ ~.44.34.47.58.59 pp qq ~ ~.7.6.67 1.6 1.4 pp qq ~~, qq ~ ~ 1.16.94 1.14 1.64 1.63 pp qg ~ ~ 1.61 1.7 1.65 1.78 1.77 pp gg ~ ~.8.1.39.3.35 total 4.63 4.49 point pp qq ~ ~.43.33.45.5.59 pp qq ~ ~.71.59.66 1.3 1. pp qq ~~, qq ~ ~ 1.13.9 1.11 1.53 1.61 pp qg ~ ~ 1.58 1.4 1.61 1.89 1.78 pp gg ~ ~.7.1.38.31.9 total 4.43 4.35 point 3 pp qq ~ ~ 1.33 1 1.1 1 1.5 1 1. 1 1.5 1 pp qq ~ ~.76 1.64 1.75 1 1. 1 1.1 1 pp qq ~~, qq ~ ~.9 1 1.74 1.7 1. 1.6 1 pp qg ~ ~ 6.88 1 5.85 1 7.3 1 6.1 1 7. 1 pp gg ~ ~ 4.4 1 3.49 1 5.3 1 4.8 1 4.4 1 total 1.38 1 3 1.55 1 3 point 4 pp qq ~ ~.58.44.6.6.6 pp qq ~ ~ 1.1.84 1.3.9 1. pp qq ~~, qq ~ ~ 1.59 1.8 1.63 1.6 1.8 pp qg ~ ~ 9.84 7.74 1.7 6.7 8.9 pp gg ~ ~ 1.45 7.89 15. 1.1 1.4 total 6.4 8.7 point 5 pp qq ~ ~.85.1 3.1 3.6 3.9 pp qq ~ ~ 3.14.59.9 4.6 4.5 pp qq ~~, qq ~ ~ 5.99 4.8 6. 8. 8.4 pp qg ~ ~ 8.95 7.7 9.15 1.9 1. pp gg ~ ~ 1.85 1.39.51.1.1 total 5.8 3.6 85

Chapter 4 Supersymmetry 4.6.3 Comparison between PYTHIA and ISAJET In table 4.6 the total production cross-sections of the various final states calculated with ISAJET are compared with the results from PYTHIA. The ISAJET (version 7.) results are taken from literature [9]. Three different PYTHIA results are given. In this table all PYTHIA results are based on the internal parton distribution function (CTEQ L, best leading order fit [19]). By default, PYTHIA and ISAJET use a somewhat different approach to evaluate the masses and couplings from the SUSY particles starting from the common value at the SUGRA scale. In ISAJET the renormalisation group equations are numerically solved to calculate the masses and couplings of the sparticles. PYTHIA is based on approximate analytic formulae where the five SUGRA parameters are used as input []. To make a better comparison between ISAJET and PYTHIA possible the evolution method of ISAJET has also been included in PYTHIA. The first PYTHIA result is taken from literature [9] and based on version 5.7 of PYTHIA using the evolution method from ISAJET 14. The result for SUGRA point is missing in [9], but will be almost similar to SUGRA point 1. The second result is a standard approximate SUGRA simulation based on version 5.7 of PYTHIA. The third result is a standard approximate SUGRA simulation based on version 6.1 of PYTHIA. For SUGRA point 1 and point 5, ISAJET and PYTHIA with the ISAJET model for mass development, have a good (although not exact) agreement. For point 3 and point 4, the differences between ISAJET and PYTHIA are much larger. The original PYTHIA version actually agrees much better with ISAJET in this case. Comparing the original version of PYTHIA with the adapted version shows that the model used for the development of masses and couplings significantly influences the cross-section. Also with the internal CTEQ L parton distribution function, there is no exact agreement between version 5.7 and version 6.1 of PYTHIA. Especially for point 3 and point 4 the new version gives significantly larger crosssection values. 4.6.4 Conclusions The production cross-sections of SUSY events calculated with somewhat different models and parameterisations differ significantly. Differences up to a factor are occurring. This means that cross-sections should always be handled with care. Next-to-leading order contributions, which are not included in most models, are significant. The current programs however give a useful indication for the order of magnitude of the production cross-section of SUSY events. There is a strong relation between the masses of the sparticles and the cross-sections. Point 3 with the lightest sparticles has a cross-section value of at least a factor 1 higher than the other points. Compared to point 1 and point, the masses of most squarks of point 4 are roughly the same. The gluino is significantly lighter. This results in roughly the same cross-section for q ~ q ~ and q ~ q ~ production, but a much larger cross-section value for q ~ g ~ and g ~ g ~ production. 14 This option is not documented in the SPYTHIA manual []. 86

4.6 Production cross-section of SUSY events for 5 points in SUGRA parameter space Table 4.6 Production cross-sections of SUSY final states calculated with ISAJET and PYTHIA [pb] (all results based on CTEQ L parton distribution function). ISAJET 7. 15 PYTHIA 5.7 16 PYTHIA 5.7 17 PYTHIA 6.1 point 1 pp qq ~ ~.4.6.58 pp qq ~ ~.79.97 1.1 pp qq ~~, qq ~ ~ 1.13 1.1 1.59 1.67 pp qg ~ ~ 1.43 1.45 1.91 1.97 pp gg ~ ~.9.9.41.36 total 3.4 3.6 4.86 4.79 point pp qq ~ ~ -.56.57 pp qq ~ ~ - 1. 1.6 pp qq ~~, qq ~ ~ 1.8-1.55 1.63 pp qg ~ ~ 1.4-1.97 1.9 pp gg ~ ~.7 -.4.3 total 3.6-4.71 4.63 point 3 pp qq ~ ~ 1. 1 1.4 1 1.5 1 pp qq ~ ~ 8 1 1 8.9 1 1 1 1 1 pp qq ~~, qq ~ ~.1 1. 1.3 1.5 1 pp qg ~ ~ 6.5 1 5.6 1 6.3 1 6.7 1 pp gg ~ ~ 4.3 1 4. 1 4.6 1 5. 1 total 1.37 1 3 1.3 1 3 1.39 1 3 1.6 1 3 point 4 pp qq ~ ~.5.7.7 pp qq ~ ~ 1.1 1. 1.5 pp qq ~~, qq ~ ~ 1.6 1.6 1.9.1 pp qg ~ ~ 8.7 5.9 6.6 1.4 pp gg ~ ~ 11.1 1.8 13. 15. total 7.1 4.9 8.1 34.3 point 5 pp qq ~ ~.5 3.7 3.7 pp qq ~ ~ 3.6 4.4 4.8 pp qq ~~, qq ~ ~ 6.1 6. 8. 8.4 pp qg ~ ~ 8.5 8.8 1.9 1.7 pp gg ~ ~ 1.9..4.3 total 19..5 6. 5. 15 Taken from literature [9]. 16 PYTHIA version 5.7 with ISAJET mass evolution method, taken from literature [9]. 17 PYTHIA version 5.7 with default method for mass evolution. 87

