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Dissertation Defense Presentation

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Dissertation Defense Presentation

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PhD dissertation defense proposal. This presentation details my research work with the Compact Muon Solenoid (CMS) Collaboration of the European Organization for Nuclear Research's (CERN) Large Hadron Collider (LHC). Specifically, my investigations of the behavior the strong nuclear force by studying the production rate of beauty and antibeauty quark pairs are presented, and a comparison with leading theoretical models is shown.

PhD dissertation defense proposal. This presentation details my research work with the Compact Muon Solenoid (CMS) Collaboration of the European Organization for Nuclear Research's (CERN) Large Hadron Collider (LHC). Specifically, my investigations of the behavior the strong nuclear force by studying the production rate of beauty and antibeauty quark pairs are presented, and a comparison with leading theoretical models is shown.

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Dissertation Defense Presentation

  1. 1. Measurement of Angular Correlation in b Quark Pair Production at the LHC as a Test of Perturbative QCD Dissertation Defense Brian L. Dorney Florida Institute of Technology Dissertation Committee: Marc Baarmand (advisor) Ugur Abdulla (outside) Daniel Batcheldor Marcus Hohlmann Ming Zhang Brian L. Dorney 07/03/13 Dissertation Defense 1
  2. 2. The Standard Model... ...of Particle Physics  Describes interactions of fermions and bosons    Image courtesy of MissMJ, “Standard Model of Elementary Particles,” Wikipedia, 2013. Fermions: half-integer spin, i.e. quarks and leptons Bosons: integer spin, i.e. γ, g, Z0, W±, and H Incorporates “two” theories  Quantum Chromodynamics  Electroweak Theory   Quantum Electrodynamics Quantum Flavordynamics (i.e. weak interactions) Brian L. Dorney 07/03/13 Dissertation Defense 2
  3. 3. Quantum Chromodynamics   Renormalizable nonabelian gauge theory that describes interactions of quarks and gluons Anticharge screening   At high energies quarks and gluons behave as free particles Color confinement    As distance between quarks and gluons increases their color charge increases Asymptotic freedom   J. Beringer et al. (Particle Data Group), Phys. Rev. D86, 010001 (2012). All searches for free quarks since 1977 have yielded negative results Quarks form color singlet bound states Perturbation Theory  Observables described by perturbative series in terms of αS Brian L. Dorney 07/03/13 Dissertation Defense 3
  4. 4. bb Production Mechanisms Left image courtesy of D. Acosta et al., Phys. Rev. D71,092001 (2005). Right image courtsey of M. Baarmand et al., CMS-AN-2010/022.  FCR gives rise to a back-to-back topology for the bb pair   In FEX a bb pair is created within the parent proton   Angle in transverse plane between the b and b is ~π radians Only one member of the bb pair is involved in collision causing a wide range of angular separations between the b and b In GSP, a gluon splits into a bb pair  The b and b are roughly collinear w/small angular separation in the transverse plane Brian L. Dorney 07/03/13 Dissertation Defense 4
  5. 5. Properties of B Hadrons  Daughters generally have high impact parameters   Perpendicular distance between particle trajectory and primary vertex Generally decay into several charged secondary particles  Makes it possible to find the location of the B hadron's decay (i.e. secondary vertex) Brian L. Dorney 07/03/13 Dissertation Defense 5
  6. 6. Properties of B Hadrons  Large semileptonic branching fraction  How often a B hadron decays to leptons+hadrons B B l l X =    Bl l X   B Y  At LO, decay proceeds via emission of virtual W boson and a charm quark νμ μ+  0.29 −0.25 B( B → μ νμ X) = 10.95 Brian L. Dorney 07/03/13 % as quoted by PDG Dissertation Defense 6
  7. 7. Proton-Proton Collision Underlying Event Spectator Partons f k  x1  h1  P 1  1 qk  x1 P 1  1 1 k  k   q1  q 2  y  1 q h2  P 2  k2 2  x2 P 2  2 FSR Included Y Jets f k  x2  2 Underlying Event ISR Protons Approach Hard Scattering 1 Parton Shower 1 Decays    h1 h2  Y  =∫0 dx 1∫0 dx2 ∑ ∑ f k  x 1  f k  x 2   q1  x1 P 1   q 2  x 2 P 2   y  Brian L. Dorney 07/03/13 7 k1 k2 1 2 Dissertation Defense  Hadronization k1 k2
  8. 8. Proton-Proton Collision  Brian L. Dorney 07/03/13 Dissertation Defense Real example 8
  9. 9. Large Hadron Collider Image courtesy of LHC@home, http://lhcathome.web.cern.ch/LHCathome/LHC/lhc.shtml, 2013. Brian L. Dorney 07/03/13 Dissertation Defense 9
  10. 10. Compact Muon Solenoid (CMS) CMS Collaboration, Lucas Talyor, “CMS detector design,” http://cms.web.cern/ch/news/cms-detector-design, 2013. Brian L. Dorney 07/03/13 Dissertation Defense 10
  11. 11. CMS Coordinate System +y +y   +z +x x-axis points out of page z-axis points into page yz-plane xy-plane  = −ln  tan   / 2     = 2 −  1  R =       p x p y   = 2 − 1  A =   or  R pT = 2 2 2 CMS Collaboration, Detector Drawings, CMS-PHO-GEN-2012-002. Brian L. Dorney 07/03/13 Dissertation Defense 11 2
  12. 12. Previous bb Angular Correlation Measurements - Tevatron DZero  s=1.8 TeV, L = 6.5 ± 0.4 pb-1 Left: DØ Collaboration, Phys. Letters B, 487 (2000), p. 264-272. Right: CDF Collaboration, CDF note 8939, 2007. Brian L. Dorney 07/03/13 Dissertation Defense 12
  13. 13. Previous bb Angular Correlation Measurements – LHC, ATLAS     Right: bb dijet production cross section ATLAS Collaboration. Eur. Phys. J. C, 71 (1846), 2011. Disagreement at low Δφ Full range of Δφ was not studied Cross section with respect to ΔR has not been presented Brian L. Dorney 07/03/13 Dissertation Defense 13
  14. 14. Previous BB Angular Correlation Measurements – LHC, CMS CMS Collaboration, JHEP03(2011)136. CMS Collaboration, JHEP03(2011)136.  BB production cross section  Overall uncertainty of 47% common to all data points Brian L. Dorney 07/03/13 Dissertation Defense 14
  15. 15. Motivation  Why perform another bb angular correlation measurement at LHC energy levels?     Large uncertainty on absolute cross section of previous CMS results Limited Δφ range covered in ATLAS study Propose a new bb angular correlation measurement to address these two concerns Complimentary measurement using different experimental technique and in differing phase-space  Angular correlations measured w.r.t. b-tagged jets Brian L. Dorney 07/03/13 Dissertation Defense 15
  16. 16. Overview   b-jet Two b-tagged jets   p Experimental Signature One of which has a muon μ Strategy  Select high purity sample of bb dijet events  X Signal purity determined in data via System4  p b-jet Selection efficiency     Calculated from simulated PYTHIA events Weighted by data trigger efficiency Corrected by data-over-simulation scale factors (muon reconstruction, jet energy resolution, b-tagging, etc...)  Data SF =  Sim. Measurement of differential cross section w.r.t. Δφ and ΔR Brian L. Dorney 07/03/13 Dissertation Defense 16
  17. 17. Simulated Samples & Monte-Carlo Event Generators  PYTHIA    Muon-enriched hard QCD process Passed through Geant4 CMS detector simulation MadGraph   CASCADE   Hard scattering: p p  b b j for j = 0, 1, & 2 additional partons Hard scattering: g g  Q Q for Q = b MadGraph and CASCADE passed to PYTHIA for parton shower and hadronization  Not passed through Geant4 CMS detector simulation Brian L. Dorney 07/03/13 Dissertation Defense 17
  18. 18. Data Samples   Proton-proton collision events collected in 2010 at  s=7 TeV with recorded integrated luminosity 3 pb-1 Two independent samples collected     Low-pT single-muon trigger, referred to as HLT_Mu7 Single-jet and multijet triggers Use of muon triggers are a natural choice to select bb data sample online Jet triggers collect statistically independent sample for measuring online selection efficiency  Online Brian L. Dorney 07/03/13 Dissertation Defense 18
  19. 19. Particle-Flow Event Reconstruction in CMS   “Global event description” Hits in CMS detector channels used to form elements   Elements are linked together to form blocks     Tracks, calorimeter clusters Charged tracks linked to calorimeter clusters Calorimeter clusters linked to calorimeter clusters Tracks linked to tracks Blocks identified as particle-flow candidates  Block formed from a charged track linked to a HCAL cluster forms a particle-flow hadron Brian L. Dorney 07/03/13 Dissertation Defense CMS Collaboration, CMS PAS PFT-10-001, 2010. 19
  20. 20. Particle-Flow Jet Reconstruction in CMS   Jets are clustered by the infrared and collinear safe anti-kT particle-flow algorithm Iterative clustering algorithm    Collection of particle-flow candidates used as input Clusters particles into jets if the particles are within a given distance parameter djet of the jet axis Characterized by two resolution variables: d kB = p 2a Tk d kl =min  p , p 2a Tk Beam Resolution  2a Tl  R d Cluster Resolution 2 kl 2 jet For a = 1 (a = -1), kT (anti-kT) clustering algorithm Brian L. Dorney 07/03/13 Dissertation Defense 20
  21. 21. Muon Reconstruction in CMS  Global Muon reconstruction, i.e. “outside-in”     Standalone-muon track: reconstructed in muon detector Standalone-muon track extrapolated to inner tracking detector and required to match a tracker track Global-muon track: track formed from combined fit of hits in the standalone-muon and tracker track Tracker Muon reconstruction, i.e. “inside-out”   Track reconstructed by inner tracking detector is extrapolated to muon detector Tracker-muon track: If this extrapolated track matches a muon segment the tracker track is called a tracker-muon  Muon segment: track stub made of drift tube or cathode-strip chamber hits Brian L. Dorney 07/03/13 Dissertation Defense 21
  22. 22. Physics Object Matching   Objects are said to be matched if they are within some parametric distance of each other Example of matching  A generator-level jet and a reconstructed jet are considered to be matched if the ΔR between them is less than 0.25 Brian L. Dorney 07/03/13 Dissertation Defense 22
  23. 23. Physics Object Selection  Anti-kT particle-flow jets   Loose PF Jet ID   Distance parameter, djet = 0.5 pT > 30 GeV & |η| < 2.4 Muons  Tight Muon Selection  pT > 8 GeV & |η| < 2.1   This pT cut corresponds to plateau in online efficiency Referred to as tight muons Brian L. Dorney 07/03/13 Dissertation Defense 23
  24. 24. Muon Association  Tight muon found within a jet referred to as the jet's associated muon   Association uses a jet's particle-flow constituents If two or more tight muons found the tight muon with Rel pT to jet axis the highest is taken p jet p ∣ ×∣ p = p ∣∣ Rel T Brian L. Dorney 07/03/13 Dissertation Defense 24
  25. 25. Event Selection  Online selection  Offline selection    Preselection B-Tagging Final event sample Brian L. Dorney 07/03/13 Dissertation Defense 25
  26. 26. Online Selection  Data has at least one “offline” reconstructed tight muon with HLT_Mu7 trigger object match  HLT_Mu7 trigger object is a muon (i.e. track) reconstructed by the HLT_Mu7 trigger algorithm    ΔR matching, with ΔR < 0.5 The tight muon must be associated to a jet Simulated PYTHIA events are weighted with  Online    Simulated trigger information not used Event weighting determined from η of highest pT tight muon associated to a jet Shown to be equivalent to a data-over-simulated efficiency scale factor weighting Brian L. Dorney 07/03/13 Dissertation Defense 26
  27. 27. Online Efficiency  85.5±1.1 stat.3.9  syst. % Online efficiency at plateau, −1.5 Brian L. Dorney 07/03/13 Dissertation Defense 27
  28. 28. Offline Preselection  At least one jet having an associated tight muon with trigger-matched (ΔR < 0.5) object     No trigger-matched object criterion for simulation At least one jet w/o an associated tight muon The highest TCHE mu-jet and the highest TCHP non-mu-jet must have ΔR > 0.6 Jets with (without) associated tight muons are referred to as mu-jets (non-mu-jets) Brian L. Dorney 07/03/13 Dissertation Defense 28
  29. 29. Preselection: Jet Kinematics Brian L. Dorney 07/03/13 Dissertation Defense 29
  30. 30. Preselection: Muon Kinematics Electroweak Contamination Brian L. Dorney 07/03/13 Dissertation Defense 30
  31. 31. B-Tagging  Identification of jets arising from the hadronization and decay of b quarks   Signed impact parameter significance (SIP)    Referred to as b jets CMS Collaboration, CMS PAS BTV_07_002, 2008. Impact parameter significance given by IP /  IP Impact parameter inherits the sign of the scalar product between the IP and jet axis, tracks from B hadron decays favor positive SIP values Track counting algo. orders a jet's tracks by decreasing SIP  Numeric discriminator formed by taking the SIP of the Nth track  Two versions, high eff. (TCHE, N = 2) and high purity (TCHP, N = 3) Brian L. Dorney 07/03/13 Dissertation Defense 31
  32. 32. B-Tagging Selection   For TC discriminator values > X, the light (u, d, s, and g) jet misidentification probability is Y Form “operating points” which give specific values of Y    Loose (L), Y = 10%; Medium (M), Y = 1%; Tight (T), Y = 0.1%; In each event highest TCHE mu-jet and highest TCHP non-mujet taken as a dijet pair Event is finally selected if mu-jet (non-mu-jet) passes TCHEM (TCHPT) operating point   TCHEM: TCHE > 3.30; TCHPT: TCHP > 3.41 Event is rejected if two or more mu-jets (non-mu-jets) pass TCHEM (TCHPT), fraction of events rejected in data (sim.) is 0.7% (0.7%). Brian L. Dorney 07/03/13 Dissertation Defense 32
  33. 33. B-Tagging Selection TCHEM TCHPT  TCHEM (N = 2) operating point: TCHE > 3.3  TCHPT (N = 3) operating point: TCHP > 3.41 Brian L. Dorney 07/03/13 Dissertation Defense 33
  34. 34. Final Selection: Jet Kinematics Brian L. Dorney 07/03/13 Dissertation Defense 34
  35. 35. Final Selection: Muon Kinematics EWK contamination does not survive b-tagging selection Brian L. Dorney 07/03/13 Dissertation Defense 35
  36. 36. Detector Response ΔRReco From true flavor bb dijets and their matched (ΔR < 0.25) generator-level jets from final selected simulated events ΔφReco  ΔφGen  ΔRGen Off diagonal elements are an order of magnitude smaller than their main diagonal counterparts  Bin-to-bin migration taken as negligible Brian L. Dorney 07/03/13 Dissertation Defense 36
  37. 37. Purity Correction with System4  System of 4 equations in 4 unknowns, System4   Solves an “S x = b” system for each bin of ΔA   Designed to determine bin-by-bin bb signal purity in data S = efficiency matrix; x = flavor vector; b = yields vector Breaks analysis into four classes of cuts   TCHPT applied to non-mu-jet  TCHEM applied to mu-jet   Preselection Both discriminators applied to both jets Unknowns are the flavor content of preselected events  Transformed to purity of final selected events Brian L. Dorney 07/03/13 Dissertation Defense 37
  38. 38. System4 Flavor Vector Efficiency Matrix Unknowns Description Contents of preselected events by flavor. First (second) letter is the flavor of the mu-jet (non-mu-jet), X = non-b. { f BB , f BX , f XB , f XX } Knowns {f TCHPT { B TCHPT ,f TCHPT TCHEM Description ,f TCHEM Both Fraction of events passing cuts } TCHEM , X , B , X {  BB ,  BX ,  XB ,  XX } {  BB ,  BX ,  XB ,  XX } {  BB ,  BX ,  XB ,  XX } Brian L. Dorney 07/03/13 Yields Vector } B-tagging efficiencies Ratios of dijet efficiency to single jet efficiency Dissertation Defense 38
  39. 39. System4 Toy MC  Use 100k pseudo-experiments for each bin of ΔA   Vary elements of yields vector & efficiency matrix by their uncertainties Solves “S x = b” via non-negative least squares algorithm   C. L. Lawson, R. H. Hanson, “Solving Least Squares Problems,” Prentice-Hall, Inc., 1974. Distributions of flavor vector elements and purity are formed from all pseudo-experiments   Purity given as P IJ =   IJ  IJ f IJ  / f Both Fit with a Gaussian, mean (standard deviation) is set to the central value (statistical uncertainty) Brian L. Dorney 07/03/13 Dissertation Defense 39
  40. 40. bb Dijet Signal Purity in Data  Overall bb dijet signal purity in data: 93.3 ± 1.7 (stat.) % Brian L. Dorney 07/03/13 Dissertation Defense 40
  41. 41. Online plus Offline Selection Efficiency H Sel Sel = H Gen   Taken from simulation as ratio of reconstructed bb dijet to generated bb dijet ΔA distributions Overall online plus offline efficiency  Sel =17.1% Brian L. Dorney 07/03/13 Dissertation Defense 41
  42. 42. Systematic Uncertainties  Calculated bin-by-bin in ΔA:   Signal purity  Muon reconstruction and identification efficiency scale factor  B-tagging efficiency scale factors  Jet energy correction (JEC)  Jet energy resolution (JER)  Fragmentation   Shape of online plus offline efficiency Proton distributions functions Taken as a flat value across all bins of ΔA:    Online efficiency Recored integrated luminosity Total syst. uncert. on absolute cross section +13.1/-9.8% Brian L. Dorney 07/03/13 Dissertation Defense 42
  43. 43. Differential bb Dijet Production Cross Section  Experimental cross section for ith bin of ΔA    N Data P bb d = d A i L  A bin  Sel  i  NData → raw number of final selected events  Pbb → bb dijet signal purity  L → recorded integrated luminosity  ΔAbin → bin width in ΔA   Sel → online plus offline selection efficiency Brian L. Dorney 07/03/13 Dissertation Defense 43
  44. 44. Differential bb Dijet Production Cross Section Brian L. Dorney 07/03/13 Dissertation Defense 44
  45. 45. Comparison to Previous CMS Results   Red: previous CMS Results Black: work presented here Brian L. Dorney 07/03/13 Dissertation Defense 45
  46. 46. Comparison with Theoretical Preidctions of Perturbative QCD All Val in n ues b e lut ion bso ect A S ss Cro Brian L. Dorney 07/03/13 Dissertation Defense 46
  47. 47. Suggestions for Future Work      Extend study to full CMS pp collision dataset Compare results with a complete NLO MC event generator Determine the fractions of bb pairs produced by the FCR, FEX, and GSP mechanisms Determine the double differential bb dijet 2 production cross section d  / d  A d E Detemine the cross section as a function of ΔA with n additional light jets in final state Brian L. Dorney 07/03/13 Dissertation Defense 47
  48. 48. Back – Up Brian L. Dorney 07/03/13 Dissertation Defense 48
  49. 49. bb Production Mechanisms  Three primary production mechanisms   NLO – Flavor Excitation   LO – Flavor Creation NLO – Gluon Splitting Additional mechanisms  NLO – Gluon Radiation  NLO Interference terms   Virtual emission Loop diagrams Brian L. Dorney 07/03/13 Image courtesy of D. Acosta et al., Phys. Rev. D71, 092001 (2005). Dissertation Defense 49
  50. 50. Proton-Proton Collision  Real example Brian L. Dorney 07/03/13 Dissertation Defense 50
  51. 51. Previous BB Angular Correlation Measurements – LHC, CMS CMS Collaboration, JHEP03(2011)136. CMS Collaboration, JHEP03(2011)136.  BB production cross section  Overall uncertainty of 47% common to all data points Brian L. Dorney 07/03/13 Dissertation Defense 51
  52. 52. Corrections Made to Simulated PYTHIA Sample   The analysis takes the online plus offline efficiency with respect to ΔA from the simulated PYTHIA sample Simulation has been weighted/corrected by:      Data-driven jet energy resolution scale factors jet-by-jet (CMS PAS JME-10-011) Semileptonic branching fraction scale factors for direct B hadron to muon decays jet-by-jet (presented herein) Data trigger efficiency event-by-event (presented herein) Data-driven muon reco. and ID efficiency scale factor, muonby-muon and mu-jet-by-mu-jet (CMS PAS MUO-10-004) Beauty, charm, and light b-tagging efficiency scale factors for TCHEM and TCHPT jet-by-jet (Official CMS SFs) Brian L. Dorney 07/03/13 Dissertation Defense 52
  53. 53. Jet Energy Resolution Scale Factor  Corrects the JER in simulated samples to what is observed in data p  prime T =p Gen T  SF JER⋅ p Reco T −p Gen T  SFJER reported in CMS PAS JME-10-011 JM E10 - 01 1 SFJER = Brian L. Dorney 07/03/13 Dissertation Defense 53
  54. 54. Branching Fraction Scale Factor   PDG branching fraction: 0.0029 B  B     X  PDG = 0.10956−0.0025 PYTHIA branching fraction: −3 B  B     X  PYTHIA = 0.1048±1.663⋅10  Measurements made from B+, B0, B0s, b-baryons, Bc, and charge conjugates   For both PDG and PYTHIA numbers given above Cascade b → c → μX decays are not considered in above PDG or PYTHIA numbers  They are not direct decays Brian L. Dorney 07/03/13 Dissertation Defense 54
  55. 55. Branching Fraction Scale Factor  For true flavor b jets w/direct b to mu decays  SF BF =  B PDG B PYTHIA  0.027 = 1.044− 0.024 For true flavor b jets w/o direct b to mu decays  non−  SF BF  = 1 − B PDG  1 − B PYTHIA 0.0032 = 0.9948−0.0028 Use the hadron ancestry chain method to identify which case generator-level true flavor b jets belong to  Reconstructed true flavor b jets use their matched generator-level jets to determine which case they belong to Brian L. Dorney 07/03/13 Dissertation Defense 55
  56. 56. Muon Reconstruction and Identification Efficiency Scale Factor  Efficiency to reconstruct and identify muons in CMS detector presented in CMS PAS MUO-10-004   For both data and simulated samples M U O -1 000 4 Observables obtained from tight muons (or the jets they are found w/in) are weighted by muon-by-muon (jet-by-jet) with the muon reconstruction and identification efficiency scale factor Brian L. Dorney 07/03/13 Dissertation Defense 56
  57. 57. B-Tagging Efficiency Scale Factors  Two sets of functions, { SF b , SF c , SF l }   Note SFc = SFb with double the quoted uncertainty   Separate functions for light, charm, and beauty jets   One set for each TCHEM and TCHPT Parameterized in terms of jet pT Scale factor functions are used jet-by-jet in simulated events Randomly upgrades (degrades) tagged (untagged) jets in simulation  Ensures b-tagging efficiencies in simulated events agree with what is observed in data Brian L. Dorney 07/03/13 Dissertation Defense 57
  58. 58. B-Tagging Efficiency Scale Factors    Jet with transverse momentum pT and flavor i will SF i = SF i  pT  and  Sim. =  Sim.  pT  have i i Obtain a uniformly distributed random number R such that R ∈ [ 0, 1 ] For SF i 1 & jet is untagged, calculate 1− SF i f= SF i 1− Sim. i    If R < f, tag the jet (i.e. upgrade) This is the fraction of jets we need to tag in simulation For SF i 1 & jet is tagged If R > SF i untag the jet (i.e. downgrade)   This is the fraction of jets we fail to tag in data Brian L. Dorney 07/03/13 Dissertation Defense 58
  59. 59. TCHEM B-Tagging Efficiency Scale Factor  Brian L. Dorney 07/03/13 Dissertation Defense Note SFb = SFc with twice the uncertainty 59
  60. 60. TCHPT B-Tagging Efficiency Scale Factor  Brian L. Dorney 07/03/13 Dissertation Defense Note SFb = SFc with twice the uncertainty 60
  61. 61. B-Tagging Efficiency Scale Factors, