ATLAS High Level Trigger Steering and Seeding Mechanism SUSY Particle Masses Determination in the Co-annihilation Model Gianluca Comune

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ATLAS High Level Trigger Steering and Seeding Mechanism SUSY Particle Masses Determination in the Co-annihilation Model

Gianluca Comune

A thesis submitted to the Faculty of High Energy Physics for the degree of

Doctor in Physics

PhD in High Energy Physics Bern University

Switzerland

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Abstract

In this thesis it will be presented the author’s research carried out in preparation for his PhD in Physics. This document is split in two parts: The implementation of the ”Steering” and of the ”seeded ” reconstruction in the ATLAS High Level Trigger, where it will be presented the author’s contribution to the creation of the software infrastructure that is responsible for the algorithm Steering and Trigger Decision mechanism, the Trigger Data Navigation and of the Trigger Event Summary formation and unpacking. There it will be presented how the seeded reconstruction is carried out and how this software has been successfully used in the online testbeds for the studies done in the preparation of the 2003 Trigger/DAQ/DCS Technical Design Report and at the 2004 Test Beam. The second part of this thesis is devoted to the presentation of a detailed analysis of a reference mSUGRA model laying in the so called ”co- annihilation” region of the SUSY parameter space. There it will be shown that regardless the slow leptons expected in the model, using the Left and Right handed slepton decays it is possible to extract accurate information about some of the supersymmetric particle masses and mSUGRA parameters.

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Acknowledgements

I wish to thank somebody

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1 Introduction

The Standard Model of elementary particle interactions has been very successful during the past few decades in describing the behaviour of nature in its most intimate details. Still the Standard Model is not the ultimate theory of fundamental particle and forces interaction because it totally lacks a coherent description of gravitational forces. Most importantly, from a phenomenological point of view, the mechanism through which particles acquire a mass has not been unveiled yet and with it the Higgs boson that is set poised, at least from a theoretical point of view, to explain how this actually happens. Higgs has eluded experimental detection up to now calling for a new generation of particle colliders to be built in order to extend the measurement reach well into the TeV scale which is believed, on both theoretical and experimental grounds, to be the energy scale at which the Higgs should manifest. Few new theories have been developed in the last decades to cure the theoretical difficulties suffered by the Standard Model. Up to now none of these new appealing theories has had any experimental confirmation but on the other hand, at least, few of these new theories have a phenomenological content that could start to appear at the TeV scale. The Large Hadron Collider (LHC) has indeed been proposed with these two reasons in mind and designed to extend the physics reach well into the TeV scale allowing the physics community to chart that region. It will indeed collide protons at a CoM of 14 TeV and at a very high

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luminosity. LHC is entering its final construction phase at the European Council for Nuclear Research (CERN) in Geneva and is set to start operation in spring 2007. Four experiments are in construction and will be operated at four different interaction points: CMS, ATLAS, ALICE and LHCb. The first two are general purpose experiments set to search for the Higgs boson and eventual physics beyond the Standard Model. The hadronic nature and the very high luminosity reached by this collider are responsible for the very harsh conditions under which the various experiments will operate.

ATLAS is one the two general purpose machines and has been designed to cope with the very demanding operating conditions imposed by the LHC and by the physics programme.

ATLAS has excellent tracking, calorimeter and muon systems and will hopefully be able to discover the Higgs and other new physics if that exists. As previously said there are several new theories posed to cure the theoretical shortcomings of the Standard Model. One of these theories is Supersymmetry. It postulates the existence of a new, yet unseen, symmetry that swaps fermions and bosons roles. This rather simple, but very far reaching, assumption naturally solves the hierarchy problem and reduces the degree of Standard Model parameters’ tuning needed in order to achieve the necessary cancellations in the Higgs mechanism.

Supersymmetry produces a very rich new phenomenology and theoretical reasons justify the strong believe that this phenomenology, if it exists, will manifest again at the TeV scale.

One of the tasks for ATLAS will be to measure supersymmetric particle masses and theory parameters. This has been proven to be possible in few use cases in the past. New use cases have been recently proposed that probe regions of the supersymmetric parameters space never charted before. One such region is the so called ”co-annihilation” region where some peculiar kinematic constraints conspire to make harder the task of measuring masses. After

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an introduction of the theoretical justification for supersymmetry in chapter 4 a detailed analysis of a constrained SUSY model point will be carried out and there it will be shown that notwithstanding the mentioned difficulties it will still be possible to reconstruct supersymmetric particle masses with a ∼ 20 − 30 GeV precision, well within the limits of other previously studied cases. One of the key elements of the ATLAS experiment, although not really part of the ATLAS detector itself, is the Trigger. Like never before the Trigger will play a pivotal role in the success of an experiment. In fact it will allow to reduce the initial 1 GHz interaction rate down to a more manageable ∼ 100 Hz. This drastic reduction rate has to be performed avoiding any possible bias and retaining the largest portion of signal events. At the very core of the Trigger selection strategy there is the seeded reconstruction paradigm that needs to be implemented at every stage of the event selection in order to achieve the desired rate reduction. The Steering is the software component that is responsible for allowing this seeded reconstruction to take place. A data navigation mechanism that embodies this seeded reconstruction idea is proposed as well and finally a Trigger Decision will use those two mechanisms to determine the event fate. In chapters 7 through 9 the main features of the ATLAS Trigger are presented and the seeded reconstruction within the Steering mechanism will be outlined.

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2 Theory

2.1 Introduction

The fundamental theory of elementary particle interactions is the Standard Model (Standard Model), which is a gauge field theory and describes with great accuracy the laws of high energy physics in terms of point-like particles and force carriers. The so called unbroken theory does not describe the actually measured mass spectrum. To account for the experimental masses of the particle the model must undergo symmetry breaking and it is necessary to introduce the Higgs boson that allows the particles to acquire the ”right” masses. There are some shortcomings which affect this theory and a whole range of new theories has been envisaged in the past few decades. Those theories present interesting features and a very rich new phenomenology that is likely to be probed by the LHC.