Chapter 4 Supersymmetry 4.7 Event characteristics of SUSY events for 5 points in SUGRA parameter space 4.7.1 Introduction For each of the five points in the SUGRA parameter space studied by the ATLAS collaboration, I have generated a sample of 1 4 events (with PYTHIA version 6.1). The generation of 1 4 events (PYTHIA) together with the response of the ATLAS detector (ATLFAST) takes about 9 minutes on an HP 9/871 computer-system. The results presented can be compared with the results of older studies [1], using ISAJET as particle generator and the program CALSIM [1] as fast detector simulation. In the current study also the effect of background is taken into account. The used background sample is described in section 4.7.. The SUSY particles produced in the primary process are described in section 4.7.3. In the other sections the event characteristics of the SUSY events are compared with the corresponding event characteristics of the background sample. Based on the event characteristics selection cuts can be defined to increase the signal to background ratio. The missing transverse energy spectrum is described in section 4.7.4. The transverse sphericity spectrum is described in section 4.7.5. The characteristics of the jets produced in the cascade decay are described in section 4.7.6. The characteristics of the leptons produced in the cascade decay are described in section 4.7.7. Conclusions are finally presented in section 4.7.8. 4.7. Background sample A sample of 1 6 background events, based on the processes given in section 4.4.3, has also been generated. The background sample has been created by a farm of Pentium Pro Windows NT and HP UNIX machines. The production cross-sections of the background processes are summarised in table 4.7. To reduce the data size of the background sample, events are only stored if the missing transverse energy is at least 5 GeV or at least two jets with a transverse momentum of 5 GeV are created. The background processes are only accepted if they are created in the pseudorapidity range η 5.5. These cuts accept about 5.7% of the background events (table 4.7). From the table it follows that only a small fraction (.17%) of the background events passes both cuts at the same time. This means that mostly either hard jets or hard neutrinos are produced, but not both at the same time. From the table it follows that the production cross-section of background is at least a factor 1 4 larger than for SUSY events, except for SUGRA point 3 which has only a factor 1 smaller cross-section. This means that for a detailed comparison between background and signal a sample of 1 8 background events is actually necessary, when 1 4 signal events are generated. 88

4.7 Event characteristics of SUSY events for 5 points in SUGRA parameter space Table 4.7 Production cross-sections of background processes and fractions passing the selection cuts. σ total [mb] 3.8 1-4 σ ( qq tt ) [mb] 1.1 1-8 σ ( gg tt )[mb] 4.6 1-7 σ ( gg gz ) [mb] 5.1 1-5 σ ( qg qz ) [mb] 7. 1-5 ± σ ( qq gw ) [mb] 1. 1-4 ± σ ( qg qw ) [mb] 1.3 1-4 miss fraction E T > 5 GeV, η < 5.5 [%].36 fraction two jets > 5 GeV, η < 5.5 [%] 3.5 fraction E > 5 GeV or two jets > 5 GeV, η < 5.5 [%] 5.71 miss T 4.7.3 SUSY particles produced in the primary processes Figure 4.5 to figure 4.9 show the particle types for SUSY particles produced in the primary processes, according to the convention used by PYTHIA version 5.7 (table 4.8) 18. Particles and antiparticles are not distinguished in this case. Vertical lines separate the squarks, the sleptons, the gluino and the charginos/neutralinos. For all points, the summed strong production and associated production are dominant. Production of sleptons occurs only very rarely, except for point 5 where the sleptons are relatively light. Point 4 has a relatively large contribution from associated production and Χ ~ pair production. This can be explained by the fact that for this point the masses of the charginos and neutralinos are relatively small compared to the masses of the squarks. The errors given in the histograms are statistical errors only. Table 4.8 PYTHIA particle codes (version 5.7 convention). code particle code particle code particle code particle code particle 41 d ~ L 4 d ~ R 43 u ~ L 44 u ~ R 45 s~ L 46 s~ R 47 c ~ L 48 c ~ ~ ~ R 49 b1 5 b 51 ~ t1 5 ~ t 53 e~ L 54 e~ R 55 ~ ν el 56 ~ ν er 57 ~ µ L 58 ~ µ R 59 ~ ν µ L 6 ~ ν µ R 61 ~ τ1 6 ~τ 63 ~ ν τl 64 ~ ν τr 65 g ~ ~ ~ ~ ~ ~ ± 66 Χ 1 67 Χ 68 Χ 3 69 Χ 4 7 Χ 1 ~ ± 71 Χ 18 The convention for the numbering of SUGRA particles used by version 6.1 of PYTHIA is according to the so called LEP standard and differs from the convention used by version 5.7 of PYTHIA [1]. 89

Chapter 4 Supersymmetry 1E-7 1E-7 1E-8 squarks sleptons gluino charginos/neutralinos 1E-8 squarks sleptons gluino charginos/neutralinos σ(mb) σ(mb) 1E-1 1E-1 1E-11 4 5 6 7 8 Particle type 1E-11 4 5 6 7 8 Particle type Figure 4.5 Particle type of SUSY particles produced, point 1. Figure 4.6 Particle type of SUSY particles produced, point. 1E-5 squarks sleptons gluino charginos/neutralinos 1E-7 squarks sleptons gluino charginos/neutralinos 1E-6 1E-8 σ(mb) 1E-7 1E-8 σ(mb) 1E-1 1E-1 4 5 6 7 8 Particle type 1E-11 4 5 6 7 8 Particle type Figure 4.7 Particle type of SUSY particles produced, point 3. Figure 4.8 Particle type of SUSY particles produced, point 4. 1E-7 squarks sleptons gluino charginos/neutralinos 1E-8 σ(mb) 1E-1 1E-11 4 5 6 7 8 Particle type Figure 4.9 Particle type of SUSY particles produced, point 5. 4.7.4 Missing transverse energy Missing transverse energy is always the clearest signature of an R-parity conserving SUSY miss event. Figure 4.1 to figure 4.14 show the missing transverse energy E T distributions, defined as: E miss T = E miss x E miss y 9 (4.17) The spectrum for the SM background is given in figure 4.15. Both the true missing transverse energy, based on particles escaping detection (muons outside detector acceptance, neutrinos and SUSY LSP), and the measured missing transverse energy (based on ATLFAST) are presented.

4.7 Event characteristics of SUSY events for 5 points in SUGRA parameter space The measured missing transverse energy gives a very good estimation of the true missing transverse energy. The measured missing energy can be obtained by summing over all calorimeter cells plus the reconstructed muons (data from the muon spectrometer): E E miss x miss y = E = E observed x observed y = = E E x y = = E E T T cosφ sinφ (4.18) with E T the measured transverse energy deposition in the cell or the reconstructed transverse energy of the muon and φ the angular position of the cell or reconstructed muon. The missing energy is directly related to the mass of the LSP. Especially point 1, point and point 5 with a relatively heavy LSP have a very hard missing transverse energy spectrum. For a missing transverse energy between GeV and 4 GeV the differential cross-section of SUGRA point 3 is comparable with the SM background. More statistics is necessary to investigate the differential cross-section for the SM background between 4 GeV and 8 GeV. The generation of more events is however problematic due to the long calculation time (section 4.7.). miss T A cut of E > GeV will keep about 8% of the SUSY events for point 1, point and point 5. This cut rejects about 97% of the background events that pass the cuts described in table 4.7. For point 3 and point 4 the E T miss spectrum is relatively soft. A cut of miss T E > 1 GeV will keep about 7% of the signal events for point 4 while still rejecting miss 75% of the background events. For point 3 only a soft cut of E T > 5 GeV is possible. Otherwise the loss of signal events is too large. 1.E-9 dσ/de T (mb/ GeV) 1E-1 Measured True dσ/de T (mb/ GeV) 1.E-1 Measured True 1E-11 4 8 1 16 Missing E T (GeV) Figure 4.1 Missing transverse energy, point 1. 1.E-11 4 8 1 16 Missing E T (GeV) Figure 4.11 Missing transverse energy, point. 1E-6 1E-8 dσ/de T (mb/ GeV) 1E-7 1E-8 Measured True dσ/de T (mb/ GeV) 1E-1 Measured True 1E-1 4 8 1 16 Missing E T (GeV) Figure 4.1 Missing transverse energy, point 3. 1E-11 4 8 1 16 Missing E T (GeV) Figure 4.13 Missing transverse energy, point 4. 91

