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Search for Supersymmetry with displaced vertices and muons using the ATLAS detector Chavez Gonzalez, Ricardo 2016

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Search for Supersymmetry with displaced vertices andmuons using the ATLAS detectorbyRicardo Chavez GonzalezB.Sc., Tecnolo´gico de Monterrey, 2012A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Physics)The University of British Columbia(Vancouver)December 2016c© Ricardo Chavez Gonzalez, 2016AbstractThe results of a search for Supersymmetry (SUSY) using the full 2012 ATLASdataset with an integrated luminosity of 20.3 fb−1 at√s = 8 TeV are interpretedand presented in the context of gauge mediated SUSY. No events with at least onelong-lived particle that decays at a significant distance from its production pointinto two muons were observed in data.No vertices passed the selection criteria which is consistent with the StandardModel background of 10−3 vertices. The strongest exclusion is observed between20 mm and 40 mm, with an upper limit of around 10 fb on the gluino pair produc-tion cross-section.iiPrefaceThe ATLAS experiment has more than 3000 members and several research pro-grams, which includes the displaced vertex group. Among other searches in thisgroup like R parity violating supersymmetry, I was involved in the gauge mediatedsupersymmetry model with a neutralino decay into a gravitino and a Z boson withmuons in the final state.I designed analysis scripts to understand several aspects of Monte Carlo samplessuch as vertex selection and reconstruction efficiencies using a cut based approach.The selection criteria used was based on previous versions, which were designedby former UBC Phd student Chang Wei Loh among others.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 The Standard Model and extensions . . . . . . . . . . . . . . . . 11.2 Supersymmetry and R-Parity . . . . . . . . . . . . . . . . . . . . 52 The Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . 82.1 The Large Hadron Colider . . . . . . . . . . . . . . . . . . . . . 82.2 The ATLAS Detector - A Toroidal LHC Apparatus . . . . . . . . 102.2.1 Inner Detector . . . . . . . . . . . . . . . . . . . . . . . 122.2.2 SCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.3 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . 152.2.4 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . 172.2.5 Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1 Data and simulated events . . . . . . . . . . . . . . . . . . . . . 213.2 Standard Model MC . . . . . . . . . . . . . . . . . . . . . . . . 24iv3.3 Event reconstruction and selection . . . . . . . . . . . . . . . . . 243.3.1 Trigger requirements . . . . . . . . . . . . . . . . . . . . 243.3.2 Offline muon object definition and selection . . . . . . . . 253.3.3 Offline filter requirements . . . . . . . . . . . . . . . . . 263.3.4 Retracking and displaced vertices . . . . . . . . . . . . . 263.3.5 Dilepton and vertex selection . . . . . . . . . . . . . . . . 273.3.6 Signal efficiency . . . . . . . . . . . . . . . . . . . . . . 293.3.7 Systematics . . . . . . . . . . . . . . . . . . . . . . . . . 313.3.8 Background estimation . . . . . . . . . . . . . . . . . . . 323.3.9 MC simulation studies of the background . . . . . . . . . 333.3.10 Validation of vertexing . . . . . . . . . . . . . . . . . . . 363.3.11 Validation on simulated events . . . . . . . . . . . . . . . 373.3.12 Validation on collision data . . . . . . . . . . . . . . . . . 423.3.13 Invariant mass validation . . . . . . . . . . . . . . . . . . 463.3.14 Choice of the rotation size step parameter . . . . . . . . . 483.3.15 Statistical uncertainty of random crossings . . . . . . . . 493.3.16 Systematic uncertainty on background normalization . . . 513.3.17 Dilepton estimate . . . . . . . . . . . . . . . . . . . . . . 523.3.18 Background to prompt physics processes . . . . . . . . . 533.3.19 Low mass displaced vertices . . . . . . . . . . . . . . . . 533.3.20 Rejection of cosmic muons . . . . . . . . . . . . . . . . . 533.3.21 Random crossing of tracks from different cosmic muons . 564 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61vList of TablesTable 1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . 2Table 1.2 Some mesons and baryons . . . . . . . . . . . . . . . . . . . . 4Table 1.3 SM particles and SUSY partners. Listed eigenstates before andmass states after electroweak symmetry breaking. Note thatwinos and charged higgsinos mix to form charginos while bi-nos, winos and higgsinos mix to form neutralinos. . . . . . . . 6Table 2.1 Inner detector components and figures of merit . . . . . . . . . 12Table 2.2 ATLAS calorimeter system and figures of merit . . . . . . . . 15Table 2.3 Muon spectrometer system and resolution . . . . . . . . . . . 18Table 3.1 MC samples for GGM, gluino mass is 1100 GeV. . . . . . . . 23Table 3.2 MC samples and background processes. . . . . . . . . . . . . 24Table 3.3 Offline filter used in the Muon stream selection. . . . . . . . . 27Table 3.4 Event level preselection. . . . . . . . . . . . . . . . . . . . . . 27Table 3.5 Vertex selection . . . . . . . . . . . . . . . . . . . . . . . . . 28Table 3.6 Sample cut flow with all the requirements. Nevt is the numberof accepter events, εrel is the efficiency with respect previouscut, and εabs is the total efficiency up to that state. Left handcolumns are unweighted and right hand are weighted to 20.3 fb−1 29Table 3.7 Systematic uncertainties for χ˜01 → ZG˜ decays in GGM modelfor samples with a target decay length of 200 mm. . . . . . . . 32Table 3.8 Vertexing efficiencies for coordinates . . . . . . . . . . . . . . 36viTable 3.9 Real crossing probabilities in MC vertices with two tracks. PVrefers to primary vertex and PU refers to pileup vertex. Uncer-tainties are statistical. . . . . . . . . . . . . . . . . . . . . . . 38Table 3.10 Displaced vertex candidates with loosened validation cuts ob-served and predicted in MC. The predicted number of verticesis obtained using the number of seed object pairs in the data Nlland the average crossing probability pxing via equation [3.2] . . 39Table 3.11 Displaced vertex candidates with loose validation cuts. The pre-dicted vertices are obtained using seed object pairs in data Nlland the average crossing probability pxing via Eq. [3.2]. Thefirst table shows two not identified as leptons track vertices forpT thresholds of 5, 10 and 15 GeV. In the second table, one lep-ton and one track not identified as lepton vertices. In the thirdtable, vertices from the second table matched to a trigger andDESD filter signature . . . . . . . . . . . . . . . . . . . . . . 43Table 3.12 Relative statistical errors from running toys and analytical for-mula for dilepton crossing probabilities. . . . . . . . . . . . . 50Table 3.13 Backround prediction for uncorrelated random crossings in sig-nal regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Table 3.14 Crossing probabilities for dicosmics and collision muons, errorsare statistical. . . . . . . . . . . . . . . . . . . . . . . . . . . 56Table 4.1 Observation and background expectation in data for the full2012 dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . 57viiList of FiguresFigure 2.1 CERN accelerator complex . . . . . . . . . . . . . . . . . . . 10Figure 2.2 The ATLAS detector . . . . . . . . . . . . . . . . . . . . . . 11Figure 2.3 The ATLAS Inner Detector . . . . . . . . . . . . . . . . . . . 13Figure 2.4 The ATLAS Inner Detector crossectional perspecive view . . 14Figure 2.5 The ATLAS Calorimeter system . . . . . . . . . . . . . . . . 16Figure 2.6 The ATLAS Muon spectrometer components . . . . . . . . . 18Figure 2.7 Cross sectional view particles and ATLAS subdetectors . . . . 20Figure 3.1 Diagram ([[7]], [[12]]) representing the GGM scenario, the Zdecays into pair of muons . . . . . . . . . . . . . . . . . . . 22Figure 3.2 Example of before and after application of the trigger and of-fline DESD filter selections. Transverse momentum of subleading reconstructed lepton associated with a displaced ver-tex. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 3.3 Vertex level efficiency curve for GGM model as a function ofthe LSP proper decay length cτ . The error combines statisticaland systematic errors. . . . . . . . . . . . . . . . . . . . . . 31Figure 3.4 no pT cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 3.5 track pT > 10 GeV . . . . . . . . . . . . . . . . . . . . . . . 34Figure 3.6 no pT cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 3.7 track pT > 10 GeV . . . . . . . . . . . . . . . . . . . . . . . 34viiiFigure 3.8 Invariant mass of displaced vertex candidates in tt¯ MC sample.First line: Left side shows the distribution of all vertex candi-dates with two ID tracks, right side shows the tracks formingthe vertex with pT > 10 GeV. Second line: Left side showsall vertex candidates with two reconstructed leptons, right sideshows leptons with pT > 10 GeV forming the vertex. . . . . . 34Figure 3.9 Position resolution of vertexing algorithm relative to ATLASshown in spacial coordinates for displaced vertex candidatesof mDV > 10 GeV with exactly two tracks, pT > 10 GeV andno leptons. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Figure 3.10 Some observables of displaced vertex candidate, two ID tracksnot identified as leptons in Z→ µµ sample. Yellow area repre-sents the prediction of uncorrelated background, the errors arestatistical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 3.11 Some observables of displaced vertex candidate, two ID tracksnot identified as leptons in tt¯ sample. Yellow area representsthe prediction of uncorrelated background, the errors are sta-tistical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Figure 3.12 Some observables of displaced vertex candidate, two ID tracksnot identified as leptons in tt¯ sample. Yellow area representsthe prediction of uncorrelated background, the errors are sta-tistical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Figure 3.13 Some observables of displaced vertex candidate, two ID tracksnot identified as leptons in tt¯ sample. Yellow area representsthe prediction of uncorrelated background, the errors are sta-tistical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Figure 3.14 Invariant mass of displaced vertex candidates consisting of twoID tracks not identified as leptons in the MC and 2012 data.Data is shown as black dots, while the yellow area depicts theprediction of the uncorrelated background. The error bars onthe prediction show the estimated statistical error. . . . . . . . 47Figure 3.15 Observed number of vertices and background as a function ofstep size. In red ∆phi = 10−3 the nominal value for the analysis. 49ixFigure 3.16 Observed number of vertices and background as a function ofstep size. In red ∆phi = 10−3 the nominal value for the analysis. 51Figure 3.17 Invariant mass and transverse opening angle for track pairs in2012 data. No trigger or DESD filter matching has been applied. 52Figure 3.18 The left plot shows the difference from the leading two muonsin an event being back to back, ∆Rcos in simulated cosmicevents. The blue histogram shows only events that contain areconstructed two track DV with mDV > 10 GeV with no lep-ton requirements. The right plot shows the reconstructed massof dimuon vertices with ∆Rcos < 0.04 . No dimuon vertices arefound with so this cut is effective to kill this background. . . . 54Figure 3.19 The left plot shows the η vs φ for the leading muon in theMuons stream DESDM RPVLL. The right plot shows ∆φ vs(η1 +η2)for the leading two muons. These plots indicate thatthe dominant background of muons in these events comes fromcosmic rays. . . . . . . . . . . . . . . . . . . . . . . . . . . 55Figure 3.20 Distribution of ∆Rcos for dimuon events observed in the cosmicmuon validation region on collision data. in red all dimuonpairs and the black dots indicate the subset forming a DV can-didate. The inclusive distribution is normalized to the DVmatched pairs to allow for shape comparison. . . . . . . . . . 55Figure 4.1 Distribution of dilepton-vertex candidates in terms of the ver-tex mass and number of candidates. The red ovals are propor-tional to the logarithm of the number of vertices in that specificbin. In grey it is possible to see the signal MC sample. . . . . 58Figure 4.2 Upper limit on the number of decays for GGM model as afuncion of cτ . 95% confidence level. . . . . . . . . . . . . . . 59Figure 4.3 Exclusion limit on the gluino production cross section for GGMmodel a function of decay length. 95% confidence level. . . . 59xChapter 1IntroductionThe Standard Model is the current understanding of matter and interactions at afundamental level. It works to a great precision but gravity is missing from themodel. There are several extensions to the Standard Model, such as supersymme-try, that could solve some of its significant theoretical shortcomings. Supersymme-try can be realized in many forms, for the specific search in this document, resultsare interpreted in the context of gauge mediated supersymmetry.1.1 The Standard Model and extensionsThe Standard Model (SM) is the current understanding of matter constituents andthree forces (electromagnetic, strong and weak) governing interactions betweenelementary particles, see Table [1.1]. The matter particles are fermions and havespin 12 . They are categorized in three generations, each of which has an electri-cally charged lepton with the corresponding same flavour neutrino and two typesof quarks. Each matter particle (fermion) is associated with an antimatter particle.To give an example, the positron is the correspondent particle for the electron witha positive charge and a similar pattern is followed by all fermions.The interaction between fermions are mediated by integer spin gauge bosons. Theelectromagnetic force by the photon, the strong force by gluons and the weak forceby W± and Z bosons. Only charged fermions will feel the effect of the correspond-ing force (hence all except neutrinos). The weak gauge bosons can interact with all1SM particles. Only the W± bosons can change one quark type into another. Theunification of electromagnetism and weak interactions is called electroweak theorydeveloped by Glashow, Salam and Weinberg based on a SU(x)×U(1) symmetry.The Standard Model of Particle PhysicsfermionsParticle symbol EM charge Weak charge Strong charge Mass(isospin) (colour) [Mev]electron e −1 −1/2 0 0.511electron neutrino νe 0 +1/2 0 ≤ 50×10−6muon µ −1 −1/2 0 105.6muon neutrino νµ 0 +1/2 0 ≤ 0.5tau τ −1 −1/2 0 1776.8tau neutrino ντ 0 +1/2 0 ≤ 70up u +2/3 −1/2 rgb ∼ 2.3down d -1/3 +1/2 rgb ∼ 4.8charm c +2/3 −1/2 rgb ∼ 1275strange s -1/3 +1/2 rgb ∼ 95top t +2/3 −1/2 rgb ∼ 173.5×103bottom b -1/3 +1/2 rgb ∼ 4180bosonsphoton γ 0 no no 0Z Z 0 yes no 91.187×103W W± ±1 yes no 80.39×103gluon g 0 no yes 0Higgs H0 0 yes no 125.09Table 1.1: The Standard ModelThe four gauge bosons (W±, Z0, γ) are the consequence of mixing the elec-troweak gauge fields (W1,2,3, B) after the electroweak symmetry breaking [[27]].2The equations for the fields are shown below.W±µ =1√2(W 1µ ∓ iW 2µ ) (1.1)Z0µ =−Bµ sinθW +W 3µ cosθW (1.2)Aµ = Bµ cosθW +W 3µ sinθW (1.3)In the relations between fields, θW is the Weinberg angle and Aµ is the pho-ton field. The weak interaction distinguishes between the left and right handedfermions:ψL = PLψ =12(1− γ5)ψ,ψR = PRψ = 12(1+ γ5)ψ, (1.4)where ψ is the fermion field, PL and PR are the projection operators and γ5 is relatedto the Dirac γ matrices. The W± bosons only interact with left handed fermionsbut the Z boson interacts with both handed fermions.The strong force is explained by Quantum Chromodynamics in which processesconsider particles with colour: red, green or blue (and antired, antigreen, antiblue).Gluons carry one colour and one anticolour charge so they can interact amongstthemselves via the strong force. Leptons do not carry colour charge.Quarks do not appear alone in nature and they quickly hadronize form cones be-cause of the boost. This isnt a general statement. The bare quarks are hadronizedinto: mesons (quark antiquark bound state) or baryons (three quark bound state),examples in Table [1.2].3Baryon Symbol Quark contentProton p uudNeutron n uddLambda Λ0 udsMeson Symbol Quark contentPion pi+ ud¯Kaon K+ us¯D D0 cu¯Table 1.2: Some mesons and baryonsThe remaining part of the SM is the Higgs boson. Through the Higgs mecha-nism, its field can generate masses to the weak bosons and fermions, and withoutthey are predicted to be zero. since in the explicit mass term m(ψ˜LψR)+ ψ˜RψL,the fermion mass m is forbidden because the left handed fermion ψL and the righthanded fermion ψR carry different quantum charges. The coupling of the Higgsfield φ to fermions via y(ψ˜LψR)+ψ˜RψL can produce a mass when the field acquiresa non zero vacuum expectation value v after the electroweak symmetry breaking.Then, the interaction term generates a mass term of the form yv(ψ˜LψR)+ ψ˜RψL inwhich the mass is proportional to the coupling. In a similar way, the Higgs cou-pling to the bosons Bµ via g2φ 2BµBµ generates a mass term the form g2v2BµBµafter electroweak symmetry breaking. Now the Higgs has been discovered, andand observed in several of its possible decays, such as ZZ, W+W− and τ+τ−. Stillthere is a fine tuning problem because the observed physical mass of a light HiggsmH,physical , a precise cancellation is needed between two uncorrelated terms: thebare mass of the Higgs mH,bare, which is a fundamental parameter in the theory,and the quantum loop corrections from other SM particles, which is proportionalto Λ2, where this parameter is the cut-off scale (the Planck scale 1019 GeV) if theSM is valid up to that scale.m2H,physical = m2H,bare+ ∑SM particlesδm2H (1.5)where the ∑SM particles δm2H is the sum of all SM particles’ loop corrections. The4loop correction can involve, for example the top quark as shown below. The loopcontains the following integral which contributes to the square of the Higgs mass.δm2H =−2y2t∫ λ d4k(2pi)4k2+m2(k2−m2t )2=− y2t8pi2Λ2+ ... (1.6)where mt is the top mass, yt is the Higgs top-top vertex coupling and k is themomentum in the loop. Since k can take very high values up toΛ, mt can be ignoredand the integration is expected to contain a negative-signed quadratically divergentterm with a dependence onΛ2. The cancellation of 32 orders of magnitude betweenthe square of the bare mass and the loop correction term (like the one to achieve a1TeV physical mass of the Higgs boson) motivates supersymmetry to be a viableextension of the SM, solving the fine-tuning problem.1.2 Supersymmetry and R-ParitySupersymmetry or SUSY is a boson-fermion symmetry [31] in which each SMparticle associated in correspondence with another supersymmetric particle. Inthis way, a SM fermion has a superpartner and a SM boson has a fermion super-partner, conserving all quantum numbers except spin, which is different by 12 . Inthe following Table [1.3] the minimal supersymmetric Standard Model (or MSSM)is presented.5minimal supersymmetric Standard ModelStandard Model particles and fields supersymmetric partnersInteraction eigenstates Energy eigenstatesSymbol Name Spin Symbol Name Symbol Name Spinq Quark 12 q˜ q˜ Squark 0l Lepton 12 l˜ Slepton l˜ Slepton 0ν Neutrino 12 ν˜ Sneutrino ν˜ Sneutrino 0g Gluon 1 g˜ Gluino g˜ Gluino 12W± W boson 1 W˜± Wino χ˜±1,2 Chargino12H− Higgs boson 0 H˜−1 Higgsino χ˜±1,2 Chargino12H+ Higgs boson 0 H˜+2 Higgsino χ˜±1,2 Chargino12B B boson 1 B˜ Bino χ˜01,2,3,4 Neutralino12W 3 W 3 boson 1 W˜ 3 Wino χ˜01,2,3,4 Neutralino12H01 Higgs boson 0H02 Higgs boson 0 H˜01 Higgsino χ˜01,2,3,4 Neutralino12H03 Higgs boson 0 H˜02 Higgsino χ˜01,2,3,4 Neutralino12Table 1.3: SM particles and SUSY partners. Listed eigenstates