2.2 The Standard Model

The mathematical description of the interaction of matter with three of the four known fundamental forces of nature is called the Standard Model [73]. The interaction of matter via the electroweak and strong interaction is described in terms of point like particles and force carriers modelled by a quantised field obeying local gauge symmetries. Matter constituents,

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namely particles that fell the strong interaction (quarks) and particles that exchange only electroweak interaction (leptons). Both types of particles have spin 1/2 unlike force carriers that carry integral spin. The dynamical behaviour of the matter and forces is described through a Lagrangian and in its initial formulation the theory can only account for massless particles which is clearly wrong given that for centuries some of those particles have been known to possess mass. In other terms the exact gauge symmetries cannot be exact and must be ’broken’. Various mechanism of symmetry breaking can be envisaged but all fall shorts of consistency because they all lead to non renormalizable theories. Mass terms could be added in an ad-hoc fashion to the analytical form of the Lagrangian but by doing so the renormalizability of the theory is again not guaranteed. A mechanism that keeps the theory renormalizable and is able to add the mass to the theory was described by Higgs ([40],[41]).

This mechanism considers the existence of two real scalar fields (φ1,φ2) interacting via a potential V (φ²₁+φ²₂) with a degenerate minimum. Those two fields are coupled to a real vector field Aµ that once quantised around the minimum of the potential produce mass terms for the force carriers whose fields are expressed in terms of the eigenstates of the original theory after spontaneous symmetry breaking has taken place. The remaining degree of freedom of this approach is a new massive excitation which represents a new yet unseen particle called the Higgs boson. Mass terms for the fermions are generated from Yukawa couplings. It is worth noticing that this can successfully describe generation changing interaction like the ones that are experimentally observed to violate the combined discrete CP symmetry.

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Figure 2.1: Electroweak precision fit: the band represents the theoretical uncertainty from missing higher order contributions to the Higgs mass calculation

2.3 The Problems with the Standard Model

The Higgs mass is a parameter of the theory and as such can take any value. Considerations on unitarity limits lead us to believe that the renormalized Higgs mass is bound to be below the TeV scale[46]. This consideration together with other global fits of existing electroweak data indeed favours a light Higgs ([45]). Problems arise when radiative corrections are included in the calculation of the Higgs mass. The Standard Model is not the ultimate theory because it does not include gravitation and indeed can be considered as an effective theory for the low energy range. We can assume that the Standard Model is valid only up to energy scales comparable with the Planck scale where gravitational forces and a more

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comprehensive description of nature takes over. Under this assumptions the corrections to the Higgs mass arising from higher order loops must be integrated up to the assumed energy scale Λ ( 10¹⁶ GeV ). It can be shown that the renormalized Higgs mass is roughly given by the following expression

m²_h = m²₀ + δm²_H ∼ m²0 − g²Λ (2.1)

where m0 is the bare Higgs mass parameter and g a dimensionless coupling constant. Such divergence would not represent an insurmountable problem if the theory was to be the final theory of the fundamental interactions but given that, as we already anticipated, the Standard Model can only be seen as an effective low energy theory of a more comprehensive theory then the theory parameters must be fine tuned to accommodate the existing limits on the Higgs mass. This fine tuning is of striking nature given that it must be precise to one part in 10¹² which makes the adjustment rater disturbing. This problem is known as the hierarchy problem and is seen as one of the most convincing arguments suggesting that the Standard Model cannot be the ultimate theory of matter and forces. Were the nature to allow this fine parameter tuning the same line of reasoning can easily be seen as a convincing supporting argument for the existence of new physics at the TeV scale and for the construction of a new generation of particle accelerators like LHC and possibly the Linear Collider. Various proposal have been made in the last few decades on what form this new physics will manifest itself: technicolor, compositeness, strings, invisible or extended extra dimensions or supersymmetry.

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2.4 Supersymmetry

Chiral and gauge symmetry conspire to keep the radiative corrections to the fermions and gauge boson masses at a manageable logarithmic level. The only sector of the Standard Model theory whose mass corrections diverge quadratically is the Higgs vector boson. Al- though fermions and gauge bosons masses’ divergence is only logarithmic these very corrections impinge on the Higgs potential and in turn on the cut-off Λ. There is no intrinsic symmetry in the theory that can help cure this divergence. From the Feynmann rules we know that any perturbative contribution to observables swap signs when the role of fermions and bosons are interchanged. This simple property has lead to the idea of supersymmetry (SUSY) ([47],[48],[49]). This symmetry envisages the existence of a whole set of yet unseen particles mirroring the existing known particles. The spin of those new particles has to differ from the standard particles by one half to allow for the mentioned sign swap and thus for the desired divergence cancellation in the perturbative expansion. In the symmetry parlance it ought to exist a set of symmetry generators Q that relate fermions and bosons:

Q|F >= |B >; Q|B >= |F > (2.2)

By assuming such a symmetry we unavoidably achieve the desired cancellation of the diverg- ing mass terms. The generators Q carry spin 1/2 and can be proven to obey, under certain restrictions, the following (anti)commutation algebraic relations

{Q, Q^†} = P^µ (2.3)

{Q, Q} = {Q^†, Q^†} = 0 (2.4)

µ µ †

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where P^µ is the space-time translation operator. From those equations we can imply that the single particles are arranged in multiplets containing both fermions and bosons. The operator −P² commutes with the operators Q and Q† hence the particles in the same multiplet have the same masses. The same two operators commute with the generators of the gauge transformations therefore the partners in the multiplet must have the same charge, isospin and colour and on the same line of reasoning it can be shown that each multiplet must contain an exact number of fermions and bosons for the commutation rules 2.3, 2.4 and 2.5 to hold true. It is remarkable that once we introduce this symmetry and the group of superparteners with it the expression 2.1 becomes

m²_h ∼ m²0+ g(m²f˜− m²f)ln(Λ/mf˜) (2.6)

it is clear that the introduction of the supersymmetry has reduced the divergence of the renormalized Higgs mass. From equation 2.6 we see that the symmetry does not have to be exact (mf˜= mf), what is required is that the dimensionless coupling constant is the same for the Standard Model particles and the superpartners and that the physical masses of the superpartners are not too far from the ones of the corresponding SM particle. In such an extension each of the known fundamental particle must be in a chiral or gauge multiplet and be coupled with a superpartner with a spin differing of 1/2 unit. The widely accepted nomenclature for this set of superpartners is to add an s (for ”scalar”) in front of the existing Standard Model particle (e.g. squark, selectron, smuon, stau) and in short notation a tilde is added to the particle name to denote the sparticle name (˜e, ˜µ, ˜u). Sleptons, although they include the symbol L or R for their helicity, do not actually carry any real handedness being bosons but this nomenclature is just kept to remind the SM lepton partner helicity. A