Chapter 4 Supersymmetry 1E-8 1E-5 dσ/de T (mb/ GeV) 1E-1 Measured True dσ/de T (mb/ GeV) 1E-6 1E-7 1E-8 Measured True 1E-11 4 8 1 16 Missing E T (GeV) Figure 4.14 Missing transverse energy, point 5. 4 8 1 16 Missing E T (GeV) Figure 4.15 Missing transverse energy, SM background. 4.7.5 Transverse sphericity A frequently used quantity in jet physics is the transverse sphericity describing the degree of isotropy of an event. The transverse sphericity S T is shown in figure 4.16 to figure 4. for the signal and in figure 4.1 for the standard model background. The transverse sphericity is given by the ratio of eigenvalues of the sphericity tensor S in the transverse plane: S T λ = λ + λ 1 S is given by: S px px = px p y p y p y (4.19) (4.) The transverse sphericity has always a value between and 1, for isotropic decays S T = 1. Both the true transverse sphericity and the measured transverse sphericity are presented. The true transverse sphericity is calculated directly from the PYTHIA event record. Only stable particles that can be detected are used. The neutrinos and LSP are excluded. The measured transverse sphericity is based on the energy deposited in the calorimeter cells and the momentum of the muons. The measured transverse sphericity slightly overestimates the true sphericity. In general a rather high transverse sphericity value will characterise SUSY events. In some studies a cut of S T >. is suggested [1]. Figure 4.1 however shows that the background distribution has a quite similar shape to the SUSY signal distributions. The fraction of events with S T >. is even larger. This means that the transverse sphericity is a quantity not well suited for discriminating on SUSY events. A cut of S T >. will even decrease the signal to background ratio. 9

4.7 Event characteristics of SUSY events for 5 points in SUGRA parameter space dσ/ds T (mb/.1) 1E-1 Measured True dσ/ds T (mb/.1) 1E-1 Measured True 1E-11.1..3.4.5.6.7.8.9 1 S T 1E-11.1..3.4.5.6.7.8.9 1 S T Figure 4.16 Transverse sphericity, point 1. Figure 4.17 Transverse sphericity, point. 1E-7 dσ/ds T (mb/.1) 1E-8 Measured True dσ/ds T (mb/.1) 1E-1 Measured True 1E-1.1..3.4.5.6.7.8.9 1 S T 1E-11.1..3.4.5.6.7.8.9 1 S T Figure 4.18 Transverse sphericity, point 3. Figure 4.19 Transverse sphericity, point 4. 1E-6 dσ/ds T (mb/.1) 1E-1 Measured True dσ/ds T (mb/.1) 1E-7 1E-8 Measured True 1E-11.1..3.4.5.6.7.8.9 1 S T.1..3.4.5.6.7.8.9 1 S T Figure 4. Transverse sphericity, point 5. Figure 4.1 Transverse sphericity, SM background. 4.7.6 Jet properties The jet E T distribution for central jets, i.e. jets that have an axis within η 3, is given in figure 4. to figure 4.6 for the signal and in figure 4.7 for the standard model background. The E T distribution for the three hardest central jets is given in figure 4.8 to figure 4.3 for the signal and in figure 4.33 for the standard model background. Especially for point 1 and point the jets produced are very hard. The multiplicity of jets, defined as the number of jets produces in the event with E T > 5, 1 and GeV, are given in figure 4.34 to figure 4.38 for the signal and in figure 4.39 for the background. SUSY events are characterised by a high multiplicity of hard jets. Almost always at least one hard jet is produced. Except for point 3, regularly at least five jets of more than 1 GeV are produced. For SUGRA point 3 the differential cross-section for the production of five jets of at least 5 GeV is significantly more than the SM background. 93

Chapter 4 Supersymmetry A cut of two jets of at least 1 GeV will keep about 9% of the SUSY events for point 1, point and point 5, and about 8% for point 4, while rejecting about 9% of the background events. 1E-7 1E-7 dσ/de T (mb/ GeV) 1E-8 1E-1 dσ/de T (mb/ GeV) 1E-8 1E-1 1E-11 4 6 8 1 E T (GeV) 1E-11 4 6 8 1 E T (GeV) Figure 4. E T distribution for central jets, point 1. Figure 4.3 E T distribution for central jets, point. 1E-5 1E-7 dσ/de T (mb/ GeV) 1E-6 1E-7 1E-8 dσ/de T (mb/ GeV) 1E-8 1E-1 4 6 8 1 E T (GeV) 1E-11 4 6 8 1 E T (GeV) Figure 4.4 E T distribution for central jets, point 3. Figure 4.5 E T distribution for central jets, point 4. 1E-7 1E-5 dσ/de T (mb/ GeV) 1E-8 1E-1 dσ/de T (mb/ GeV) 1E-6 1E-7 1E-8 1E-11 4 6 8 1 E T (GeV) 4 6 8 1 E T (GeV) Figure 4.6 E T distribution for central jets, point 5. Figure 4.7 E T distribution for central jets, SM background. 94

4.7 Event characteristics of SUSY events for 5 points in SUGRA parameter space dσ/de T (mb/ GeV) 1E-1 1E-11 hardest nd hardest 3rd hardest dσ/de T (mb/ GeV) 1E-1 1E-11 hardest nd hardest 3rd hardest 1E-1 4 6 8 1 E T (GeV) 1E-1 4 6 8 1 E T (GeV) Figure 4.8 E T distribution for three hardest jets, point 1. Figure 4.9 E T distribution for three hardest jets, point. 1E-6 1E-8 dσ/de T (mb/ GeV) 1E-7 1E-8 hardest nd hardest 3rd hardest dσ/de T (mb/ GeV) 1E-1 hardest nd hardest 3rd hardest 4 6 8 1 E T (GeV) 1E-11 4 6 8 1 E T (GeV) Figure 4.3 E T distribution for three hardest jets, point 3. Figure 4.31 E T distribution for three hardest jets, point 4. 1E-8 dσ/de T (mb/ GeV) 1E-1 hardest nd hardest 3rd hardest dσ/de T (mb/ GeV) 1E-5 1E-6 1E-7 1E-8 hardest nd hardest 3rd hardest 1E-11 4 6 8 1 E T (GeV) 4 6 8 1 E T (GeV) Figure 4.3 E T distribution for three hardest jets, point 5. Figure 4.33 E T distribution for three hardest jets, SM background. 1E-8 1E-8 σ(mb) 1E-1 > 5 GeV > 1 GeV > GeV σ(mb) 1E-1 > 5 GeV > 1 GeV > GeV 1E-11 1E-11 1E-1 5 1 15 Multiplicity Figure 4.34 Jet multiplicity, point 1. 1E-1 5 1 15 Multiplicity Figure 4.35 Jet multiplicity, point. 95