before andmass states after electroweak symmetry breaking. Note that winos andcharged higgsinos mix to form charginos while binos, winos and higgsi-nos mix to form neutralinos.SM particles and superpartners are listed as interaction eigenstates and afterelectroweak symmetry breaking the mass eigenstates. Notice that in this model 5physical Higgs bosons are present. The charged Higgsinos and the winos mix toform four charginos (χ˜±1,2)and the neutral Higgsinos and bino mix to form neutrali-nos (χ˜01,2,3,4). The convention to name lepton superpartners is to use a -s prefix andand for bosons an -ino suffix, all with tildes. With SUSY the Higgs boson baremass and the superpartrners receive a contribution from SM particle loop correc-tion. For example, in the case of the top loop, its superparrner the stop gives aHiggs mass loop correction containing a quadratic divergence term given by:δm2H =+yt˜16pi2Λ2+ ... (1.7)6in which yt˜ is the coupling of the stop to the Higgs boson. This divergence canbe cancelled by two scalar stops if y2t = yt˜ . In a similar way, fermion loops givenegative quadratic divergences while bosons give positive ones, and since each SMparticles has a SUSY partner, all correction loops should be cancelled which solvesthe SM Higgs fine tuning problem. This a a strong motivation for SUSY searches.In this context, each particle is associated with a multiplicative quantum numbercalled R-parity:Rp = (−1)3(B−L)+2s (1.8)in which s is the spin, B is the baryon number and L is the lepton number. Thebaryon number is a 13 for quarks, −13 for antiquarks and 0 for the rest of the parti-cles. L is 1 for leptons, −1 for antileptons and 0 for all other particles. Pluggingthe corresponding numbers to the formula gives Rp = +1 for SM particles andRp =−1 for superpartners. Thus, if Rp is conseved, SUSY particles are producedin pairs, and they decay to produce two stable lightest SUSY particles (LSP), fur-ther decays to SUSY particles are kinematically forbidden and to SM particles arealso forbidden due to conservation of R−parity. The stable LSP neutralino χ˜01 is acandidate for dark matter because its neutral and weakly interacting.When R−parity is violated (RPV) ([24], [15], [25], [26]), neutralino decaysinto two charged leptons via λ121 or λ122 RPV coupling.For the specific search described in this document, a general gauge mediatedsupersymmetry [23] was considered in which R-parity is conserved. In this type ofmodel the LSP, instead of being the neutralino, is the gravitino G˜ (very light mass. GeV [[32], [20], [34]]), which is the superpartner of the graviton G˜. SUSY candecay, in principle to LSP but the coupling is so weak that decays to the next-to-lightest SUSY particle (NLSP) are more likely to occur. The NLSP will decay tothe SM partner and the gravitino LSP with the lifetime that varies as the square ofthe gravitino mass. In the parameter space considered it is possible for the NLSP todecay promptly at the LHC (cτ . 0.1) mm or give rise to displaced decays insidethe detector region.7Chapter 2The Experimental Setup2.1 The Large Hadron ColiderThe large hadron collider is a 27 km machine, located in the border between Franceand Switzerland, that accelerates protons and ions at high energies. Protons areaccelerated to 7 TeV, so the CM (center of mass) energy of a collision is√s = 14TeV. The data and simulations used for this analysis were produced with a centerof mass energy√s = 8 TeV. This data set is known as Run 1.Another outstanding feature of this machine is the high instantaneous luminosityL , a measure of the number of collisions per unit area per unit time, designed toreach 1034 cm−2 s−1. The rate of this collisions or events observed are given by,R = εσL (2.1)where σ is the cross section and ε is the detection efficiency. The total number ofevents is given byN = εσL (2.2)where L =∫L dt is the integrated luminosity. σ is the cross section, a quantitythan can be measured and expresses the likelihood of interaction between parti-cles, the luminosity is determined by the accelerator and the efficiency ε by thedetector.The CERN Accelerator Complex in Figure [2.1] is a series of accelerators in chain8to accelerate protons and ions to the mentioned energies. The beam starts by in-troducing hydrogen gas into a Duoplasmatron device. The gas in vacuum is bom-barded with electrons and as a result the gas ionizes. This plasma is acceleratedinside that cavity forming a beam which then is accelerated using the Linac-2 upto an energy of 50 MeV. After this stage, the beam is introduced to the Proton Syn-chrotron Booster (PSB), which is a circular accelerator with four superimposedsynchrotron rings where bunches of 1.8× 1012 protons are formed. The energyreached is 1.4 GeV. The next in the chain is the Proton Synchrotron (PS) accelerat-ing the beam up to 26 GeV which delivers to the Super Proton Synchrotron (SPS)with a final energy of 450 GeV.The accelerator is filled with 2808 bunches of protons, each containing approx-imately 1011 protons, which collide every 25 ns. Along the ring there are fourinteraction points in which general purpose detectors are located, ALICE, ATLAS,CMS and LHC-b.9fFigure 2.1: CERN accelerator complex2.2 The ATLAS Detector - A Toroidal LHC ApparatusThe ATLAS detector [21], Figure [2.2], is a cylindrical device of 7000 tonnes, 25mhigh and 44m long, located 100 m underground at the Point 1 interaction region ofthe LHC Ref. [22]. It consists of several special purpose subdetectors optimizedfor a specific task.10Figure 2.2: The ATLAS detectorCoordinate system• The nominal interaction point is the origin.• The z-axis runs parallel to the beam, positive towards the center of the LHC.The positive y-axis point upwards towards the surface. With this two axiswe can define a right handed cartesian coordinate system.• Given the cylindrical structure of the detector is natural to use polar coor-dinates defined in the following way. The azimuthal angle φ ∈ [−pi,pi] ismeasured around the z-axis and the polar angle θ ∈ [0,pi] is measured fromthe z-axis.• The polar angle runs on the x-z plane with θ = 0 on the positive z-axis. Thisis replaced for the quantity pseudorapidity η , (when calculating the differ-ence in η between two particles η1−η2, this quantity is Lorentz invariant11because it transforms under boosts):η =− ln(tanθ2)(2.3)• The distance between two particles ∆R is invariant under boosts along thebeam axis, defined as:∆R =√(∆φ)2+(∆η)2 (2.4)2.2.1 Inner DetectorThe Inner Detector (ID) (schematic in Figure [2.3]) is a subdetector that providedcharged particle identification and measurements of the vertices at which hard in-teractions occurred. It has a magnetic field parallel to the beam pipe of 2 T due tothe solenoid superconducting magnet and the range extends up to |η | = 2.5. Thissub detector consists of 3 instruments: the Pixel Detector, Semiconductor Tracker(SCT )and Transition Radiation Tracker (TRT), whose characteristics are summa-rized in Table [2.1]. A cross sectional view in Figure [2.4].Subdetector section Radius Element Spatial Hits Readout[cm] size resolution [µm] channelsPIXEL 5−12 50µm×400µm 3 80×106Barrel 10(R−φ)×115(z)End-cap 10(R−φ)×115(R)SCT 80µm 8 6×106Barrel 25−55 17(R−φ)×580(z)End-cap 25−61 17(R−φ)×580(R)TRT 4mm 30−36 3.5×105Barrel 55−108 130End-cap 61−110 130Table 2.1: Inner detector components and figures of merit12Figure 2.3: The ATLAS Inner DetectorPixelBefore summer 2015 the Pixel Detector (included in schematic in Figure [2.4]) wasthe closest to the interaction point. Currently, the Insertable B-Layer (IBL) is theone closest to the beam pipe and is an additional point for tracking particles.The Pixel detector consists of 288 modules each with 46080 elements. Becauseof this feature, a high granularity provides high precision measurements of tracksas close to the interaction point as possible. At a radius of 5 cm, the innermostlayer of this detector performs the highest precision reconstruction of secondaryvertices of decays. The highest precision in the position measurement are 10µm inthe R−φ plane and 115µm in z.2.2.2 SCTThe SCT (included in schematic in Figure [2.4]) is the second subdetector of theID. It provides eight strip measurements which corresponds to 4 spacial points forparticles originating in the beam interaction region. Silicon microstrip technology13is used for tracking charged particles: sensors are segmented in strips and they cangive position measurements. The barrel region consists of 4 cylindrical layers at aradii of 30, 37, 44 and 51 cm of silicon arranged in a way that one set is parallelto the beam beam pipe and another one tilted by 40 mrad to measure radial andlongitudinal positions of hits. Momentum can be obtained due to the curvature ofcharged particles in the magnetic field.Figure 2.4: The ATLAS Inner Detector crossectional perspecive viewTransition Radiation TrackerThe TRT (included in schematic Figure [2.4]) is the outermost device of the ID. Itis made from straw tubes of 4mm diameter with a gas mixture of xenon at 70%,carbon dioxide at 27% and Oxygen at 3%. Charged particles traversing the gas ion-ize it, and due to the large electric field (the potential difference between the outer14part of the straw and the wire in the center is about 1.5 kV), the electrons drift tothe wire and are detected. This sub detector is designed to operate in the regimeof particles with pT > 0.5 GeV and |η | < 2.0. When a particle enters the tube,the gas inside is ionized and this signal is detected by the wires, providing R− φinformation with an accuracy of 130µm per straw. When ultra-relativistic particleschange media X-ray photos are emitted, and xenon gas is used as an absorber ofthe produced ionization. The discrimination process is possible because the energydeposition of the ionization is much smaller (∼ 200eV) in comparison to the tran-sition radiation (∼ keV). This ionization