MSc Thesis

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MSc Thesis

  1. 1. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at √ The Large Hadron Collider using s=7 TeV data Kuhan Wang Supervisor: Richard Keeler Committee Members: Michel Lefebvre, Rob McPherson External Examiner: Michel C. Vetterli July 1st, 2011 1 / 41
  2. 2. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d OutlineOutline 1 Introduction 2 The Standard Model 3 Minimum Bias 4 The Large Hadron Collider 5 ATLAS 6 Pile-up 7 Missing Transverse Energy 8 Data Selection and Monte Carlo 9 Analysis 10 Conclusions 11 Backup 2 / 41
  3. 3. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d IntroductionIntroduction We examined approximately L dt = 3668 nb −1 of data √ taken at the LHC at s =7 TeV during 2010 Minimum bias events are selected using a “single arm” MBTS trigger We examine the Missing Transverse Energy (MET) of minimum bias events after selection for run, timing, jet and track quality The events are sorted by the number of primary vertices so as to study the effects of in-time pile-up We compare and contrast the resolution, mean and asymmetry of the MET with respects to global calibration schemes and Monte Carlo results The resolution of minimum bias events parametrized in ET does not vary with respects to in-time pile-up, up to at least 4 vertices 3 / 41
  4. 4. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d The Standard Model IThe Standard Model SM is the current theory of particle physics 3 forces mediated by Bosons, 3 generations of Fermions Fermions: Quarks and Leptons Quarks and Gluons carry color charge Quarks are color confined and must exist in a color neutral combination 4 / 41
  5. 5. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Minimum Bias IMinimum Bias The term “minimum bias events“ refers to selecting collision events using an inclusive as possible trigger, with the least amount of selection, kinematic or topological Define the minimum bias cross section σMB , σMB = σSD + σDD + σND + σCD . (1) Minimum bias events are typically soft hadronic processes characterized by low momentum transfer between the interacting particles. 5 / 41
  6. 6. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d The Large Hadron Collider IThe Large Hadron Collider Most powerful particle accelerator built to date Located near Geneva, Switzerland. Built by CERN. 26.7 km circumference synchrotron accelerator Peak performance - 14 TeV √ s, 1034 cm−2 s −1 luminosity Probe of new physics and precision studies of the SM 6 / 41
  7. 7. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d The Large Hadron Collider IIThe Large Hadron Collider Define the luminosity, 2 Nb nb frev γr 1 L= F [ 2 ]. (2) 4π n β∗ cm s The average number of interactions per bunch crossing is given by, Lσevent Nc = . (3) RC For 2010, assuming an inelastic p-p cross section of 57.2 ± 6.3 this is, 5.1 Nc . (4) NB 7 / 41
  8. 8. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d ATLAS IATLAS 8 / 41
  9. 9. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d ATLAS IIATLAS A Toroidal LHC ApparatuS, One of four major detector experiments at the LHC Approximately 7000 tonnes, 25 m x 44 m length by width Inner Detector - Tracking, momentum and vertex measurements and electron identification Calorimetry - energy measurements of particles except neutrinos and muons Muon Spectrometer - tracks charged particles that exit the calorimeter, measures their momentum 9 / 41
  10. 10. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d ATLAS IIIATLAS Minimum Bias Trigger Scintillator (MBTS) is the primary device for observing minimum bias events in ATLAS Dedicated machine for observing minimum bias events Mounted on the A and C sides of the detector 10 / 41
  11. 11. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Pile-up I In-time Pile-up is the phenomena of multiple proton-proton collisions occuring in one bunch crossing This is estimated by the number of primary vertices in the event. The probability of in-time pile-up is governed by Poisson statistics The probability P(n) for n independent events occuring in one bunch crossing is given by, e −λ λn P(n) = A . (5) n! The number spectrum, λ, is a function of the luminosity, L, bunch separation, Tc and cross section for the interaction, σpp , λ = LTc σpp. (6) 11 / 41
  12. 12. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Missing Transverse Energy IMissing Transverse Energy N N Miss Miss EX = − Ei sin θi cos φi , EY = − Ei sin θi sin φi . (7) i=1 i=1 Miss Miss Miss ET = (EX )2 + (EY )2 , (8) Miss EY φX ,Y = arctan( Miss ). (9) EX The missing transverse energy per event is the negative of the vector sum of the energy deposited into the calorimeter in an event Closely related to this concept is the scalar sum given by, N ET = Ei sin θi . (10) i 12 / 41
  13. 13. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Missing Transverse Energy IIMissing Transverse Energy Miss EX ,Y are constructed as, Miss Miss,calo Miss,cryo Miss,muon EX ,Y = EX ,Y + EX ,Y + EX ,Y . (11) Miss,calo In the case of refined calibrations, EX ,Y is constructed such that, Miss,calo Miss,e Miss,γ Miss,τ Miss,jets Miss,µ Miss,CellOut EX ,Y = EX ,Y +EX ,Y +EX ,Y +EX ,Y +EX ,Y +EX ,Y . (12) Constructing the MET as seen above will give the measurement at electromagnetic energy scale There are two global calibration schemes Global Cell energy-density Weighting (GCW) Local Cluster Weighting (LCW) These correct for dead and malfunctioning cells and correct for hadronic energy signals in the calorimeter 13 / 41
  14. 14. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Data Selection and Monte Carlo IData Selection and Monte Carlo Our data selection criteria is as follows - Trigger: L1 MBTS 1 GRL Timing - LAr Calorimeters - MBTS Bad jets - HEC Spike - e/m Coherent Noise - Beam Background Ugly Jets Track Quality - ≥ 1 Primary vertex, > 5 Tracks, Pt > 150 MeV 14 / 41
  15. 15. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Analysis Selection IAnalysis Selection histograms, electromagnetic energy scale 15 / 41
  16. 16. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Analysis Selection IIAnalysis Selection histograms, GCW energy scale 16 / 41
  17. 17. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Analysis Selection IIIAnalysis Selection histograms, LCW energy scale 17 / 41
  18. 18. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Analysis Pile-up IAnalysis Distribution of vertices per event, Data (left) and Monte Carlo (right). 18 / 41
  19. 19. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Analysis Pile-up IIAnalysis Miss Miss Miss ET , E T , EX and EY . Data (crosses) and Monte Carlo (bars). Electromagnetic energy scale. 19 / 41
  20. 20. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Analysis Pile-up IIIAnalysis Miss Miss Miss ET , E T , EX and EY . Data (crosses) and Monte Carlo (bars). GCW energy scale. 20 / 41
  21. 21. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Analysis Pile-up IVAnalysis Miss Miss Miss ET , E T , EX and EY . Data (crosses) and Monte Carlo (bars). LCW energy scale. 21 / 41
  22. 22. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Analysis Pile-up VAnalysis Average ET as a function of the number of primary vertices per event. 22 / 41
  23. 23. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Analysis Resolution IAnalysis Let’s quantify the resolution Miss and E Miss in Parametrize EX ET Y 23 / 41
  24. 24. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Analysis Resolution IIAnalysis Slice the result in vertical segments of ET . Each slice is Gaussian distributed in EX Miss and E Miss . Y Miss If you did this for ET , the slices would be Rayleigh distributed. Add the histograms of EX Miss versus ET and EY Miss versus ET together - This assumes that σX = σY . Fit each slice of this new 2D histogram to a gaussian function, 2 2 f (x) = √ 1 2 e −(x−µ) /2σ 2πσ Plot the values of the fitted σ as a function of the ET , do this for 1 vertex events, 2 vertex events...so forth 24 / 41
  25. 25. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Analysis Resolution IIIAnalysis 25 / 41
  26. 26. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Analysis Resolution IVAnalysis Miss Since σX = σY , σT for ET goes as, Miss ∂ET ∂E Miss (∆ET )2 = ( Miss Miss ∆EX )2 + ( T ∆EY )2 Miss Miss Miss (13) ∂EX ∂EY (EX ∆EX )2 + (EY ∆EY )2 Miss Miss Miss Miss = Miss (14) (ET )2 Miss Miss ∆EX = ∆EY (EX )2 + (EY )2 Miss Miss =( Miss )2 )(∆EX ,Y )2 = (∆EX ,Y )2 Miss Miss (15) (ET Miss Miss Thus, if σX = σY , the resolution of EX ,Y is the resolution of ET . Miss Miss Assumption: EX and EY are uncorrelated. 26 / 41
  27. 27. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Analysis Resolution VAnalysis We quantify the resolution with respect to the ET as, √ σX ,Y = A ET ⊕ B ET , (16) We are interested in how the behaviour of the resolution parametrized in ET changes as a function of the number of primary vertices in events, i.e. in-time pile-up Qualitatively, from the plots shown above, they don’t really change. NOTE TO SELF THIS IS: σX ,Y = A ET + B( ET )2 27 / 41
  28. 28. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Analysis Resolution VIIIAnalysis Fit Parameters with respect to the resolution for data (left) and Monte Carlo (right). 28 / 41
  29. 29. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Conclusions IConclusions We analyzed the MET in minimum bias events in the context of in-time pile-up Our primary was goal was to study the MET resolution with respects to in-time pile-up We find that the MET resolution parametrized in ET does not qualitatively change with regards to the number of primary vertices These results are reproduced in Monte Carlo and at e/m, GCW and LCW calibrated energy scales. 29 / 41
  30. 30. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Backup IBackup In addition to the resolution we examined the bias of the MET parametrized in ET and the asymmetry in the φX ,Y Miss distribution of ET We find a bias in the mean, µX and µY , that is approximately linear with respects to ET We examine this effect by looking at the asymmetry in the φX ,Y distribution, sorted with respects to the number of primary vertices per event We can approximate the asymmetry using a simple model of detector misalignment as shown. 30 / 41
  31. 31. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Backup Resolution IXAnalysis Is σX = σY ? Easy to check in terms of ET 31 / 41
  32. 32. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Backup Resolution XAnalysis 32 / 41
  33. 33. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Backup Resolution XIAnalysis 33 / 41
  34. 34. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Backup Mean IAnalysis How is the mean, µX ,Y , effected by pile-up? 34 / 41
  35. 35. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Backup Mean IIAnalysis 35 / 41
  36. 36. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Backup Mean IIIAnalysis 36 / 41
  37. 37. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Backup Asymmetry IAnalysis A good way to understand the mean is to examine the E Miss quantity φX ,Y = arctan( EY ), this is the azimuthal direction Miss X Miss of the ET 37 / 41
  38. 38. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Backup Asymmetry IIAnalysis 38 / 41
  39. 39. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Backup Asymmetry IIIAnalysis 39 / 41
  40. 40. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Backup Asymmetry IVAnalysis We quantify this as a misalignment of the nominal and real origins of the detector If we source the MET from the incorrect O’ the azimuthal angle φ will be related to φ by, k + r sin φ φX ,Y = arctan( ). h + r cos φ (17) dN This gives dφ , dN h cos φ + k sin φ + 1 ∼ 2 dφ h + k 2 + 1 + 2(h cos φ + k sin φ ) (18) 40 / 41
  41. 41. √A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using s=7 TeV d Backup Asymmetry VAnalysis We can see how well this simple model works by making a fit. 1 Vertex events at electromagnetic scale from data 41 / 41

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