Chapter 4 Supersymmetry 1E-6 1E-7 σ(mb) 1E-7 1E-8 > 5 GeV > 1 GeV > GeV σ(mb) 1E-8 1E-1 > 5 GeV > 1 GeV > GeV 1E-11 1E-1 5 1 15 Multiplicity Figure 4.36 Jet multiplicity, point 3. 1E-1 5 1 15 Multiplicity Figure 4.37 Jet multiplicity, point 4. 1E-7 1E-5 σ(mb) 1E-8 1E-1 > 5 GeV > 1 GeV > GeV σ(mb) 1E-6 1E-7 > 5 GeV > 1 GeV > GeV 1E-11 1E-8 1E-1 5 1 15 Multiplicity Figure 4.38 Jet multiplicity, point 5. 5 1 15 Multiplicity Figure 4.39 Jet multiplicity, SM background. 4.7.7 Lepton properties Figure 4.4 to figure 4.44 show the p T distribution for the three hardest leptons for the signal. The corresponding plot for the background is shown in figure 4.45. The histograms are based on the p T reconstructed in the calorimeter for the electrons and the p T reconstructed by the combined inner detector/muon spectrometer for the muons. The lepton p T distribution of SUSY events is significantly softer than for jets. None of the five SUGRA points gives a clear signal above the SM background. Figure 4.46 to figure 4.5 show the multiplicity distribution for leptons for the SUSY signal. Figure 4.51 shows the corresponding plot for the background. From the multiplicity plots it can be concluded that the biggest part of the SUSY events decays in zero or one lepton. The decay in two leptons is only a small fraction (except for point 3). Decays in more than two leptons are very rare, except for point 3 where about 5% of the events decays in three leptons. The cross-section of background events causing two leptons is always a factor 1 3 till 1 5 larger than signal events. 96

4.7 Event characteristics of SUSY events for 5 points in SUGRA parameter space dσ/dp T (mb/1 Gev) 1E-1 1E-11 hardest nd hardest 3rd hardest dσ/dp T (mb/1 Gev) 1E-1 1E-11 hardest nd hardest 3rd hardest 1E-1 5 1 15 5 3 35 4 45 5 p T (GeV) 1E-1 5 1 15 5 3 35 4 45 5 p T (GeV) Figure 4.4 p T distribution for three hardest leptons, point 1. Figure 4.41 p T distribution for three hardest leptons, point. 1E-6 1E-8 dσ/dp T (mb/1 Gev) 1E-7 1E-8 hardest nd hardest 3rd hardest dσ/dp T (mb/1 Gev) 1E-1 hardest nd hardest 3rd hardest 1 3 4 5 p T (GeV) 1E-11 1 3 4 5 p T (GeV) Figure 4.4 p T distribution for three hardest leptons, point 3. Figure 4.43 p T distribution for three hardest leptons, point 4. 1E-8 1E-6 dσ/dp T (mb/1 Gev) 1E-1 hardest nd hardest 3rd hardest dσ/dp T (mb/1 Gev) 1E-7 hardest nd hardest 3rd hardest 1E-11 1 3 4 5 p T (GeV) 1E-8 1 3 4 5 p T (GeV) Figure 4.44 p T distribution for three hardest leptons, point 5. Figure 4.45 p T distribution for three hardest leptons, SM background. σ(mb) 1E-7 1E-8 1E-1 1E-11 1E-1 1 3 4 5 6 7 8 9 1 Multiplicity Figure 4.46 Lepton multiplicity, point 1. σ(mb) 1E-7 1E-8 1E-1 1E-11 1E-1 1E-13 1 3 4 5 6 7 8 9 1 Multiplicity Figure 4.47 Lepton multiplicity, point. 97

Chapter 4 Supersymmetry 1E-5 1E-7 1E-6 1E-8 σ(mb) 1E-7 1E-8 σ(mb) 1E-1 1E-11 1E-1 1 3 4 5 6 7 8 9 1 Multiplicity Figure 4.48 Lepton multiplicity, point 3. 1E-1 1 3 4 5 6 7 8 9 1 Multiplicity Figure 4.49 Lepton multiplicity, point 4. 1E-7 1E-3 1E-8 1E-4 σ(mb) 1E-1 1E-11 σ(mb) 1E-5 1E-6 1E-1 1 3 4 5 6 7 8 9 1 Multiplicity 1E-7 1 3 4 5 6 7 8 9 1 Multiplicity Figure 4.5 Lepton multiplicity, point 5. Figure 4.51 Lepton multiplicity, SM background. 4.7.8 Conclusions In general there is a very good agreement between the histograms presented in the previous sections, and the results of older studies [1], using ISAJET [3] as particle generator and CALSIM [1] as fast detector simulation. From the presented plots it can be concluded that for all points studied the most clear signature of a SUSY event is missing transverse energy and a large multiplicity of hard jets. This means that the easiest channel for discovering SUSY is the full hadronic decay (no leptons). Requiring missing transverse energy, hard jets and vetoing on isolated leptons can select this channel. The transverse sphericity is not a wellsuited quantity for discriminating on SUSY events. The drawback of the full hadronic decay channel is that it gives only rather restricted information about sparticle properties. Many different sub-processes contribute to this signal and the subsequent cascade decays channels can be numerous and complicated, especially for relatively heavy sparticles. Older studies show that a rough determination of m~ can m~ q and g be made [9, 1]. The SUSY mass scale M SUSY can be determined with an accuracy of about 1%, with M SUSY defined as: ( m~, m ) M SUSY = min g ~ u R More detailed studies with larger background samples are however necessary. (4.1) 98

4.8 Scan over SUGRA parameter space 4.8 Scan over SUGRA parameter space 4.8.1 Two-dimensional scan over m and mò I have investigated with ISAJET the total production cross-section of SUSY events as function of m and mò for two different values of tanβ (tanβ = and tanβ = 1). The parameters m and mò have been varied between 1 GeV and 15 GeV in steps of 1 GeV. The other parameters have been kept constant (A =, sign(µ) = +). The results are presented in figure 4.5 (tanβ = ) and figure 4.53 (tanβ = 1). The production cross-section depends very strongly on the mass parameter m ½. For m ½ = 1 GeV, the total SUSY production cross-section is more than a factor 1 6 larger than for m ½ = 15 GeV. The production cross-section depends much less strongly on m than on m ½. The cross-section for m = 1 GeV is less than a factor 1 more than for m = 15 GeV. The results for tanβ = and tanβ = 1 are almost identical. σ (mb) 1E-5 1E-6 1E-7 1E-8 1E-1 1E-11 1E-1 1E-13 1 5 9 m ½ (GeV) 13 1 6 11 m (GeV) Figure 4.5 Total SUSY production cross-section σ against m and m ò, tanβ =, A =, sign(µ) = +. σ (mb) 1E-5 1E-6 1E-7 1E-8 1E-1 1E-11 1E-1 1E-13 1 5 9 m ½ (GeV) 13 1 7 13 m (GeV) Figure 4.53 Total SUSY production cross-section σ against m and m ò, tanβ = 1, A =, sign(µ) = +. 99