only occurs for particles with a Lorentzgamma of more than about 1,000. This allows the discrimination of electrons frompions, for example, at the same momentum.2.2.3 CalorimetersThis sub detectors (schematic visible in Figure [2.5] and figures of merit in Table[2.2]) can provide position and energy measurements of particles due to absorptionwith the exception of weakly interacting particles such as muons, measurements inthis case are provided by combining information from the inner detector and themuon spectrometer.Calorimeter Energy resolution (σE/E) η coverageElectromagnetic 10%/√E⊕0.7% ±3.2HadronicBarrel & End-Cap 50%/√E⊕0.3% ±3.2Forward 100%/√E⊕3.1% ±4.9Table 2.2: ATLAS calorimeter system and figures of merit15Figure 2.5: The ATLAS Calorimeter systemElectromagnetic CalorimeterThis sub detector (included in schematic Figure [2.5]) is mainly used to measurethe energy of electrons and photons. It has an accordion shape with layers oflead and stainless steel using liquid argon in between, cooled to a temperatureof −185◦ C with a copper grid which acts as an electrode. When a high energyelectron passes through the absorbers it produces a shower of electron, positronsand photons before it stops, the shower of low energy electrons ionizes the liquidargon creating more electrons and positive ions, the negative charge is attracted tothe electrodes and energy measurements are performed.Hadronic CalorimeterThe hadronic calorimeter (included in schematic Figure [2.5]) is located after theEM cal with respect to the beam pipe and measures the energy of particles due tonuclear interactions (hadronic showers) with the material. The calorimeter detects16hadrons not absorbed by the EM cal like neutrons, pions, protons, etc. A differ-ence with respect to the electromagnetic calorimeter is that in this case the energydeposited by the hadronic showers depends linearly with respect the interactionlength λ of the material.Tile CalorimeterFor |η |< 1.0 and 0.8< |η |< 1.7 central and extended barrels (included in schematicFigure [2.5]), consisting of 64 modular wedges of 3mm trick of plastic scintillatoras active medium surrounded by a 5 mm absorber made of steel. The signals aretransmitted from the scintillating tiles to the PMTs via wavelength-shifting fibers.This calorimeter has 4672 read-out channels and a test beam energy resolution forisolated pions of 56% GeV1/2/√E⊕5.5% at η = 0.35.2.2.4 Muon SpectrometerThe Muon Spectrometer (MS, components and resolution in Table [2.3] and schematicFigure [2.6]) is the outermost sub-detector of ATLAS and provides high precisiontracking and triggering. Charged particles bend due to the magnetic field, so mo-mentum and charge can be identified. This detector is composed of MonitoredDrift Tubes (MDTs) and Cathode Strip Chambers (CSC). Wires in the drift tubesfilled with gas, which is ionized by muons and detected by the wire inside eachone. The distance of the passing particle to the central wire in the tube is mea-sured with timing of cluster arrival, electrons from the cascade move towards theanode due to the voltage applied. For large values of |η | CSC technology is usedfor tracking, multi-proportional chambers filled with a gas mixture of Ar(80%) andCO2(20%), charged particles traveling would ionize creating an avalanche of elec-trons. Resistive Plate Chambers (RPCs) are used in the barrel section while ThinGap Chambers (TGC) in the end-cap regions. The triggering in the muon systemcovers |η | < 2.4, chambers provide bunch crossing identification and coordinatemeasurements in the direction orthogonal to the one determined by the MDT andCSC. The efficiency of this system is heavily constrained by the position mappingof the MDT chambers and also the magnetic field.17Detector component Chamber resolution Chamber resolutionz/R φMDT 35 µm in z N/ACSC 60 µm in R 5 mmRPC 10 mm in z 10 mmTGC 2-6 mm in z 3-7 mmTable 2.3: Muon spectrometer system and resolutionFigure 2.6: The ATLAS Muon spectrometer components2.2.5 TriggersBecause it is impossible to record every single ATLAS event, triggers are used toonly record those events that may be potentially interesting to the physics program.With a collision rate of 20 MHz, and 1 MB of disc per event few of those events are18for offline physics analysis. Different triggers are used to make decisions to studyfurther objects with high PT .Level-1 TriggerThis trigger has a decision time of 2.5 µs and uses the calorimeters and the muonspectrometer to identify events with possible high PT jets, τ leptons, missing en-ergy, photos, electrons and muons. In the case of muons, hits are used to computethe deviation between each region of interest (place of the hit) with infinite momen-tum trajectory. A Look-Up table is then used to obtain the transverse momentumand events are passed at a reate of 75 kHz to the Level-2 trigger.Level-2 TriggerThis trigger has a decision time of 40 ms and the input from Level-1 is processedwith detail and full granularity. In the case of muons, this trigger, for example,can be used to reject fake muons. Several algorithms are used, muFast reconstructcandidates in the Muon Spectrometer while muComb links the inner detector in-formation with the muon spectrometer. Events are passed then at a rate of 3.5 kHz.Event FilterIn this stage reconstruction algorithms are used to find particles, it takes less thanfour seconds and the output rate is 200-400 Hz. The EF can examine an eventbased on the entire input, if it passes will be recorded for offline analysis.In Figure [2.7] it is possible to see a cross sectional view from most of the systemsdescribed before and several particles traveling through the detector.19Figure 2.7: Cross sectional view particles and ATLAS subdetectors20Chapter 3AnalysisThis search looks for pair of muons originating from a displaced vertex ([12] ,[7]).The vertex requirements are designed to eliminate SM background. Previous AT-LAS searches examined final states with one high pT muon [2], and a highlycollimated pair of muons [9]. Similar searches have been done by CMS, mas-sive particles decaying into dilepton pairs [4] and highly displaced leptons thatnot necessarily come from the same vertex [3]. The results are interpreted in asupersymmetry (SUSY) model with general gauge-mediated symmetry breaking(GGM), where the next-to-lightest SUSY particle (NLSP) decays into a Z bosonand a gravitino. This search is complementary to the one presented in [16] andsimilar to multi-leptonic searches [11] and [36]. A technique named re-trackingwhere modified track reconstruction improves the efficiency for high-impact pa-rameter tracks is used in this analysis and also in [14], which is a complementaryhigh mass displaced vertex search.3.1 Data and simulated eventsThe data used in this analysis, identical the one in [16], was collected in 2012 witha center of mass energy of√s = 8 TeV of pp collisions with an integrated lumi-nosity of 20.3 fb−1. The uncertainty on the integrated luminosity is±2.8% derivedwith the methodology in [6]. With respect to the center of the detector, the meanpp collisions occurred at 〈x〉=−0.3 mm, 〈y〉= 0.7 mm, 〈z〉=−7.7 mm.21Monte Carlo events are generated to study reconstruction and trigger efficiency, ineach event two gluinos or two squarks are created in a pp collision, and after theydecay in chain. In this analysis the LSP is the lightest neutralino χ˜01 .Figure 3.1: Diagram ([[7]], [[12]]) representing the GGM scenario, the Z de-cays into pair of muonsAll the samples are generated with AUET2B ATLAS underlying-event tune [1]and the CTEQ6L1 parton distribution function (PDF) set [33]. Events are gener-ated consistent with the position of the pp luminous region and weighted to cor-rect the z distribution of collisions. Next, a GEANT4 [13] based ATLAS detectorsimulation [5] processes each event, treated in the same way as real collision inthe detector. The samples include a realistic modeling of the effects proton colli-sions per bunch crossing, obtained by overlaying additional simulated pp eventsgenerated using PYTHIA 8 [35], in addition to hard scattering, and reweighting22events such that the simulation and data distributions match. PYTHIA 6.426.2was used to produce GGM samples (Feynman diagram provided in Figure [3.1])g˜→ qq[χ˜01 → G˜Z], note that the NLSP is a higgsino-like neutralino χ˜01 , Z→ µ+µ−decays are considered for this analysis but for simulation Z decays into leptons andhadrons. Within the allowed parameter space, the NLSP can decay promptly atthe LHC (cτ . 