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summarised in table 2.7

Names spin 0 spin 1/2 spin 1 SU(3)_C, SU(2)_L, U(1)_Y squarks, quarks (˜u_L, ˜d_L) (u_L,d_L) (3, 2, 1/6)

(×3 families) u˜^∗_R u^†_R (¯3, 1, −2/3)

d˜^∗_R d^†_R (¯3, 1, 1/3)

sleptons, leptons (˜ν, ˜eL) (ν, eL) (1, 2, −1/2)

(×3 families) e˜^∗_R e^†_R (1, 1, 1)

Higgs, higgsinos (H_u⁺, H_u⁰) ( ˜H_u⁺, ˜H_u⁰) (1, 2, +1/2) (H_d⁰, H_d⁻) ( ˜H_d⁰, ˜H_d⁻) (1, 2, −1/2)

gluino, gluon ˜g g (8, 1, 0)

winos, W bosons W˜^± W˜⁰ W^± W⁰ (1, 3, 0)

bino, B boson B˜⁰ B⁰ (1, 1, 0)

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In this table e = (e, µ, τ ) are the three leptons, u = (u, s, b) and d = (d, c, t) are the quarks. The fifth column indicates the transformation properties of the supermultiplet under the action of the Standard Model gauge symmetries. The superpartners of the unbroken Standard Model bosons are the the gluino, the Wino and the Bino while the Higgsinos are the counterparts of the vector bosons fields. This exact symmetry must be broken otherwise we would have observed the superpartners long time ago. After symmetry breaking the new mass eigenstates of the theory are expressed as a linear combination of the unbroken model eigenstates. The charged Higgsinos and the Winos combine to give two charginos ( ˜χ^±_1,2) while the neutral ones together with the Bino mix into four neutralinos ( ˜χ⁰_1,2,3,4). In the

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M_χ =







M1 0 −M^Zcos(β)sW MZsin(β)sW

0 M1 MZcos(β)cW −M^Zsin(β)cW

−M^Zcos(β)sW MZcos(β)cW 0 −µ

MZsin(β)sW −M^Zsin(β)cW −µ 0







The extension to the Standard Model with the minimal particle content is called MSSM.

In this model every particle has a superpartner differing only in the spin properties as already mentioned. It is interesting to highlight that there are already two know particles whose spin differs 1/2 units and with identical gauge quantum numbers: the Higgs boson and the neutrino. It must be said that those two particles cannot be part of the same supermultiplet because this would lead to lepton number violation and this is indeed ruled out on phenomenological grounds. In principle SUSY theories admit the presence of barion and lepton number violating interactions in the Lagrangian. Such an occurrence would lead to an unobserved high proton decay rate and other processes like µ → eγ or µ → eee would have already been detected. This freedom is completely different from the Standard Model where gauge invariance guarantees the absence of any barion/lepton number violating interaction. If we define the global discrete symmetry

RP = (−1)^3B+L+2s (2.8)

where B(L) is the barion(lepton) number while s is the particle spin. There are two broad classes of supersymmetric theories namely the ones that violate (R_PV ) and the ones that conserve (RPC) R parity. The most important phenomenological difference between those

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and the decay chains always end up into the lightest supersymmetric particle (LSP). In this theories the LSP is actually stable and if electrically neutral and only weakly interacting it will escape detection at the experimental facilities accounting for a large fraction of the initial energy at collision to escape undetected (e.g. large missing energy) providing a very effective way of discriminating supersymmetric events. There is strong experimental evidence that if the LSP does exist it must be weakly interacting and neutral because otherwise it could be possible to find relic LSP bound into atoms and this is ruled out with a very good precision. Within MSSM the LSP can be only the lightest neutralino or the sneutrino and the neutralino is a top candidate for dark matter. In SUSY theories that include gravitation the gravitino can be the LSP but although of cosmological relevance such an occurrence would prove meaningless in an experimental framework because the LSP would interact only gravitationally. In RPV theories the superparticles can decay completely into Standard Model particles and the analysis is thus much more complex.

2.5 The Minimal Supergravity Model

In the formulation of the unbroken MSSM ([47],[48],[49]) very few assumptions are made, namely a minimal particle content of the theory together with its Poincar´e and gauge invariance. This leads to a final theory depending upon 105 free parameters. If MSSM is indeed the ruling theory at the TeV scale it will likely show up at the LHC and the challenge of determining those parameters will be there for the experimental particle physicists. The approach of sampling the entire parameter space in search for the set of parameters that best fit the measurements is clearly impossible to follow because, as a crude estimation could show,

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unification would already restrict vastly the number of independent parameters. Additional assumptions on how the supersymmetry is broken further reduce the number of degrees of freedom of the theory. The exact mechanism of symmetry breaking will be the subject of initial study when the LHC will be switched on but at the moment only pure speculations can be made. The particular breaking mechanism chosen influences dramatically how the MSSM parameters relate to each other and most importantly the phenomenological content of the theory can be very different in the various breaking scenarios. The phenomenological approach has been to probe different constrained SUSY theories in search for defining features that hold true in a vast region of parameters space in an attempt to characterise the otherwise uncharted SUSY geography. All constrained versions of the MSSM imply the existence of a hidden sector of the theory that communicates the symmetry breaking behaviour to the Standard Model and supersymmetric particles sectors via a specific mechanism.

One such constrained model is the minimal SUperGRAvity (mSUGRA) postulating that the hidden and observable sectors communicate only gravitationally [95]. Super gravity is known to be not renormalizable so mSUGRA can be seen as an effective theory valid at energies below a very ultra high energy scale. Despite this limitations mSUGRA can still be taken as a viable framework in which try to extract more general SUSY phenomenological features that can be generalised to much broader variety of models. Under the aforementioned and with other, rather arbitrary, assumptions the mSUGRA parameters space is greatly reduced as compared to the original MSSM parameter space. There are indeed five independent parameters in mSUGRA

m0, m1/2, A0, tan(β), sgn(µ) (2.9)

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where m0 is the common supersymmetry breaking scalar mass, m1/2 is the common gaugino mass, A0 is the common trilinear interaction factor, tan(β) = hH^ui/hH^di is the VEV of the two supersymmetric Higgses and µ is the mass parameter. For simplicity one can view this constrained model simply as a MSSM where universal scalar and gaugino masses and common A terms have been assumed at some ultra high mass scale. Universality of scalar masses does not imply that the physical scalar masses of all sfermions are the same. Indeed using renormalization group equations (RGE) it can be shown that to a first approximation,

m²_q_˜= m²₀+ m²_q− m²1/2+ o.c. (2.10)

m_˜²_l = m²₀+ m²_` − 3.5m²1/2+ o.c. (2.11)

and finally

m²_q_˜= m²_`_˜− 0.1m²g˜ (2.12)

where we have implied a common averaged mass of the first and second squarks and sleptons generations. Parameters in this space can take any value but if we take into consideration various phenomenological constraints we can see that considerable regions in this space are instead forbidden or at least disfavored.