Chapter 4 Supersymmetry 4.8. One-dimensional scan over mò The total production cross-section of SUSY events, calculated both with ISAJET and PYTHIA, against mò for a fixed value of the other parameters ( point 1 : m = 4, A =, sign(µ) = +, tanβ = ) is given in figure 4.54. Also here the mass mò varies between 1 GeV and 15 GeV, in steps of 1 GeV. The PYTHIA (version 6.1) cross-section is based on events for each studied point. Above mò = 1 GeV, PYTHIA gives a significantly larger cross-section than ISAJET. In figure 4.55 the detected fraction (based on PYTHIA and ATLFAST) is given for eight different selection criteria: miss 1. E T > 5 GeV miss. E T > 1 GeV miss 3. E T > 15 GeV 4. at least two jets with E T > 5 GeV 5. at least two jets with E T > 1 GeV miss 6. E T > 1 GeV and at least two jets with E T > 5 GeV miss 7. E T > 15 GeV and at least two jets with E T > 1 GeV miss 8. E T > 5 GeV and at least two jets with E T > 5 GeV The fractions of events passing the missing transverse energy cuts increase rapidly for increasing m ½. Above m ½ = 3 GeV, this fraction is almost constant. For m ½ = 1 GeV, about 95% of the events pass the softest jets cut (at least two jets with E T > 5 GeV). For the hardest cut (at least two jets with E T > 1 GeV), this fraction is much smaller, but increases rapidly for increasing m ½. For very high values of m ½ (above 1 GeV), the fraction of events passing the jets cuts (and also the combined cuts) decreases again. This can be explained by the fact that for very large values of m ½ the fraction of produced sleptons, charginos and neutralinos in the primary interaction will increase. The fraction of produced squarks and gluinos will decrease (due to the very large mass, see also the mass plots), causing a reduced jet multiplicity. The most significant sparticle masses as function of m ½ are given in figure 4.56, figure 4.57 and figure 4.58. Given are the masses of the squarks d ~ L, ~ t 1, ~ t, the gluino g ~, the sleptons ~ τ 1, ~τ, ~ ~ ~ ~ ~ ~ ± ~ ± υ τl, the four neutralinos Χ 1, Χ, Χ 3, Χ 4, the two charginos Χ 1, Χ and the Higgs bosons A, h, H ± and H. From the figures it follows that the masses of the sleptons, squarks, gluino, charginos and neutralinos depend strongly on the value of the mass ~ parameter m ½. Over the complete studied range the lightest neutralino Χ 1 is the LSP; except for very small values of m ½ the gluino g ~ is the heaviest sparticle. For the other sparticles, the order in mass is not fixed. From figure 4.57 it follows that the masses of the Higgs bosons H, A and H ± depend strongly on the value of the mass parameter m ½. The masses of these Higgs bosons are almost equal to each other over the complete studied range, which follows also from equation (4.3). The mass of the lightest Higgs boson h is almost independent of the mass parameter m ½. 1

4.8 Scan over SUGRA parameter space σ (mb) 1E-6 1E-7 1E-8 1E-1 1E-11 1E-1 1E-13 5 1 15 m ½ (GeV) PYTHIA ISAJET Fraction 1.9.8.7.6.5.4.3..1 cut 1 cut cut 3 cut 4 cut 5 cut 6 cut 7 cut 8 5 1 15 m ½ Figure 4.54 Total SUSY production crosssection σ versus m ò, m = 4 GeV, tanβ =, A =, sign(µ) = +. Figure 4.55 Detected fraction versus m ò, m = 4 GeV, tanβ =, A =, sign(µ) = +. m (GeV) 35 3 5 15 1 ~d_l ~t_1 ~t_ ~g ~tau_1- ~tau_- ~nu_taul m (GeV) 4 35 3 5 15 1 h H A H+ 5 5 5 1 15 m ½ (GeV) Figure 4.56 Spin sparticle masses versus m ò, m = 4 GeV, tanβ =, A =, sign(µ) = +. 5 1 15 m ½ (GeV) Figure 4.57 Higgs bosons masses versus m ò, m = 4 GeV, tanβ =, A =, sign(µ) = +. m (GeV) 35 3 5 15 1 5 ~chi_1 ~chi_1+ ~chi_4 ~chi_ ~chi_3 ~chi_+ 5 1 15 m ½ (GeV) Figure 4.58 Spin ½ sparticle masses versus m ò, m = 4 GeV, tanβ =, A =, sign(µ) = +. The corresponding plots for tanβ = 1 ( point ) are given in figure 4.59 (production cross-section) and figure 4.6 (detected fraction). The spectrum for the cross-section and the detected fraction are very similar to tanβ =, except for two small regions around m ½ = 3 GeV and m ½ = 1 GeV. In these regions the PYTHIA cross-section drops sharply. This behaviour does not happen with ISAJET. Also the fraction of events passing the missing transverse energy cuts drops sharply. The fraction of events passing the cuts on two hard jets drops much less sharply or even increases. I think the PYTHIA results in these small regions are wrong, due to an error in the PYTHIA program. The author of PYTHIA has been informed. 11

Chapter 4 Supersymmetry The mass spectrum is given in figure 4.61, figure 4.6 and figure 4.63. The mass spectrum of the squarks and sleptons is very similar to the spectrum for tanβ =. The masses of the ~ ± charginos and neutralinos increase less sharply. The mass of the heaviest chargino Χ for m ½ = 15 GeV, drops from 3 GeV for tanβ = to GeV for tanβ = 1. The lightest ~ neutralino Χ 1 is the LSP over the complete studied range. The shape of the mass spectrum of the Higgs bosons masses is very similar to the shape for tanβ =. The absolute values however are significantly less. For m ½ = 15 GeV, the mass of the heavy Higgs boson H drops from 35 GeV at tanβ = to 5 GeV at tanβ = 1. σ (mb) 1E-6 1E-7 1E-8 1E-1 1E-11 1E-1 1E-13 5 1 15 m ½ (GeV) PYTHIA ISAJET Figure 4.59 Total SUSY production crosssection σ versus m ò, m = 4 GeV, tanβ = 1, A =, sign(µ) = +. Fraction 1.9.8.7.6.5.4 cut 1 cut cut 3.3 cut 4 cut 5 cut 6. cut 7 cut 8.1 5 1 15 m ½ (GeV) Figure 4.6 Detected fraction versus m ò, m = 4 GeV, tanβ = 1, A =, sign(µ) = +. m (GeV) 35 3 5 15 1 ~d_l ~t_1 ~t_ ~g ~tau_1- ~tau_- ~nu_taul m (GeV) 3 5 15 1 h H A H+ 5 5 5 1 15 m ½ (GeV) Figure 4.61 Spin sparticle masses versus m ò, m = 4 GeV, tanβ = 1, A =, sign(µ) = +. 5 1 15 m ½ (GeV) Figure 4.6 Higgs boson masses versus m ò, m = 4 GeV, tanβ = 1, A =, sign(µ) = +. m (GeV) 5 15 1 ~chi_1 ~chi_1+ ~chi_4 ~chi_ ~chi_3 ~chi_+ 5 5 1 15 m ½ (GeV) Figure 4.63 Spin ½ sparticle masses versus m ò, m = 4 GeV, tanβ = 1, A =, sign(µ) = +. 1