0.1mm), appear stable (cτ & 10m) or give rise to displaced decayswithin the detector. In the model we are considering, the NLSP is a higgsino-likeneutralino, with a lifetime that is set by varying the gravitino mass, as this changeshave negligible effect on χ˜01 decay kinematics. Using tanβ = 2 and µ > 0 givesbranching fraction (χ˜01 → ZG˜) of 90 %. In addition the samples are filtered to im-prove statistical precision by requiring Z→ ll vertices within the fiducial volume ofr < 300 mm and z < 1000 mm. The masses and lifetimes of the generated modelsare listed in the following Table [3.1].cτ m(χ01 ) [GeV] Filter efficiency11.6 400 100 %230.2 400 65.6 %9.2 1000 100 %183.3 1000 93.0 %Table 3.1: MC samples for GGM, gluino mass is 1100 GeV.The RMS spread of the z distribution of the collisions is σz = 47.7 mm andin the other directions σ < 0.1 mm. Signal cross sections are calculated at next toleading order in the strong coupling constant, adding the resummation of soft gluonemission at the next-to-leading logarithmic accuracy ([[17]], [30]], [[29]], [[18]],[[19]]). The nominal cross section is calculated from an envelope of cross sectionpredictions several PDF sets, factorization and renormalization scales [28]. QCDdijet events, Drell-Yan and cosmic-ray muons were taken into account to estimatethe systematic uncertainties and backgrounds.233.2 Standard Model MCFor this analysis the SM background is estimated from data because the track mod-elling at low radii and random crossings from pileup at large radii may not be accu-rate, however its possible to understand the sources of background and to test theestimation methods [7]. In Table [3.2] are listed the samples used. In particular,the tt¯ sample helps for testing as it contains high momentum isolated leptons fromW boson decays, displaced tracks in b-jets and tracks from pile-up vertices. Thesamples are used to test and validate estimation techniques for random crossingpile-up tracks and to understand the relative contributions from various two-trackvertices source.Name Generator σ [pb] (NLO) Filter efficiency Effective L [fb−1]tt¯ MC NLO 253 0.543 7.0Z→ µµ+ jets POWHEG + Pythia 8 1110 1.0 3.6Z→ ττ+ jets Pythia 8 1150 1.0 6.5Table 3.2: MC samples and background processes.3.3 Event reconstruction and selectionThe event reconstruction is based on MC and experience with similar previousanalyses ([8] and [10]). Selected events are required to have at least one muoncandidate and the further offline selection criteria are used to filter events. Eventsthat pass such requirements undergo a process called retracking which reconstructstracks with large impact parameter d0 with respect to the transverse position of anyprimary vertex from pp collisions. At the final stage events are required to have aprimary vertex (PV) formed from at least five tracks and located at |z|< 200 mm,consistent with the interaction point (IP).3.3.1 Trigger requirementsEvents must satisfy trigger requirements, each muon candidate need to be identi-fied by algorithms in the MS with a transverse momentum of pT > 50 GeV. Itspseudorapidity must be in the muon spectrometer MS-barrel region |η | < 1.07 to24reduce the trigger rate from fake muons due to beam background in the endcapregion. The effect of this selection can be seen in Figure [3.2].Figure 3.2: Example of before and after application of the trigger and offlineDESD filter selections. Transverse momentum of sub leading recon-structed lepton associated with a displaced vertex.3.3.2 Offline muon object definition and selectionMuon candidates are required to be reconstructed in the MS and also in the ID. TheID track associated with a muon candidate must at least have four SCT hits, but thenumber is reduced if the track crosses nonoperational sensors. The track mustalso satisfy |η |-dependent requirement on the number of TRT hits. In this caseno pixel hit requirement is applied to the muon-candidate track which is differentfrom standard ATLAS muon reconstruction algorithm.253.3.3 Offline filter requirementsThis events are selected for retracking and offline analysis requiere the presence ofa muon with pT > 50 GeV with an impact parameter |d0|> 1.5 mm.3.3.4 Retracking and displaced verticesIn the standard ATLAS tracking [22] several algorithms are used to reconstructcharged particle tracks. in the silicon seeded approach, combinations of hits inthe pixel and SCT detectors are used to form initial track candidates (seeds) thatare then extended intro the TRT. Another algorithm starts at the TRT and thenextrapolates back to SCT. This methods place constraints on the transverse andlongitudinal impact parameters of track candidates (many have large |d0| mm) andas a results low efficiency of tracking for particles that come from a very displacedposition with respect to the beam axis, a displaced vertex (DV). To increase theefficiency of tracking the retracking method is used. A silicon seeded trackingalgorithm is rerun offline using only hits that are not associated with existing tracks,for the events that satisfy the trigger and filter requirements. This procedure isperformed with looser cuts |d0| < 300 mm and |z0| < 1500 mm, and requieres atrack to have at least five detector hits that are not shared with other tracks (in thestandard procedure six at least hits are required). Finally, to reduce the false seedtracks, it is required pT > 1 GeV (in the standard tracking it is required pT > 400MeV). The main steps for displaced vertex reconstruction are listed, using standardtracks and from re-tracking.• Construction of two track seed vertices using high d0 tracks.• Construction of N-track vertices from seeds.• Analysis-level selection cuts on the final vertices.The analysis selects primarily two-track vertices, from which the seed tracks arerequired to have |d0|> 2 mm and no silicon tracks with a radius less than a vertexposition to suppress background effectively, also at least two SCT hits are required.263.3.5 Dilepton and vertex selectionSeveral event level quality criteria, listed in Table [3.4], are required for all signalevents containing a displaced lepton pair [7]. In addition, events are discardedwhen two reconstructed muons are back to back in the η−φ space to reject cosmicmuons which would dominate this channel. The cosmic veto is designed using thefollowing variable ∆Rcos =√(η1+η2)2)+(|∆φ |−pi)2 which is zero when thetwo objects are back to back (η2 = −η1 and φ2 = φ1±pi). Also events in whichleptons are reconstructed on the same side of the detector are rejected, they arerequired to be separated by ∆R > 0.04Filter Object pT cut |η | cut |d0| cutµ Muon 50 GeV 1.07 1.5 mmTable 3.3: Offline filter used in the Muon stream selection.LAr noise bursts vetoTile errors (incl. trips) vetoIncomplete events (TTC restart) vetoGRL TO ADDCosmic veto ∆Rcos > 0.04 and ∆R > 0.04Primary vertices > 1 PV candidatePV position |z|< 200mmNPVtrack > 5 tracksTable 3.4: Event level preselection.Muon candidates are required to to have a transverse momentum pT > 10 GeV,pseudorapidity |η | < 2.5 and transverse impact parameter d0 > 2.5mm. They arediscarded if its ID track is in a region where background estimation is not reli-able, such as |η | < 0.02. To avoid double counting, in a given DV, muons mustnot share same ID track, if they do, the one with lowest pT is discarded. Finally,a DV is formed by at least two opposite charge candidates identified as muons.After this, it is verified that the dilepton DV passes the trigger and offline selec-27tion requirement described before. Next, each DV’s reduced χ2 is required to besmaller than 5, the position must be within the feducial region of rDV < 300mm and|zDV | < 300mm (radial and longitudinal with respect to the origin). To minimizebackground originated from PV tracks ∆xy =√(xDV − xPV )2+(yDV − yPV )2 has tobe at least 4 mm (x and y are transverse coordinated of a vertex). Vertices locatedin dense detector regions are vetoed, the number of tracks in the vertex has to beNtr ≥ 2 and the mass of a DV has to be mDV ≥ 10 GeV (to supress SM backgroundresonances that produce displaced vertex pairs, beyond non-prompt resonences).The summarized selection can be seen in Table [3.5]. No explicit request or vetois made for the presence of further tracks or leptons in the vertex. Because of nu-merical instability in the background estimate for tracks with low pseudorapidityη , tracks with |η | < 0.02 are rejected. Muons are reconstructed with the MuIDalgorithm and they are required to be combined muons with a pIDT > 10 GeV and|η |< 2.5. There is also an overlap removal in the cases in which pairs of particlesshare the same track, the one with lowest pT is removed. If muons form a displacedvertex they must pass the filter listed in Table [3.3] and it must also pass the criteriafor the EF mu50 MSonly barrel trigger.Fiducial acceptance |rDV |< 300 mm, |zDV |< 300 mmDistance to any PV ∆xy > 4 mmVertex quality χ2/n.d. f .≤ 5Material veto Based on 3D mapCentral track veto η ID > 0.02 for all vertex tracksDilepton Two leptons associated with vertexLepton pT pIDT > 10 GeV fir both leptonsTrigge matching Leptons in the vertex matched to the triggerDESD filter matching Leptons in the vertex pass DESD filter criteriaDilepton charge ql1 ·ql2 < 0Invariant mass mDV > 10 GeVTable 3.5: Vertex selection283.3.6 Signal efficiencyTo test the efficiency of the vertex selection described above, Monte Carlos simu-lations are used.Unweighted Unweighted Unweighted Weighted Weighted WeightedCut Nevt εrel[%] εabs[%] Nevt εrel[%] εabs[%]No cuts 5000 100.00 100.00 28.42 100.00 100.00Trigger 42848 85.70 85.70 24.37 85.74 85.74Cosmic veto 41130 95.99 82.26 23.38 95.97 82.29Primary vertex (PV) 41130 100.00 82.26 23.39 100.00 82.32PV |z| 41042 99.79 82.08 22.54 96.36 79.32PV Ntracks 40913 99.69 81.83 22.46 99.64 79.04Reco DV 9054 22.13 18.11 2.58 11.47 9.06Fiducial acceptance 8906 98.37 17.81 2.53 98.35 8.91DV displacement 8679 97.45 17.36 2.46 97.26 8.67χ2 8679 100.00 17.36 2.46 100.00 8.67Material veto 6413 73.89 12.83 1.81 73.52 6.37Central track veto 6220 96.99 12.44 1.75 96.72 6.171 lepton matched 6201 99.69 12.40 1.75 99.74 6.152 leptons matched 5647 91.07 11.29 1.58 90.69 5.58Lepton kinematics 5450 96.51 10.90 1.53 96.33 5.37Lepton ID 5350 98.17 10.70 1.48 97.12 5.22Overlap removal 5350 100.00 10.70 1.48 100.00 5.22Trigger matching 4109 76.80 8.22 1.09 73.75 3.85DESD offline cuts 4099 99.76 8.20 1.09 99.74 3.84DV mass 4098 99.98 8.20 1.09 100.00 3.82Opposite charge 4091 99.83 8.18 1.09 99.88 3.83Table 3.6: Sample cut flow with all the requirements. Nevt is the number of accepter events,εrel is the efficiency with respect previous cut, and εabs is the total efficiency up to thatstate. Left hand columns are unweighted and right hand are weighted to 20.3 fb−1.For the event-level cutflow in Table [3.6], m(g˜)= 1100 GeV, m(χ˜01 )= 1000GeV29and cτ(χ˜01 ) = 200 mm. The relative efficiency εrel is with respect the precious cutand εabs is up to that cut. The weighted events are normalized to a luminosity of20.3 fb−1. This sample in particular is filtered at generator level such that bothχ01 decays occur at rDV < 300 mm and zDV < 1000 mm. The reconstructed (reco)displaces vertices are required to be matched to a true LSP decay. Its clear fromthe table that the biggest efficiency loss occurs when matching a reco displacedvertices.Extrapolated signal efficiency curvesTo obtain the final signal prediction for arbitrary lifetimes of the χ01 a reweightingprocedure is used as follows. With two GGM samples, this technique allows a widecoverage for the lifetime (about six orders of magnitude), ranges between 0.1 mmup to 1 km of decay length. The value of the decay length cτ depends on the boostand mass of the neutralino χ01 , and also the mass of the gluino. If the neutralinomass if light compared to the mass of the gluino, the decaying χ01 is highly boosted,and for situations with a more massive χ01 , the efficiency peaks at higher values ofproper decay length.In Figure [3.3], the efficiency includes the 10 % Z boson decay to leptons, whichcauses a low efficiency. The uncertainty increase (band width) is due the widespace of interpolation of the two fixed lifetimes.30Figure 3.3: Vertex level efficiency curve for GGM model as a function ofthe LSP proper decay length cτ . The error combines statistical andsystematic errors..3.3.7 SystematicsSystematic uncertainties for this analysis arise from several sources:• MC Statistics: The uncertainty is on the order of 4 -10 % for cτ > 1 cm andincreases for lower lifetimes because of the reweighting procedure, whichgives large weights when interpolating to lower χ01 lifetimes.• Pileup: The uncertainty on pileup weights applied to simulated events areevaluated based on PAT recommendation of varying the data scale factor.This is in the order of 2 - 5 % except when the lifetime reweighting procedureassigns a large weight to single events, going up to 20 %.• Trigger: The trigger efficiencies simulated are corrected by scale factors.31The uncertainty on these factors is propagated to the efficiency results foreach trigger used, less than 5 % for the final state.• Muon Efficiency: The lepton efficiency scale factors applied are varied bytheir uncertainties. For the muon reconstruction efficiency reaches up to 4 %per muon.In Table [3.7], numerical values of systematic contributions.m(g˜)[GeV] /m(χ˜01 )[GeV]Systematic 1100/400, cτ = 230 mm 1100/1000, cτ = 183mmMC Statistics 1.9% 1.4 %Pileup 4.0 % 1.2 %Trigger 1.4 % 1.4 %Electron Identification 7.3 % 9.3 %Muon Identification 4.4 % 3.7 %Overall 9.7 % 10.3 %Table 3.7: Systematic uncertainties for χ˜01 → ZG˜ decays in GGM model forsamples with a target decay length of 200 mm.3.3.8 Background estimationFor this analysis there are no irreducible backgrounds in the sense that there are noSM particles with a mass greater than 10 GeV that decay into leptons and are long-lived to enter the signal region without misreconstruction. The sources of reduciblebackground would be listed:• SM such as J/Ψ, ϒ and Z boson decay promptly into leptons also includingDrell-Yan. A DV can be formed if the tracks are poorly reconstructed. Toreduce this source of background it is required that the DV is away from allPV’s by 4 mm in the transverse plane.• Non-prompt B-hadron decays, which include semileptonic decays in whichone hadron is identified as a lepton and the production of displaced J/Ψ’s32(which should peak mdv ∼3 GeV). This is strongly reduced by lepton pT , d0and mDV cuts.• Cosmic muons which are rejected using the ∆cos requirement.• Cosmic muons whose tracks are sufficiently separated can be a source ofdisplaced vertices surviving the cosmic veto.• Random crossing of two tracks in the event which are suppressed by DVseed tracks selections and lepton identification criteria. An example can beone lepton from a PV such as W → lν or heavy flavour quarks decays andanother track from a pile-up event.Note that in the last four background sources, each muon is produced indepen-dently which will be refered are uncorrelated.3.3.9 MC simulation studies of the backgroundTo have a sense of which backgrounds are dominant in this analysis, a tt¯ samplewas used because it provides a lepton rich environment from W and heavy flavourdecays. Using a track classifier, they can come from different sources:• Track pairs from photon (generator-level ancestor) conversions are Conver-sion Pairs.• Track pairs from hadrons (generator-level ancestor) are Hadron decays.• If the tracks do not share common generator-level ancestor they are RandomCrossing. In this case tracks from the primary vertex and tracks not matchedto a generator level particle (pileup) produce three categories of track pairs,PV+PV, PV+PU and PU+PU.Using a track classifier it is found that conversion vertices have an invariant massclose to zero which is expected from the process, hadrons also peak at very lowmasses with a sharp decline beyond typical resonances. In the case of the randomcrossing the turn-on occurs at ∼ 3 GeV in Figure [3.4] and if pT > 10 GeV isapplied, at ∼ 15 GeV like in Figure [3.5]. The vertex mass is defined as follows:m12 =√2E1E2(1− cos(φ12)) (3.1)33Figure 3.4: no pT cut Figure 3.5: track pT > 10 GeVFigure 3.6: no pT cut Figure 3.7: track pT > 10 GeVFigure 3.8: Invariant mass of displaced vertex candidates in tt¯ MC sample.First line: Left side shows the distribution of all vertex candidateswith two ID tracks, right side shows the tracks forming the vertex withpT > 10 GeV.Second line: Left side shows all vertex candidates with two recon-structed leptons, right side shows leptons with pT > 10 GeV formingthe vertex.34This means thats masses can go up to 2√E1E2 and even for not very high mo-mentum, it is beyond the mass scale of hadron decays, for this reason the invariablemass shape of random crossings depends on the momentum threshold applied tothe tracks. For example, when a requirement of pT < 10 GeV is applied, the shapeof hadrons and conversions is unaltered, but random crossings are shifted to highermasses. When no lepton identification is applied the largest contribution to randomcrossing background is from crossings between two tracks from different pileupvertices. Then if the tracks are required to be matched to leptons, the number ofcandidates is strongly reduced. Hadron decays have a significant contribution, butafter cutting on the transverse momentum only random crossing survives. At thisstage, the random crossing is dominated by events where both leptons come fromthe primary vertex, which come from hadron decays. From this study its possibleto identify that random crossing is an important contribution which later will bequantified.Background due to accidental lepton crossingFor this estimation leptons from different events are paired and them combined tosee if they can form a vertex, in this case all leptons satisfy signal requirements.It is assumed that kinematic variables such as φ of two tracks forming a vertexare uncorrelated which is true if they come from primary interactions. The nextalgorithm is designed to perform the background estimation:• Seed tracks (which pass the lepton requirement) are collected.• Those tracks are paired to build vertices and the ID is extracted.• One track is randomly selected and the vertexing algorithm is performedevery time the track is rotated in φ from −pi to pi in steps with a maximumvalue before the algorithm fails.• If the vertex procedure is successful a background vertex candidate is recordedand a weight is assigned, wrot = δrot/2pi to account for all the rotation range.• The vertices generated as mentioned are assigned another multiplicative weightwhich account for the data set, wnorm =Nll/Nsample, Nll is the number of lep-35ton pairs observed in data which may or may not form a vertex and Nsampleis the number of leptons for the estimate.This is equivalent to multiplying the dilepton yield Nll by the probability pxing thatthe two lepton tracks will form a displaced vertex:Nvx = Nll× pxing (3.2)For this method the full ATLAS tracking code was not used, instead a simplifiedversion was used which does not include material interaction and assumes idealhelices.3.3.10 Validation of vertexingThe vertexing performance can be studied using displaced vertices found by thestandard ATLAS reconstruction. Displaced vertex candidates are required to passTable [3.5], except leptons so the signal region is blind, without matching to triggeror DESD filter objects. Now the algorithm is run on tracks without rotation form-ing vertex candidates. The efficiency is now defined as the ratio found with respectthe standard procedure. It is found that 86 % of the vertices (Figure [3.9])recon-structed by ATLAS can be reproduced by the vertexer within 1 mm of their nominallocation. Efficiency for spacial coordinates is listed in Table [3.8].Coordinate Efficiencyx 60 %y 60 %z 47 %Table 3.8: Vertexing efficiencies for coordinates36Figure 3.9: Position resolution of vertexing algorithm relative to ATLASshown in spacial coordinates for displaced vertex candidates of mDV >10 GeV with exactly two tracks, pT > 10 GeV and no leptons.3.3.11 Validation on simulated eventsThe validation of the background is done using MC simulation, with a looser se-lection criteria is used in tracks and vertices to enhance statistics. Tracks forming avertex candidate are required to have a pT > 5 GeV and no trigger or DESD filtersare applied. The statistics can be further enhanced by also considering ID tracksnot classified as leptons, which are more common. A cosmic veto is also used tobe consistent with procedures used with data. Two samples are used, one Z→ µµ37and one with tt¯, the results can be seen in Table [3.9]. The highest statistics areobtained for events with two track vertices and a good agreement between totaland predicted number of vertices is observed at a level of 10 %, results can be seenin Figure [3.10] and [3.11]. The main features of the distributions are reproducedwith this selection, which is sufficient since shapes are not used to discriminatesignal from background.Table [3.10] provides an overview of the prediction and observation, findingthat the probability of muon pairs to form a vertex to be 10−4, consistent in thetwo samples used. Notice that this number is less than the two tracks because thelepton identification and opposite charge.MC simulation can also be used, using truth matching the crossing probabilitiescan be estimated depending of the origin of tracks or leptons, primary vertex (PV)or pileup vertices (PU), in the three possible combinations. The probability isthe number of DV candidates divided by the number of track pairs and as beforeZ→ µµ and also tt¯ samples are used. In general results are consistent and they fallinto a similar range of values.Z→ µµ MCType Track Pairs DV candidates Crossing ProbabilityPU+PU 2.28×106 841 (3.7±0.1)×10−4PV+PU 2.2×105 89 (4.0±0.4)×10−4PV+PV 9567 7 (7.3±2.8)×10−4tt¯ MCType Track Pairs DV candidates Crossing ProbabilityPU+PU 8.0×105 291 (3.7±0.2)×10−4PV+PU 4.0×105 169 (4.3±0.3)×10−4PV+PV 9.1×104 20 (2.2±0.5)×10−4Table 3.9: Real crossing probabilities in MC vertices with two tracks. PVrefers to primary vertex and PU refers to pileup vertex. Uncertainties arestatistical.38Z→ µµ 2 tracks 2 muonsNll 2.5×106 1Avg. crossing probability 3.4×10−4 8.3×10−5Predicted vertices 841 8.3×10−5Observed vertices 937 0tt¯ 2 tracks 2 muonsNll 1.3×106 10Avg. crossing probability 3.4×10−4 5.9×10−4Predicted vertices 442 5.9×10−3Observed vertices 480 0Table 3.10: Displaced vertex candidates with loosened validation cuts ob-served and predicted in MC. The predicted number of vertices is ob-tained using the number of seed object pairs in the data Nll and theaverage crossing probability pxing via equation [3.2]39Figure 3.10: Some observables of displaced vertex candidate, two ID tracksnot identified as leptons in Z→ µµ sample. Yellow area represents theprediction of uncorrelated background, the errors are statistical.40Figure 3.11: Some observables of displaced vertex candidate, two ID tracksnot identified as leptons in tt¯ sample. Yellow area represents the pre-diction of uncorrelated background, the errors are statistical.413.3.12 Validation on collision dataFor this validation 2012 collision data is used. To obtain a signal depleted sample,two lepton vertices are not considered. Two cases are investigated: two tracks andone track plus a lepton. Objects are required to to pass the vertex selection and also∆Rcos > 0.04, applied at vertex level to tracks and leptons to remove potential con-tamination from cosmic events not fully reconstructed. For data at least one triggermust be fired without matching. The two tracks sample contains more events thanthe MC simulation so PT cuts at 5,10,15 GeV on the leptons in the vertex can betested with significant statistics. In the case of one track plus a lepton only a 10GeV cut is used.Table [Table 3.11] shows the expected and observed vertex yield, while Figure[3.12] and Figure [3.13] show results of two track and electron plus track categoriesfor 10 GeV cut. For the two track samples with large statistics, the backgroundestimation provides a prediction of the number of observed vertices better than 15%. I tighter selection can be applied, DESD and trigger matching to the lepton plustrack vertex candidates, which would be closer to the signal selection cuts. Resultscan be seen in Table [3.11], prediction and observation is conserved after applyingfilters.422 tracks (PT > 5 GeV ) 2 tracks (PT > 10 GeV ) 2 tracks (PT > 15 GeV )Nll 2.3×107 4.4×106 1.8×106Avg. crossing probability 3.7×10−4 4.4×10−4 4.4×10−4Predicted vertices 8587 1934 795Observed vertices 8742 1845 726PT > 10 GeVelectron + track muon + trackNll 4.1×104 8557Avg. crossing probability 4.9×10−4 3.9×10−4Predicted vertices 19.8 3.3Observed vertices 23 2PT > 10 GeV + DESD/Trigger matchingelectron + track muon + trackNll 2.1×104 3025Avg. crossing probability 4.3×10−4 4.4×10−4Predicted vertices 9.0 1.3Observed vertices 11 0Table 3.11: Displaced vertex candidates with loose validation cuts. The pre-dicted vertices are obtained using seed object pairs in data Nll and theaverage crossing probability pxing via Eq. [3.2]. The first table showstwo not identified as leptons track vertices for pT thresholds of 5, 10and 15 GeV. In the second table, one lepton and one track not identi-fied as lepton vertices. In the third table, vertices from the second tablematched to a trigger and DESD filter signature43Figure 3.12: Some observables of displaced vertex candidate, two ID tracksnot identified as leptons in tt¯ sample. Yellow area represents the pre-diction of uncorrelated background, the errors are statistical.44Figure 3.13: Some observables of displaced vertex candidate, two ID tracksnot identified as leptons in tt¯ sample. Yellow area represents the pre-diction of uncorrelated background, the errors are statistical.453.3.13 Invariant mass validationTo study a region in which an uncorrelated dominant background is valid, the usualcut on the mass mDV > 10 GeV is removed. Two or more track (not identifiedas leptons) vertices are considered. The usual vertex selection cuts are appliedwith exception of the mass cut. In the Figure [3.14] two main component can beidentified, the first part is falling and data doesn’t match the simulation becauseof correlated background from hard processes, but the second part describes toa good extent the shape of the data, corresponding to uncorrelated background.This transition is well below the 10 GeV cut used in the analysis proving that thisprocedure is adequate and reduces background significantly.46Figure 3.14: Invariant mass of displaced vertex candidates consisting of twoID tracks not identified as leptons in the MC and 2012 data. Data isshown as black dots, while the yellow area depicts the prediction ofthe uncorrelated background. The error bars on the prediction showthe estimated statistical error.473.3.14 Choice of the rotation size step parameterAs described before, for some studies the leptons are rotated in the angle φ insteadof generating more of them. Because this rotation is arbitrary, a step size has to bepicked making sure the calculations remain stable.Seed leptons pairs from data are selected randomly and processed using differ-ent values of δφrot (result in Figure [3.15]), for large values the observation isoverestimated and when it decreases, starts to converge and remains stable forδφrot < 3×10−2.The weight assigned to a vertex is proportional to δφrot :ωrot = nsteps× δφrot2pi >δφrot2piwhere nsteps is the number of rotation steps that produce a displaced vertex (as-sumed to be at least one). If the fraction of rotation angles leading to a vertexis pxing = Φ/2 with an acceptance interval of Φ, the inaccuracy introduced by adiscrete step is:ωrot − pxingpxing= nstepsδφrotΦ−1> δφrotΦ−1If the step size δφrot is larger than the angle interval Φ the results will bealways positive and an overestimate can be observed, in the plot around δφrot >10−3. If the step size is small enough, the weights nstepsδφrot/2pi can scattersymmetrically around Φ/2pi and converge to correct number of sampled vertexpairs. For computing reasons a value of δφrot = 10−3 is picked, because if smallerthe computing time would be excessive.48Figure 3.15: Observed number of vertices and background as a function ofstep size. In red ∆phi = 10−3 the nominal value for the analysis.3.3.15 Statistical uncertainty of random crossingsThis uncertainty is expected to be much smaller than the uncertainty on Nll andit can be estimated by running several independent subsamples from a large seedtrack collection and measuring the crossing probability. This method would notwork in the validation region because much higher numbers of seed tracks are used,which is not the case for signal region. The spread can be seen in Figure [3.16] with100 toys for the final state and and estimate of the statistical error including 68 %of the toys is used. For a cross-check, this estimate is compared to the width ofa gaussian function fitted to the distribution of toys with compatible results within6%. For this comparison the standard formula for estimating efficiency error for49weighted counts is used:σ =√(h×δm)2+(m×δh)2(h+m)4where h is the number of sampled muon pairs which a vertex was found, weightedby ωrot , δh is the statistical error of h and m is the number of pairs that did not leadto a vertex and δm is the error.The efficiency can be calculated as ε = hh+m and the relative error σ/ε can be com-pared to the relative uncertainty from toys. This assumes that no pair is sampledtwice and this depends on the total number of seed tracks and the pairs. Resultsshown in Table [3.12].Channel Rel. stat. error (toys) Rel. stat error (analytical)Muon+Muon 4.1% 2.4%Table 3.12: Relative statistical errors from running toys and analytical for-mula for dilepton crossing probabilities.50Figure 3.16: Observed number of vertices and background as a function ofstep size. In red ∆phi = 10−3 the nominal value for the analysis.3.3.16 Systematic uncertainty on background normalizationTo normalize the uncorrelated background it is important to count the number oflepton pairs Nll that could seed a displaced vertices. Samples with reasonableprobability of producing high mass displaced vertices are not suitable, like elec-trons from the same photo conversion or muons from J/Ψ decay, or lepton pairsproduced in bb¯ events. In principle the uncorrelated background is expected to beflat in ∆φ(ll) before vertexing is required and also be used to remove this contribu-tions, but this is not true since it is observed that the distribution has a structure asseen in Figure [3.17]. Is not possible to proceed and study this without unblindingso Nll is recalculated without any extra cuts. Possible contamination from corre-lated backgrounds is considered in systematics.Nll is recalculated by requiring lepton pairs |∆ψ(l, l)| > 0.5 to remove hadron de-51cays and conversions, and |∆ψ(l, l)| > pi − 0.5 to remove long range correlatedleptons, this number is corrected by a factor of pipi−0.5 before taking the differencewith respect the central value and obtain the systematic uncertainty.Figure 3.17: Invariant mass and transverse opening angle for track pairs in2012 data. No trigger or DESD filter matching has been applied.3.3.17 Dilepton estimateIn Table [3.13] the predicted uncorrelated background vertices from random cross-ings for data. The probability of crossing for the signal region include the require-ment of the vertex with opposite charged tracks, which is not the case for validationregions with higher probabilities. To calculate pxing a systematic uncertainty of15% was assigned based on validation with collision and simulated events. Statis-tical uncertainties from the normalization to data and systematic uncertainties fromvalidation of background estimation (pxing) and uncertainty of background Nll arein the same order or magnitude.52Channel Nll pxing/10−4 Nestex /10−3µµ 18+0−9.7 (syst.) 1.1±0.05 (stat.) ±0.2 (syst.) 2.0±0.05 (stat.) +0.3−1.4 (syst.)Table 3.13: Backround prediction for uncorrelated random crossings in signalregions.3.3.18 Background to prompt physics processesStandard Model processes can produce particles with similar characteristics to theones considered in this analysis, such as high pT charged lepton pairs, however itis not very likely for them to be misreconstructed to the point of passing the DVcriteria selection. Example processes can be Drell-Yan Z/γ∗ and tt¯ production. Tostudy the possible effects, the validation region ∆xy > 4 mm (measured from thePV to a DV) is considered. This means examining those that failed the originalrequirement for the analysis. To have more statistics cuts are loosened, triggermatching is not considered as well mDV . No vertices were found, and furthermoreeven if the track pT cut is lowered to 4 GeV.3.3.19 Low mass displaced verticesFor contribution coming from long-lived light hadronic resonances, like Ks theregion defined by inverting the mass cut is used, that it mDV < 10 GeV. Similarto the last case DESD and trigger matching is not applied, as well as the oppositecharge. For the dimuon cases, the vertices found are very collimated in φ and alsothe transverse displacement is between 2 - 10 cm. In addition, the muons have lowvalue of pT , so these characteristic are consistent with low mass hadron decayssuch as J/ψ . In all the pairs found only one has a mass close to 5 GeV, away fromthe signal region.3.3.20 Rejection of cosmic muonsA cosmic muon entering the inner detector can be misreconstructed as a pair ofmuons associated to a high-mass DV. One muon would be pointing in the oppositedirection so it will appear as though they have opposite charge. It is possible toobtain an upper limit in the background cross section using MC samples. Studies53(Figure [3.18]) considering the two leading muons show that no high-mass dileptonvertices are found in events that pass the cosmic veto, in this case statistic areinsufficient for a background estimation.To further study cosmics, collision data is used in a validation region. In thiscase, the muon trigger and the filter used in the DESD selects events containingcosmic muons Figure [3.19]. Events are required to fail the cosmic veto but passthe other preselection cuts: two muons passing the vertex seed cuts. Events withmore than one cosmic muon are identified and each case (single or more than onemuon) is studied. Events in which more than one muon appear, would be removedwith a sum of transverse mass impact parameter and difference of longitudinalimpact parameters cut (below 1 cm for each muon).7% of the DV candidates inside the fiducial acceptance that pass the materialveto, consistent with the observation on simulated signal. The shape of the distri-bution in Figure [3.20] is compatible with the distribution of all dimuon pairs, adeep decline is observed, with no pairs in the data showing at Rcos > 0.014, whichis far from the actual cut Rcos = 0.4, indicating that events with a single cosmicmuon are not an important source of background.Figure 3.18: The left plot shows the difference from the leading two muonsin an event being back to back, ∆Rcos in simulated cosmic events.The blue histogram shows only events that contain a reconstructedtwo track DV with mDV > 10 GeV with no lepton requirements.The right plot shows the reconstructed mass of dimuon vertices with∆Rcos < 0.04 . No dimuon vertices are found with so this cut is effec-tive to kill this background.54Figure 3.19: The left plot shows the η vs φ for the leading muon in the Muonsstream DESDM RPVLL. The right plot shows ∆φ vs (η1+η2)for theleading two muons. These plots indicate that the dominant backgroundof muons in these events comes from cosmic rays.Figure 3.20: Distribution of ∆Rcos for dimuon events observed in the cosmicmuon validation region on collision data. in red all dimuon pairs andthe black dots indicate the subset forming a DV candidate. The inclu-sive distribution is normalized to the DV matched pairs to allow forshape comparison.553.3.21 Random crossing of tracks from different cosmic muonsThe contribution from events with more than one cosmic muon in which tracksfrom different cosmic cross and form a vertex is studied and estimated indepen-dently from the case in which muons in a vertex candidate originate from the samecosmic muon. Muons pairs that fail the cosmic veto from different events are ran-domly sampled and then the vertexing algorithm is run to estimate how many pairscan form a vertex. In this case there is no angular rotation because muons arrivein a confined η/φ regions like in Figure [3.19]. The crossing probabilities for di-cosmic are consistent with the collision track. Results are shown in Table [3.14],where statistical uncertainty on dicosmics is computed using standard propagationof uncertainties. The crossing probabilities are consistent within a factor of 2, withdicosmic probability lower than crossing probability for collision tracks. To pre-vent a false discovery we it is used the crossing probability for collision tracks.Assumption pxingCollision Crossings (1.1±0.05)×10−4Dicosmics (6.4±0.6)×10−5Table 3.14: Crossing probabilities for dicosmics and collision muons, errorsare statistical.56Chapter 4ResultsIn Table [4.1] the background prediction and the displaced vertices in the signalregion is shown. For the Run 1 data, no vertices were found. The background asexpected is small ≈ 2.5× 10−3 events and the uncertainty is ∼ 30%. No vertexpassed the selection even when it was loosened on the number of leptons in thevertex and vertex mass, the distribution can be seen in Figure [4.1].Channel Nestex Nobsexµ+µ−(2.0±0.5(stat)+0.3−1.4(syst.))×10−3 0Table 4.1: Observation and background expectation in data for the full 2012datasetThe exclusion limits as a function of the neutralino χ01 decay lentgh can se beenin Figure [4.3] and in Figure [4.2] can be seen the excluded number of χ˜10 → ZG˜decays assuming a SM branching ratio of the Z into leptons. No decay lengthwas excluded in this model, the strongest exclusion occurs between 20 mm and 40mm with an upper limit of 10 fb on the gluino pair production cross section. Nodisplaced vertices candidates passed the selection criteria, this is consistent withthe SM background expecatation ∼ 10−3 vertices. Since no excess is observed,exclusion limits can be used to interpret results according to each SUSY model.To derive the model dependent cross section limits, per-event efficiencies based on57per-vertex efficiency distributions are used. The following formula is used:εevt = 2×B× εDV −B2× ε2DV (4.1)where εDV refers to the per vertex efficiency andB is the branching fraction ofthe decay into the decay mode yielding a DV. The resulting event level efficiencydistributions can be seen in Figure [4.2] and Figure [4.3], efficiency distributions asa function of decay length in combination with an input production cross-sectioncan be translated into predicted signal yields. For each decay length value, an upperlimit on the gluino production cross-section is obtained at a 95 % confidence level.Upper limit on the number of decays assuming a SM branching ratio Z → ll inthe 2012 data are shown in Figure [4.3] and in Figure [4.2]. No decay length isexcluded, the strongest exclusion is observed between 20 mm and 40 mm with anupper limit of 10 fb on the gluino pair production cross section.Figure 4.1: Distribution of dilepton-vertex candidates in terms of the vertexmass and number of candidates. The red ovals are proportional to thelogarithm of the number of vertices in that specific bin. In grey it ispossible to see the signal MC sample.58Figure 4.2: Upper limit on the number of decays for GGM model as a funcionof cτ . 95% confidence level.Figure 4.3: Exclusion limit on the gluino production cross section for GGMmodel a function of decay length. 95% confidence level.59Chapter 5ConclusionsIn this search the full 2012 ATLAS dataset is used with an integrated luminosityof 20.3 fb−1 at√s = 8 TeV. No events with supersymmetric particles in decaysleading to displaced vertices with at least two muons were observed in data.No vertices passed the selection criteria which is consistent with the StandardModel background of 10−3 vertices. Gluino production cross section of more than13(8) fb can be excluded for a µ parameter of 1000(400) GeV with LSP decaylength of 20-40 cm.60Bibliography[1] ATLAS tunes of PYTHIA 6 and Pythia 8 for MC11. Technical ReportATL-PHYS-PUB-2011-009, CERN, Geneva, Jul 2011. → pages 22[2] Search for long-lived, heavy particles in final states with a muon and amulti-track displaced vertex in proton-proton collisions at√s = 8 TeV withthe ATLAS detector. Technical Report ATLAS-CONF-2013-092, CERN,Geneva, Aug 2013. → pages 21[3] Search for Displaced SUSY in Dilepton Final States. 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