2.5.1 Anomalous muon magnetic moment

The anomalous magnetic moment of the muon, if supersymmetry exists, receives contributions from diagrams involving SUSY particles like the ones in figure 2.2 The most recent com-

bined measurement of the anomalous magnetic moment stands at a^±_µ = 11659208(6) × 10⁻¹⁰ ([68],[69]). Every model point in the parameter space must be compatible with this value

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Figure 2.2: Two main SUSY contributions to the muon magnetic moment

and from figure 2.4 we can see that the medium (pink) shading band is the forbidden region for fixed tan(β), A, µ.

2.5.2 b → s + γ

Similar arguments hold true ([70],[71]) for the b → sγ process. It receives contributions from radiative corrections involving charged Higgs, chargino and ˜t loops as shown in figure 2.3

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Again in figure 2.4 we can see the forbidden region for this constraint in medium (green) shading.

2.5.3 Relic dark matter density of the universe

Experimental measurements of the the previous two constraints together with direct Higgs and long lived chargino searches have changed very little during recent years. The com- patibility of the model predictions with the measured relic hot dark matter density of the universe (ΩCDM) instead has greatly reduced the allowed regions of parameter space. A very useful representation of such situation is the one in which at fixed tanβ, A0 and µ the (m0,m1/2) is scanned in search for the allowed portions of the parameter space. An example of such plot is given in figure 2.4. While most of the aforementioned constraints have had little modifications in the recent years more accurate results from the WMAP experiment [109]

have a quite remarkable impact on the size and shape of the allowed regions [93]. It is indeed the case where regions have now actually shrank down to be lines of which is even possible to give a parametric expression of the relation between m0 and m1/2. The phenomenological content of the mSUGRA theory varies dramatically along those lines and particular care must be taken in the physics analysis strategy used to extract the SUSY signal. In the spirit of the SUSY searches already performed in the past ([75],[76],[76],[106],[107]) once a constrained model is chosen and the allowed portions of the parameter space are pinpointed a set of model points in this space is chosen in such a way that the detailed analysis carried out in this specific point can unveil the characteristics of that point and more generally of the surrounding region. Despite its several shortcomings the mSUGRA model it is still a good learning ground and it is remarkable that although very artificially constrained, mSUGRA

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100 200 300 400 500 600 700 800 900 1000 0

100 200 300 400 500 600 700 800

100 200 300 400 500 600 700 800 900 1000 0

100 200 300 400 500 600 700 800

mh = 114 GeV

m

0

(GeV)

m

_1/2

(GeV)

tan β = 10 , µ > 0

m_χ± = 104 GeV

Figure 2.4: Post WMAP updated (m0, m_1/2) plane [?] for tan β = 10.0 and sign(µ) > 0.

The allowed region is marked in very dark shade (blue). The disallowed region where m_τ_˜₁ < m_χ0

1 has dark (red) shading. The region excluded by b → sγ has medium (green) shading and the region favoured by g_µ− 2 has medium (pink) shading. A dot-dashed line delineates the LEP constraint on the ˜emass and the contours m_χ±

1 = 104 GeV (mh = 114 GeV) are shown as near-vertical black dashed (red dot-dashed) lines.

is still consistent with all existing phenomenological and cosmological constraints.

2.6 SUSY Particle Phenomenology

It is clear that by extending the Standard Model including supersymmetry there is a great

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spectrum in figure 2.5 immediately shows the wide range of new processes that can hopefully be studied at LHC. We shall see in more detail how some of those decay chains can and shall

Figure 2.5: An example of a mSUGRA mass spectrum and some of the possible decays

be used to extract underlying theory parameters like particle masses, mSUGRA parameters and eventually to give an estimate of the LSP relic dark matter density of the universe.

2.7 SUSY and Cosmology

As we have seen the SUSY phenomenology includes, in a large portion of its parameter space, the existence of a colour blind, electrically neutral and only weakly interacting massive particle (WIMP) the lightest neutralino. The neutralino is a very good candidate, but not the only, as a source of relic dark matter. The current observed content of hot relic dark matter

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in the universe is the result of the early universe expansion with subsequent ”freeze out” of the remaining content of surviving LSPs [108]. In the very early universe all particles are in thermal equilibrium. In fact as soon as the universe starts to expand the particle interaction rate becomes too low and particles are said to ”freeze out” namely unstable particles start to decay into more stable states and so they start to disappear from the universe. The number of final stable particles starts to increase and those particles survive in the current universe.

Of course there is a reasonable chance that such stable particles can be destroyed in an annihilation process (χχ → f ¯f) and at the same time WIMPs can be create in annihilation process of non-WIMP particles (f ¯f → χχ). It can be shown that the relic dark matter density for WIMPs at freeze out is

Ωχ ∼ 10⁻¹⁰GeV⁻²

hσ^Avi (2.13)

where hσ^Avi is the WIMP annihilation cross section that for a typical value

hσAvi ∼ α²

M_weak² ∼ 10⁻⁹GeV⁻² (2.14)

leads to a thermal relic density of Ωh² ∼ 0.1 which is in very good agreement with observed value. This surprising result is seen as one of more stringent arguments in favour of the validity of supersymmetry. An exact calculation of the relic dark matter density implies the exact knowledge of all the mentioned cross section. If the WIMP is the lightest neutralino the exact estimate of that cross section is rather difficult because of the several annihilation channel open for the LSP some of which are depicted in figure 2.6

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Figure 2.6: Few (co)annihilition diagrams that could have contributed to lower the LSP relic density to the measured levels

2.7.1 ”Bulk region”

The region of mSUGRA parameter space where the neutralino is Bino like and where the relic density is compatible with the one observed today is called ”bulk region” (0 < m0 <

100, 100 < m1/2 < 200) the name stems from the fact the in the early days of SUSY studies this was the widest region in the parameter space while after recent improved WMAP results this region is reduced to a very narrow band.

2.7.2 ”Focus point region”

For large m0 the LSP becomes a gaugino-higgsino mixture. The region where this happens is called ”focus point region”, a name derived from some renormalization group equations properties that allow large scalar masses without fine tuning of the parameters. In this region the first diagram in figure 2.6 is strongly suppressed while the 2nd diagram (χχ → W⁺W⁻) is enhanced. This provides a second method by which neutralinos can annihilate efficiently enough to produce the observed relic dark matter density.

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2.7.3 ”Funnel region”

A third possibility is that the third graph in figure 2.6 is enhanced. This happens for relatively large tan(β) and when the mass of a Higgs is roughly twice the mass of the LSP.

The existence of this resonance effectively depletes the amount of relic dark matter, so efficiently indeed to justify the name of the region where this occurs.

2.7.4 ”Co-annihilation region”

The desired neutralino relic density may be achieved even if χ − χ annihilation is inefficient.

The neutralino density might have been brought down through ”co-annihilation” with other non-LSP particles. Co-annihilation is enhanced when the LSP and other non LSP particle are degenerated or at least very close in mass. The co-annihilation line extends towards large m_1/2 and with relatively small values of m₀. It is interesting to notice that recent improved measurements of the WMAP experiment have narrowed down this, and other regions, to be almost a line [99]. An example of this parametric form for the co-annihilation line with tan(β) = 10 is given by

m0 = 11.97 + 0.163m1/2+ 4.90 × 10⁻5m²_1/2 (2.15)

The three competing processes that influence the density of relic dark matter are the annihilation of LSP pairs, the annihilation of non-LSP pairs and the co-annihilation of LSP with non-LSP particles. The resulting dynamic equilibrium is controlled by the relative cross section ratios

σ_χ6χ/σ_χχ , σ_6χ6χ/σ_χχ (2.16)

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It is interesting to highlight that the co-annihilation processes conspire at the same time in raising the expected mass for the LSP from about 200 GeV to above 600 GeV with possible repercussions on the experimental ability to detect of the LSP at LHC [100]. It can be shown that the co-annihilation processes become particularly important when

m6χ˜− m^χ^˜ ∼ m^χ/20 (2.17)

and this is exactly what happens along most part of the co-annihilation line where the LSP and NLSP have masses only few GeVs apart. This is particularly true in regions of the MSSM space where the LSP is mainly Bino and the next to lightest supersymmetric particle (NLSP) is the ˜τR altough co-annihilation with other sleptons still plays a very important role.

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3 The Large Hadron Collider

The Large Hadron Collider (LHC) is in construction in the former LEP II ring at CERN and it is foreseen to start its activity in spring 2007 when an initial short period of data taking is expected to deliver 10 f b⁻¹ of integrated luminosity before a further period of inactivity.

The shutdown period will enable the completion of the staged components of the ATLAS detector.. The LHC will accelerate protons to a centre of mass energy of 14 TeV from an injection energy of 450 GeV allowing to perform physics studes in the energy range between 100 GeV up to 2 TeV extending the current reach of one order of magnitude. During its lifetime it is foreseen to operate at two different luminosity regimes namely the initial so called low luminosity regime (2 × 10³³cm⁻²s⁻¹) and a final high luminosity regime (10³⁴cm⁻²s⁻¹).

The low luminosity quoted is actually twice as much as the original luminosity foreseen for the initial period of data taking, this is due to collider and detectors staging that has to take place for the installation completion. At the design (high) luminosity protons will be accelerated in bunches 25 ns apart from each other. At every bunch crossing there will be

∼ 23 proton-proton interactions, this effect is called pile-up. In the design of the LHC an extensive use of super conducting magnets has been done to achieve the desired bending power in the logistical and geographical limits of the already existing ring.

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3.1 LHC General Parameter

In figure 3.1 and 3.2 are shown two schematic views of the LHC accelerator. There we can see the interaction points and the underground experimental areas while in table 3.1 are listed some of the LHC collider operating parameters:

Figure 3.1: Surface schematic view of the LHC ring

Figure 3.2: Underground schematic view of the LHC ring

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Energy at collision 7 TeV

Energy at injection 450 GeV

Dipole field at 7 TeV 8.33 T

Coil inner diameter 56 mm

Distance between aperture axes (1.9 K) 194 mm

Luminosity 1 ∗ 10³⁴cm⁻²s⁻¹

Beam beam parameter 3.6⁻³

DC beam current 0.56 A

Bunch spacing 7.48 m

Bunch separation 24.95 ns

Normalised transverse emittance (r.m.s.) 3.75 m

Total crossing angle 300 rad

Luminosity lifetime 10 h

Energy loss per turn 7 keV

Critical photon energy 44.1 eV

Total radiated power per beam 3.8 kW

Stored energy per beam 350 MJ

Filling time per ring 4.3 min

Table 3.1: Main parameters of the LHC

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4 The ATLAS Detector

4.1 Detector Overview

Figure 4.1: The ATLAS Detector

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are set to carry out complementary searches for new physics at the LHC. A pictorial representation of the ATLAS detector can be seen in figure 4.1.

The detector has been designed to be able to cope with the very harsh operating conditions of the LHC environment in terms of luminosity, latency, radiation, occupancy and last but not least the necessity to be as inclusive as possible towards new physics at the TeV scale.

ATLSA has exceptional tracking and calorimetry systems and makes use of super-conducting magnets to achieve the needed bending power both in the inner and the outer part of the detector for precise momentum resolution of electrons and muons. The Inner Detector is set to provide precise tracking and vertexing capabilities especially in the innermost layer where the vertexing is most important for jet flavour tagging and tau identification. The calorimeters are especially designed to provide excellent photon/electron identification and in the hadronic parts are hermetic enough to allow precise measurement of missing energy and jet energy scale. The ATLAS characteristics are of unprecedented complexity. Its dimension (46 m length, 25 m eight) and weight (7000 tons) represent a serious civil engineering challenge and its completion is foreseen to go along with the LHC schedule to be ready for data taking, at least in its initial layout, in spring 2007.

4.2 Inner Detector

The Inner Detector (ID) makes use of three different tracking technologies [52] to fullfil the following requirement: very precise measurement in the innermost layer to allow vertex detection at the very high occupancy expected, keep the material introduced between the ID and the outer detector layers at a minimum and provide continuous tracking at a low

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Figure 4.2: Schematic representation of the ATLAS Inner Detector system

The ID is embedded in a 2T magnetic field produced by super-conducting magnets to achieve the necessary trajectory bending needed for particle momentum determination and identification.

4.2.1 Magnetic Field

The magnetic field in the Inner Detector is generated by a solenoidal coil laying between the inner part of the ATLAS detector and the more external calorimeter. The size of the tracking detector is actually larger than the solenoid itself slightly impairing the momentum resolution at large pseudorapidity (η > 2.5).

4.2.2 Pixel Detector

As already mentioned the innermost detector at ATLAS is based on pixel technology [53].

This allows excellent resolution and enables efficient vertexing in the very crowded environment expected at ATLAS. Vertexing is of paramount importance for jet b tagging and tau

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in the case of a charged particle passing near the pixel element. The diode dimensions are 80x400 µm and there are 50000 of them in every of the almost 2000 detector modules. The Pixel Detector consists of three layers laying parallel to the z axis at 4, 10 and 13 cm and of five discs at each end to allow full spatial coverage. The innermost layer (called B-layer) provides the vertexing capabilities and is designed to be replaced in few years time when the current detector will eventually be severely damaged by radiation.

4.2.3 Semiconductor Tracker

The Semiconductor Tracker (SCT) envelopes the Pixel layers and consists of eight layers of silicon micro-strip modules and of nine wheels at each side of the interaction point. Like the Pixel Detector its basic detecting elements is a semiconductor diode that records the ionising effect of a charged particle passing nearby. This technology offers high resolution for pattern recognition tracking allowing to separate tracks 200 µm apart. Both pixel and silicon detectors need to be cooled to maintain their efficiency, to safeguard the electronics and to keep a perfect allignment avoiding thermal expansion.

4.2.4 Transition Radiation Tracker

The Transition Radiation Tracker (TRT) uses 4 mm straw tubes of a maximum 144 cm length. The barrel extends up to a radius of 107 cm and contains 50000 tubes. The two end-caps consist of 18 wheels each and contain 320000 straws. Every straw tube records the transition radiation emitted by the relativistic particles entering the medium with high refractive index in the tube. The ionising charge is amplified by the voltage applied at

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allows to do some basic particle identification at the detector level. TRT technology provides continuous tracking and on average the very high number of hits (∼36) compensate for the limited spacial resolution as compared with Pixel and SCT detectors. The large number of straws per track allows to achieve 50 µm precision.

4.3 Calorimeters

The calorimeters (figure 4.4) play a very important role in the physics reach of the ATLAS detector. They are responsible for the precise energy and position measurement of electron and photons over a large geometrical range, the characterisation of jets, particle identification and separation from QCD background, tau identification and total missing transverse momentum (pT) measurement. Last but not least the calorimeters provide the signal for the first trigger level.

Figure 4.3: Schematic representation of the ATLAS calorimeter system

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4.3.1 Electromagnetic Calorimeter

The Electromagnetic Calorimeter (figure 4.3) is a LAr lead detector with an accordion shape that allows for full symmetric coverage over the full azimuthal range [55]. In the central region of precise measurements the EM calorimeter is proceeded by a pre-sampler that accounts for the energy losses in the material of the ID and in the cryostat. In the energy range of physical interest it achieves an energy resolution of 1%.

Figure 4.4: Schematic representation of the electromagnetic calorimeter

4.3.2 Hadronic Calorimeters

The main purpose of the Hadronic calorimeters (HCal) is to provide precise measurement of the jet energy and to provide an accurate estimate of the missing p_T. The HCal is built with different technologies to be able to cope with the different required precision and for the

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part an iron scintillating technology is used while in the forward region the LAr is used to cope with the harder radiation expected in that region.

4.4 Muon Spectrometer

The ATLAS Muon Spectrometer (figure 4.5) is built using four different chamber technologies [57] and its main purpose is to identify and measure muons momenta and provide a match with the track in the inner detector. It must provide the trigger signal and provide muon to bunch crossing association. Again the momentum resolution must be precise to the order of 1% to allow precise mass reconstruction. The muon system’s geometry is such that particles traverse three stations of chambers optimised for full coverage and momentum resolution. The trigger signal is provided by three layers of Resistive Plat Chambers (RPC) in the barrel and of Monitored Drift Tubes (MDT) in the forward regions. The spectrometer geometry follows closely that of the eightfold superconducting toroids that provide the bending magnetic field in the muon system.

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Figure 4.5: End view of the Muon system

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5 ATLAS detector simulation and reconstruction

5.1 Introduction

In this chapter we will present ATLFAST [63], the fast ATLAS detector simulation and reconstruction program that has been used to generate the physics samples used in the analysis chapter for the physics study. No attempt is made in this chapter to compare fast simulation with the full detector simulation.

5.2 ATLFAST

The ATLFAST simulation program bears on the necessity to have a viable tool to produce physics events for analysis. Viable in the sense that the accurate full simulation and reconstruction machinery requires an incredible amount of computing power which is not easily accessible to single physicists for their analysis purposes. ATLFAST compromises exact detector simulation for a coarser one and particle smearing is done directly on the Monte- carlo generated particles instead of being induced from the detailed detector and material simulation.

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5.2.1 Calorimeter cells

The starting point of ATLFAST reconstruction are calorimetric cells. Cells are a geometrical portion of the detector where some particle momentum has been deposited. Cell are 0.1×0.1 in η and φ in the region η < 3.0 and 0.2 × 0.2 for the rest of the rapidity range (3 < η < 5).

No difference is made between electromagnetic and hadronic cells, and the ATLFAST cell should be regarded as geometrical entities. The initial input to the cell maker algorithm are the Montecarlo generated particles. Final stable particles are considered at this stage and only particles with pT > 0.5 GeV are considered. Muons, neutrinos and the LSP, in the case of SUSY, are excluded because they leave no energy deposition in the cells. The magnetic field effect is parametrised assuming uniform field over the full rapidity range. Energy deposition efficiencies and secondary particle effects are all simulated through smearing of the cell energy.

5.2.2 Clusters

All calorimetric cells with p_T > 1.5 GeV are considered by the clustering algorithms as potential cluster initiators. A cone algorithm is used to search for cells within a radius

∆R = 0.4. Cell energies are added in this cone and only clusters with total energy deposition greater than the minimum particle energy (5 GeV) are retained. The barycentre of the cluster is taken as its coordinates. Cells in overlapping cluster share their energy with both clusters.

5.2.3 Electron and photons

Electrons and photons in the η < 2.5 region and with energy above minimum required are

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is ∆Rγ,clus < 0.1. The generated particle momenta are smeared before the procedure and effects of pile-up are simulated at this stage by applying different smearing. Isolation criteria are applied to the particles. A photon must be separated from any neighbouring cluster by the standard cluster size assumed (∆R > 0.4) and the total energy deposited around the generated position must be less than 10 GeV. If an electron or a photon is found to fullfil the isolation criteria it is removed from the list of particles together with the associated cluster which will not be considered at any later stage.

5.2.4 Muons

A procedure similar to the one used for electrons and photons is applied to generated muons.

Identical cuts are applied for the isolation from cluster and from activity. Particular care is taken in parametrising to muon resolution. A muon momenta in the real ATLAS detector will be reconstructed using two different sets of measurements coming from the muon spectrometer and the inner detector. The smearing of the muon momenta must receive two different contributions because of the intrinsic different technologies and geometrical set ups implied. The magnetic field is homogeneous in the inner detector so the smearing can easily be simulated assuming a cilindrical geometry with a sudden drop at η = 2.5. The spectrometer on the other hand shows a much more complex magnetic field pattern and detector/material layout so the muon resolution from this detector is heavily dependant on the energy and coordinates of the muon. ATLFAST holds a database of this muon momenta resolution and uses it to apply the ”right” smearing to the generated particle.

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5.2.5 Jets

The clusters that survived the previous reconstruction step are considered for jet activity.

The energy of non isolated muons in the cluster cone is added to the smeared ”reconstructed”

jet energy.

5.2.6 Missing transverse momentum

All visible momentum is added to give the total reconstructed momentum of the event.

Reconstructed momentum comes in two forms: the momentum carried by the reconstructed particles and the momentum of the cells that were not associated to any cluster because associated with a variety of different possible activities like soft particles, jet leakage and other. The vector difference of the total reconstructed particles momenta and this summed momentum coming from unclustered cells is recorded as the missing transverse momentum.

5.2.7 Consideration on energy scales

Throughout the analysis we will assume a conservative approach for reconstructed particle energy scale: 0.1% for electrons and muons and 1% for jets.

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6 Physics Analysis of a mSUGRA model

We have now all the elements to perform a detailed analysis of a specific SUSY model. The aim of this analysis is to show that SUSY particle masses can be reconstructed by using a kinematic end-point technique. This technique has been extensively used to characterise supersymmetric models and extract SUSY parameters from the observed invariant mass distributions.

We know that mSUGRA is a constrained MSSM RPC theory and consequently it has a stable LSP which happens to be neutral and colour blind for most of the parameter space and produced in pairs in every mSUGRA event. The event selection benefits from this peculiarity and the Standard Model background is dramatically reduced by accepting only events with large missing transverse energy and jet multiplicity. For the specific model under investigation it is of paramount importance being able to establish the sparticle masses because in the co-annihilation region, where we have chosen to perform our detailed analysis, the near degeneracy of the LSP with the sleptons helps keeping the amount of relic cold dark matter to the levels observed today. This is achieved thanks to co-annihilation processes between the LSP and the degenerate particles like staus, selectrons and smuons.

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6.1 Co-annihilation mSUGRA model

For this detailed analysis we have chosen to operate in the framework of constrained MSSM model mSUGRA. We have already seen in Chapter 7 that mSUGRA lives in a five dimen- sional parameters space. We have chosen a model lying in the so called stau co-annihilation region where the LSP is nearly degenerate with the stau and to a lesser extent with the ˜`R

(` = e, µ). The exact chosen parameter values are:

m0 = 70.0 GeV ; m1/2= 350.0 GeV ; tan(β) = 10.0 ; sign(µ) = +

A = 0.0 GeV ; mtop = 175.0 GeV (6.1)

To calculate particle mass spectrum and cross sections we have used the RGE code provided by Isajet 7.67 [62], for the SUSY signal generation we have used Herwig v6.5.0 [59] interfaced through Isawig v1.0.2 [87] to the mass spectrum produced by Isajet. The Standard Model

˜

g d˜L d˜R u˜L u˜R ˜b2 ˜b1 t˜2 ˜t₁ 832.33 764.90 733.53 760.42 735.41 722.86 697.90 749.46 572.96

`˜L `˜R τ˜2 τ˜1 ν˜` ˜ντ H˜^± A˜⁰ 255.13 154.06 256.98 146.50 238.31 237.56 521.90 512.39

˜

χ⁰₄ χ˜⁰₃ χ˜⁰₂ χ˜⁰₁ χ˜^±₂ χ˜^±₁ H˜⁰ h⁰ 483.30 -466.44 263.64 136.98 483.62 262.06 515.99 115.81

Table 6.1: Masses [GeV] for the chosen co-annihilation point

background sample has been generated using Pythia v6.2.0 [85]. For this model the total

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6.2 Cross sections

The SUSY hard sub-process cross sections have been calculated by direct counting over the generated signal sample and an excerpt of the most relevant processes is reported in table 6.2. As we can see the total cross section is dominated, quite predictably, by ˜g − ˜q, g − ˜g and ˜q− ˜q processes. All the SUSY particles produced in these primary hard processes˜ undergo subsequent decays into lighter sparticles generating long decay chains that end all up eventually into the LSP. Being mSUGRA an RPC theory there will always be two concurrent such decay chains in every SUSY event. Given the large mass difference between some of the particles involved some of the final stable decay products, like jets and leptons, will acquire very large transverse momentae. This characteristic gives us the handle to isolate and study some decay chains. We shall explain in more detail this later on in this chapter.

process C. sec. (fb) process C. sec. (fb) p + p → ˜g + ˜q^R 1757.0 p + p → ˜t¹+ ˜t1 160.0 p + p → ˜g + ˜q^L 1620.0 p + p → ˜χ⁰₂+ ˜qL 154.0 p + p → ˜q^L+ ˜qR 885.0 p + p → ˜χ^±₁ + ˜χ^±₁ 140.0 p + p → ˜q^R+ ˜qR 779.0 p + p → ˜b¹+ ˜b1 49.0 p + p → ˜qL+ ˜q_L 665.0 p + p → ˜b2+ ˜b₂ 38.0 p + p → ˜g + ˜g 554.0 p + p → ˜t2+ ˜t₂ 32.0 p + p → ˜χ⁰₂+ ˜χ^±₁ 258.0 p + p → ˜`+ ˜` 15.0

Table 6.2: List of the most relevant SUSY production processes (fb)

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6.3 Branching ratios

In the task of isolating specific decay chains the branching fractions play a key role. The main branching ratios for the co-annihilation point can be found in table 6.3. The large branching ratio of the process ˜q_L → ˜χ⁰₂ + q → ˜`L,R+ ` + q → ˜χ⁰₁ + ` + ` + q together with the large squark and gluino production CS will enable us to perform a detailed analysis and to reconstruct SUSY particle masses.

6.4 The Standard Model background

All analyses have been carried out including what is believed to be the major sources of Standard Model backgrounds for the SUSY searches. Large samples of filtered t − ¯t, W → ν + ` and Z → ` + ` and QCD jets in different energy ranges have been simulated. Pre filtering has been applied mainly on the missing transverse momentum in the event to keep the number of events on disk to a manageable level.

6.5 Establishing SUSY mass scale through effective mass analysis

We are considering mSUGRA but all RPC theories have a stable final particle. If we restrict to the physically acceptable region of the theory parameter where the stable final particle is colour blind and electrically neutral we immediately realise that RPC theories all lead to very large missing energy due to two escaping lightest neutralino. Another very interesting feature of SUSY events is the large jet multiplicity. We can see that not only jets are numerous but also carry large transverse momentum because many of them come from the decays of very

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gluinos squarks higgs charginos g → ˜q˜ ^R+ q (9%) q˜L→ ˜χ^±₁ + q (60%) h → b + ¯b (83%) χ˜^±₁ → ˜χ⁰₁ + W (7%) g → ˜q˜ ^L+ q (9%) q˜L → ˜χ⁰₂+ q (31%) h → τ^∓+ τ^∓ (5%) χ˜^±₁ → ˜τ1^±+ ντ (16%)

˜g → ˜b¹+ b (16%) q˜L → ˜χ^±₂ + q (4%) χ˜^±₁ → ˜τ2^±+ ντ (1%)

˜g → ˜t¹+ t (15%) q˜R→ ˜χ⁰₁+ q (99%) χ˜^±₂ → ˜χ⁰₂+ W (29%)

˜g → ˜b²+ b (11%) χ˜^±₂ → ˜χ^±₁ + Z⁰ (23%)

˜

χ^±₂ → ˜χ^±₁ + h (19%)

˜

χ^±₂ → ˜`^L+ νl (8%)

neutralinos sleptons sbottoms stops

˜

χ⁰₂ → ˜τ1^±+ τ^∓ (19%) `˜^±_R → ˜χ⁰₁+ l^± (100%) ˜b1 → ˜χ^±₁ + t (38%) ˜t1 → ˜χ^±₁ + b (47%)

˜

χ⁰₂ → ˜`^±L + l∓ (5%) `˜^±_L → ˜χ⁰₁+ l^∓ (99%) ˜b1 → ˜χ⁰₂+ b (24%) ˜t1 → ˜χ⁰₁+ t (24%)

˜

χ⁰₂ → ˜`^±R+ l∓ (2%) τ˜₁^± → ˜χ⁰₁+ τ^∓ (100%) ˜b₁ → ˜χ^±₂ + t (23%) ˜t₁ → ˜χ⁰₂+ t (14%)

˜

χ⁰₂ → ˜χ⁰₁+ h (5%) τ˜₂^± → ˜χ⁰₁ + τ^∓ (94%) ˜b1 → W + ˜t1 (9%) ˜t₁ → ˜χ^±₂ + b (13%)

˜

χ⁰₃ → ˜χ^±₁ + W (59%) ˜b1 → ˜χ⁰₁ + b (2%) ˜t₂ → ˜χ^±₁ + b (24%)

˜

χ⁰₃ → ˜χ⁰₂+ Z⁰ (22%) ˜b2 → ˜χ^±₂ + t (32%) ˜t2 → ˜χ⁰₄+ t (22%)

˜

χ⁰₃ → ˜χ⁰₁+ Z⁰ (10%) ˜b2 → ˜χ⁰₁+ b (21%) ˜t2 → ˜χ^±₂ + b (14%)

˜

χ⁰₄ → ˜χ^±₁ + W (47%) ˜b2 → ˜χ^±₁ + t (14%) t˜2 → Z⁰+ ˜t1 (10%)

˜

χ⁰₄ → ˜χ⁰₂+ h (19%) ˜t2 → ˜χ⁰₂+ t (10%)

˜

χ⁰₄ → ˜χ⁰₁+ h (8%)

˜

χ⁰₄ → ˜`^±L + l^∓ (3%)

Table 6.3: main SUSY decays branching ratios

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to get large fractions of the large momentum carried by the mother sparticle. Previous investigations performed in the past ([75],[76][77]) show that an initial crude estimate of the SUSY mass scale can be obtained by the extraction of the effective mass distribution. The effective mass is defined as

Mef f = /ET +

X4 i=1

(p^j_Tⁱ) (6.2)

and the sum is carried out over the four hardest jet in the event. The choice of including the hardest four jets is inspired by the idea that in the two simultaneous SUSY decays chains there can be up to four relatively hard or very hard jets produced, the actual jet multiplicity depending on the exact number of initial squarks and/or gluinos produced in the event. This variable has a very powerful potential for discovery although it must be said that our capability to predict the actual discovery potential through this analysis depends very strongly on our understanding of the Standard Model and QCD backgrounds and any other possible sources of large missing transverse energy in the ATLAS detector like dead detector regions or very energetic jet mis-calibrations. The effective mass distribution for our model has been obtained imposing the following cuts on the signal and background sample

• /ET > 200.0 GeV or /ET > 0.2 · M^{ef f}

• at least 4 jets with p^jT¹ > 100.0 GeV, p^j_T² > 50.0 GeV, p^j_T³ > 50.0 GeV, p^j_T⁴ > 50.0 GeV

• no isolated leptons or muons with p^T > 10.0 GeV

The main sources of Standard Model background are included and we can see in figure 6.1 how well the distribution of the SUSY effective mass can be discriminated from the background.

ATLAS High Level Trigger Steering and Seeding Mechanism SUSY Particle Masses Determination in the Co-annihilation Model Gianluca Comune