4.8 Scan over SUGRA parameter space 4.8.3 One-dimensional scan over m The corresponding plots for the cross-sections and detected fractions with m varying and mò fixed at 4 GeV are given in figure 4.64 and figure 4.65 for tanβ = and in figure 4.69 and figure 4.7 for tanβ = 1. For m = 1 GeV and tanβ =, the PYTHIA production cross-section drops sharply. From figure 4.65 it follows that also the fraction of events passing the missing transverse energy cuts is much less in this case. Again this behaviour does not happen with ISAJET and also not with PYTHIA for tanβ = 1. The corresponding mass spectrum is given figure 4.66, figure 4.67 and figure 4.68 for tanβ = and in figure 4.71, figure 4.7 and figure 4.73 for tanβ = 1. The lightest neutralino ~ Χ 1 is the LSP over the complete studied range. Below m = 5 GeV the gluino g ~ is the heaviest sparticle. Above m = 5 GeV, the upper squark d ~ L is the heaviest sparticle. As expected, the masses of the scalar sleptons and squarks depend strongly on the scalar mass parameter m. The masses of the gluino, charginos and neutralinos depend much less on the scalar mass parameter. The masses of the Higgs bosons H, H ± and A depend strongly on the mass parameter m. The mass of h is almost constant over the complete studied range. The masses of the Higgs bosons H, H ±, A for tanβ = 1 are significantly less than for tanβ =. σ (mb) 1E-7 1E-8 1E-1 5 1 15 m (GeV) PYTHIA ISAJET Fraction 1.9.8.7.6.5.4.3..1 cut 1 cut cut 3 cut 4 cut 5 cut 6 cut 7 cut 8 5 1 15 m (GeV) Figure 4.64 Total SUSY production crosssection σ versus m, m ò = 4 GeV, tanβ =, A =, sign(µ) = +. Figure 4.65 Detected fraction versus m, m ò = 4 GeV, tanβ =, A =, sign(µ) = +. m (GeV) 18 16 14 1 1 8 6 4 ~d_l ~t_1 ~t_ ~g ~tau_1- ~nu_taul ~tau_- 5 1 15 m (GeV) Figure 4.66 Spin sparticle masses versus m, m ò = 4 GeV, tanβ =, A =, sign(µ) = +. m (GeV) 3 5 15 1 5 h H A H+ 5 1 15 m (GeV) Figure 4.67 Higgs boson masses versus m, m ò = 4 GeV, tanβ =, A =, sign(µ) = +. 13

Chapter 4 Supersymmetry m (GeV) 16 14 1 1 8 6 4 ~chi_1 ~chi_1+ ~chi_4 ~chi_ ~chi_3 ~chi_+ 5 1 15 m (GeV) Figure 4.68 Spin ½ sparticle masses versus m, m ò = 4 GeV, tanβ =, A =, sign(µ) = +. σ (mb) 1E-7 1E-8 1E-1 5 1 15 m (GeV) PYTHIA ISAJET Fraction 1.9.8.7.6.5.4 cut 1 cut cut 3.3 cut 4 cut 5 cut 6. cut 7 cut 8.1 5 1 15 m (GeV) Figure 4.69 Total SUSY production crosssection σ versus m, m ò = 4 GeV, tanβ = 1, A =, sign(µ) = +. Figure 4.7 Detected fraction versus m, m ò = 4 GeV, tanβ = 1, A =, sign(µ) = +. m (GeV) 18 16 14 1 1 8 6 4 ~d_l ~t_1 ~t_ ~g ~tau_1- ~nu_taul ~tau_- 5 1 15 m (GeV) Figure 4.71 Spin sparticle masses versus m, m ò = 4 GeV, tanβ = 1, A =, sign(µ) = +. m (GeV) 18 16 14 1 1 8 6 4 h H A H+ 5 1 15 m (GeV) Figure 4.7 Higgs boson masses versus m, m ò = 4 GeV, tanβ = 1, A =, sign(µ) = +. 14

4.9 Conclusions m (GeV) 8 7 6 5 4 3 1 ~chi_1 ~chi_1+ ~chi_4 ~chi_ ~chi_3 ~chi_+ 5 1 15 m (GeV) Figure 4.73 Spin ½ sparticle masses versus m, m ò = 4 GeV, tanβ = 1, A =, sign(µ) = +. 4.9 Conclusions 4.9.1 Discovery potential of SUSY with ATLAS The current studies give results indicating that for the five points in SUGRA parameter space studied by the ATLAS collaboration, SUSY can be discovered in ATLAS by selecting on missing transverse energy, hard jets and vetoing on isolated leptons (section 4.7, [1, 9]). However more detailed studies with larger background samples and improved versions of the simulation packages are necessary. One should also take into account that the cross-sections are dependent on the exact model and parameters and can be too optimistic, even when only leading order effects are taken into account, while the next-to-leading order effects can be significant (section 4.6, [5]). The m ½ parameter almost completely determines the production cross-section of SUSY events (section 4.8). The current five points studied cover only the range up to m ½ = 4 GeV. This should be extended to higher values. For m ½ = 15 GeV, the production cross-section will be more than a factor 1 3 smaller. Discovery will be much more difficult in this case. Extending to higher mass values is especially important when next-toleading order contributions are included in the production cross-section. Next-to-leading order contributions will not only increase the cross-sections but will also increase the mass range of the sparticles that is excluded by currently existing experimental results. The discovery of SUSY events will also be much more difficult if R-parity is not an absolutely conserved quantity because the missing transverse energy spectrum, the clearest signature of a SUSY event, will be much softer in this case. In any case SUSY will be excluded if no light Higgs with a mass below 135 GeV will be found in ATLAS. For the discovery of SUSY the calorimeter is the most important detector. The calorimeter is essential for the missing transverse energy measurements and the reconstruction of jets. The inner detector contributes to the reconstruction of jets and is necessary for the veto measurements on isolated leptons. The muon spectrometer contributes to the veto measurements on isolated muons. 4.9. Potential of ATLAS to determine sparticle masses and SUSY parameters Much more difficult than the discovery of SUSY is the determination of the mass spectrum of the sparticles and the SUSY parameter set and the test of the correctness of the SUGRA model. Also in this field studies have started, based on the five points in SUGRA parameter 15

Chapter 4 Supersymmetry space [1, 13, 15, 17]. The first results are promising, although only a few masses can be determined directly. One can get a rough estimation of the m~ q and m~ g masses. The reconstructed effective mass can be calculated from the detected missing transverse energy and energy of the hardest jets and leptons. To some extent one can distinguish g ~ g ~ from q ~ q ~ events using the fact that due to their normally higher mass in first approximation g ~ g ~ events have a higher jet multiplicity than q ~ q ~ events 19. One can also get a rough estimation of the masses of the sparticles using the relation between the masses and the production cross-section. More work is necessary to investigate this in further detail. Some combinations of masses can be measured more precisely. Precision measurements can be made at the bottom of the cascade decay where a sparticle decays into the LSP. For the ~ ~ + decay channel Χ Χ 1 l l the mass difference m ~ m ~ can be measured precisely Χ Χ 1 from the energy distribution of the l + l - pair. Already with a few precision measurements of combination of masses, the parameters of the SUGRA model can be restricted dramatically by fitting the measurements. One can get an indication of how well the mass spectrum can be described using only the five parameters from the SUGRA model. This means that information about physics at very high-energy scales is yielded. For the precision measurements the contribution of the inner detector is essential in view of precision measurement of the transverse momentum of the leptons. However also these studies should be extended to larger values of m ½ and to improved versions of the simulation packages. Also more detailed studies of the background should be made. 4.1 References 1. R. Arnowitt and P. Nath, Supersymmetry and Supergravity: Phenomenology and Grand Unification, SSCL-Prepint-53 (1993).. D. Griffiths, Introduction to Elementary Particles, 1987. 3. M. Drees, An Introduction to Supersymmetry, HEP-PH/961149 (1996). 4. U. Amaldi, W. de Boer and H. Fürstenau, Comparison of Grand Unified Theories with Electroweak and Strong Coupling Constants Measured at LEP, CERN PPE 91-44, Phys. Lett. 6 B 447-455 (1991). 5. E. Richter-Was, D. Froidevaux and others, MSSM Higgs Rates and Backgrounds in ATLAS, ATLAS PHYS-N-74 (1996). 6. H.E. Haber, The Status of the Minimal Supersymmetric Standard Model and Beyond, SCIPP 97/7, HEP-PH/97945 (1997). 7. S. Groot Nibbelink, Private communication. 8. J.W. van Holten, Private communication. 9. I. Hinchliffe, F.E. Paige, G. Polesello and E. Richter-Was, Precision SUSY Measurements with ATLAS: Introduction and Inclusive Measurements, ATLAS PHYS-NO-17 (1997). 1. F.E. Paige, Toy Simulation of ATLAS SUSY Points, ATLAS PHYS-NO-85 (1996). 19 This has not been shown explicitly but can easily be proved. 16

4.1 References 11. F.E. Paige, Precision SUSY Measurements with ATLAS: Simulation Tools and Inclusive Analysis, Transparencies presented at LHCC SUSY workshop, 1996. 1. E. Richter-Was, D. Froidevaux and J. Söderqvist, Precision SUSY Measurements with ATLAS for SUGRA Points 1 and, ATLAS PHYS-NO-18 (1997). 13. G. Polesello, Precision SUSY Measurements with ATLAS: Reconstruction of Exclusive Final States, Part II, Transparencies presented at LHCC SUSY workshop, 1996. 14. I. Hinchliffe, F.E. Paige, E. Nagy, M.D. Shapiro, J. Söderqvist and W. Yao, Precision SUSY Measurements at LHC: Point 3, ATLAS PHYS-NO-19 (1997). 15. F. Gianotti, Precision SUSY Measurements with ATLAS: Reconstruction of Exclusive Final States, Part I, Transparencies presented at LHCC SUSY workshop, 1996. 16. F. Gianotti, Precision SUSY Measurements with ATLAS, SUGRA Point 4, ATLAS PHYS-NO-11 (1997). 17. G. Polesello, L. Poggioli, E. Richter-Was and J. Söderqvist, Precision SUSY Measurements with ATLAS for SUGRA Point 5, ATLAS PHYS-NO-111 (1997). 18. H. Baer, H. Murayama and X. Tata, Low Energy Supersymmetry Phenomenology, HEP-PH/953479 (1995). 19. T. Sjöstrand, PYTHIA 5.7 and JETSET 7.4, Physics and Manual, CERN-TH/711/93 (1993).. S. Mrenna, SPYTHIA, A Supersymmetric Extension of PYTHIA 5.7, ANL-HEP-PR-96-63 (1996). 1. T. Sjöstrand, PYTHIA 6.1 Update Note Describing New Features in PYTHIA, 1997.. Particle Data Group, R.M. Barnett et al., Review of Particle Properties, Physics Review D54 (1996). 3. F.E. Paige and S.D. Protopopescu, ISAJET 7., a Monte Carlo Event Generator for p p and p p Reactions, Documentation file of ISAJET 7.. 4. W. Beenakker, R. Höpker, M. Spira, PROSPINO, a Program for the Production of Supersymmetric Particles in Next-to-Leading Order QCD, HEP-PH/96113 (1996). 5. W. Beenakker, R. Höpker, M. Spira and P.M. Zerwas, Squark and Gluino Production at Hadron Colliders, CERN-TH/96-15 (1996). 6. E. Richter-Was, D. Froidevaux and L. Poggioli, ATLFAST 1., a Package for Particle Level Analysis, ATLAS PHYS-NO-79 (1996). 7. H. Plothow-Besch, PDFLIB, Nucleon, Pion and Photon Parton Density Functions and Alpha(s) Calculations, Version 7.9 user s manual, CERN W551 (1997). 8. D. Froidevaux, Precision SUSY measurements with ATLAS: Extraction of Model Parameters and Conclusions, Transparencies presented at LHCC SUSY workshop, 1996. 17

Chapter 5 The ATLAS trigger and data acquisition system Contents 5.1 Introduction... 11 5. Set-up of ATLAS T/DAQ system... 11 5.3 LVL1 trigger... 113 5.3.1 Introduction... 113 5.3. Regions of interest... 114 5.3.3 Trigger algorithms... 114 5.3.4 Trigger menu... 116 5.4 LVL trigger... 118 5.4.1 Introduction... 118 5.4. Trigger menu... 118 5.4.3 Trigger algorithms... 118 5.5 Event filter... 119 5.6 ATLAS LVL architectures... 1 5.6.1 Introduction... 1 5.6. Local-global system... 1 5.6.3 Single farm system... 1 5.6.4 Architecture A, B, C and C... 11 5.6.5 System components... 1 5.7 Test set-up of a farm based system... 16 5.7.1 Introduction... 16 5.7. TMS3C4 DSP... 16 5.7.3 System components... 17 5.7.4 Measurements... 18 5.8 ROB - RoI relations for the inner detector... 19 5.8.1 Introduction... 19 5.8. RoI pointers defined by LVL1... 19 5.8.3 RoIs in the inner detector ( z = )... 13 5.8.4 RoIs in the inner detector ( z = 11. cm)... 13 5.8.5 Mapping of the SCT onto ROBs... 133 5.8.6 Mapping of the TRT onto ROBs... 134 5.8.7 Number of ROBs per RoI and fraction of RoI requests received by a single ROB.. 135 5.8.8 Number of ROBs per event and RoI request rate... 139 5.9 References... 141 19

Chapter 5 The ATLAS trigger and data acquisition system 5.1 Introduction The bunch-crossing frequency of the LHC collider will be 4 MHz. The collision frequency will even be higher because each bunch-crossing will cause more than one collision. Most of those collisions however will be soft hadronic collisions of no interest (minimum bias background). The production cross-section of interesting events is only a very small fraction of the total proton-proton production cross-section. This is shown in figure 5.1, giving the production cross-section of some characteristic processes against the total proton-proton crosssection. At LHC a Higgs boson for example is only produced in every 1 1 proton-proton collisions on average. The number of observable events produced will even be less as only a fraction of the decays has an unique signature, like the gold plated decay into four charged leptons for the Higgs boson. The task of the ATLAS trigger system is online selecting the bunch-crossings probably containing an interesting collision. In general only data from the bunch-crossings that pass the trigger system will be permanently stored for further offline analysis. Additionally also the data of a very small fraction of the bunch-crossings that does not pass the trigger system is stored for monitoring purposes. The expectation is that the ATLAS trigger system will bring the 4 MHz input rate back to a permanent storage rate of about 1 Hz. This corresponds to a data rate of about 1-1 MB/s. The task of the ATLAS trigger system is extremely challenging. The event rate should be reduced by a factor of 4 1 5 with the smallest possible loss of interesting events and without introducing long decision times (latencies). The ATLAS trigger is organised in three levels (LVL1, LVL and event filter). The ATLAS DAQ (Data AcQuisition) system takes care of the data flow from the frontend electronics to the permanent storage. The DAQ system also controls the storage of the data generated within the trigger system. The set-up of the ATLAS T/DAQ (trigger and data acquisition) system is described in section 5.. Each trigger level is described in a separate section. The LVL1 system is described in more detail in section 5.3. The LVL system is described in section 5.4, the event filter in section 5.5. Possible architectures for the LVL system are described in section 5.6. A smallscale test set-up of a LVL system is described in section 5.7. Calculations of the number of data buffers (ROBs) of the inner detector per RoI and per event that will be requested to supply data for analysis by the LVL system are finally presented in section 5.8. 11

5.1 Introduction Cross sections and event rates at hadron colliders Fermilab SSC CERN LHC σ tot UA4/5 E71 9 1 1 mb σ b b CDF 7 1 (proton - proton) σ 1 µ b 1 nb 1 pb σ σ jet jet E >.5 TeV t (W ν) H.1.1.1 1. 1 1 s TeV Figure 5.1 The cross-section of some characteristic processes like the production of a Higgs boson and the total proton-proton cross-section, as function of the proton-proton centre-ofmass energy. The energies reached with different present colliders and the LHC are indicated. Taken from [1] (updated version). UA1 CDF (p p) UA1/ (p p) σ~~ gg (m~ g = 5 GeV) σ CDF/DO t t m = 174 GeV m = 175 GeV top top σ H m H = 1 GeV σ z' m = 1 TeV z' σ Higgs m = 5 GeV 5 1 3 1 1-1 1-3 1 34 - -1 Events / sec for = 1 cm sec D_D_354c 111

Chapter 5 The ATLAS trigger and data acquisition system 5. Set-up of ATLAS T/DAQ system An overview of the ATLAS T/DAQ system with the different components is given in figure 5.. The first level trigger (LVL1) system must be placed as close as possible to the ATLAS detector to minimise the latency due to propagation delays in the cables. Some parts of the system will even be placed on the detector itself. During LVL1 processing the data of all the detectors is held in pipeline memories. Due to the very short latency allowed, the LVL1 system needs to be built from special purpose hardware. The data in the pipeline memories belonging to events passing the LVL1 trigger is sent via the RODs (ReadOut Drivers) to the data buffers of the LVL system (ROB, ReadOut Buffer). The typical tasks of a ROD are the data collection from multiple front-end sources, the adaptation of data formats, the addition of bunch-crossing and LVL1 trigger number information to the data and outputting the resulting data via a single high-bandwidth link. The high-bandwidth communication links between the RODs and the ROBs will probably be based on optical fibre technology. The ROBs keep the data of all the detectors during the LVL decision. They are described in more detail in section 5.6.5. In the case of a LVL1 acceptance decision also additional region of interest information (see section 5.3.) is sent from the LVL1 to the LVL system. The (detector) data belonging to events accepted by LVL are sent from the ROBs via the event builder to the processor farm of the event filter (marked as level 3 in figure 5.). In the event builder usually full information from all parts of all detectors is collected, for a given bunch-crossing. Only partial collection may be sufficient for certain classes of events. The event builder will be implemented on a high-speed switching network. The detector data belonging to events that passed all three levels of the trigger are stored permanently for further offline analysis. To monitor the performance of the trigger systems there are additional data streams internally generated within the trigger systems. These data flows are not shown in figure 5.. 11

5.3 LVL1 trigger DETECTOR Level 1 ~ µs Pipeline memory Derandomizer ROD Read-Out Driver RoI Level < 1 ms Read-Out Buffer Event building Switch-Farm interface Level 3 Processor farm Data Storage Figure 5. ATLAS T/DAQ system, consisting of LVL1, LVL and LVL3 (event filter). 5.3 LVL1 trigger 5.3.1 Introduction At LVL1 special purpose processors act on coarse granularity data from the calorimeter and the data from dedicated muon detectors (RPCs and TGCs, see section.6). The data from the calorimeter is based on trigger cells with a granularity of φ η =.1.1. The LVL1 system does not use inner detector data. The LVL1 trigger can handle data at the full LHC bunch-crossing rate of 4 MHz (every 5 ns). The acceptance rate is at maximum 1 khz, depending on the trigger selection criteria. The latency (the time necessary to form and distribute the LVL1 trigger decision to the front-end electronics) is about µs. During the LVL1 processing, data of the ATLAS detector is held in pipeline memories. It is necessary to determine unambiguously which data held in the memories belongs to which bunch-crossing. 113

Chapter 5 The ATLAS trigger and data acquisition system 5.3. Regions of interest Apart from reducing the event rate, a second task of the LVL1 system is to define regions (RoI: Region of Interest) of the detector in the (η, φ) space probably containing interesting information that needs to be analysed further at LVL. Primary RoIs and secondary RoIs can be distinguished. A primary RoI contributes to the LVL1 trigger acceptance decision. A secondary RoI does not. Four different types of RoIs are distinguished at LVL1: electromagnetic RoIs, single hadron/tau RoIs, jet RoIs and muon RoIs. The shower profile can distinguish single hadron/tau RoIs from electromagnetic RoIs (see section.5). An example of two electromagnetic RoIs and one muon RoI in the ATLAS detector is given in figure 5.3. The muon trigger chambers constrain the η limits of the muon RoIs. The calorimeter geometry constrains the η limits of the electromagnetic and single hadron RoIs. The jet RoIs can be contained in the barrel and end-cap calorimeters; the forward calorimeter tagged jets will only be used in the final event analysis. The limits in η of the RoIs are: muon RoIs: η <.4 electromagnetic and single hadrons RoIs: η <.5 jet RoIs: η < 3. Figure 5.3 Two electromagnetic RoIs and one muon RoI in the ATLAS detector. 5.3.3 Trigger algorithms The LVL1 system consists of sub-trigger processors that work independently and in parallel and the CTP (Central Trigger Processor) [3] that produces the final LVL1 acceptance/rejection decision combining the results of the sub-trigger processors (e.g. multiplicity of calorimeter clusters, multiplicity of muons and missing transverse energy). The block diagram of the LVL1 system is given in figure 5.4. Six different sub-triggers are distinguished: the electromagnetic trigger, the single hadron/tau trigger, the jet trigger, the muon trigger, the missing transverse energy trigger and the total transverse energy trigger. The single hadron/tau trigger and the total transverse energy trigger are not shown in figure 5.4. 114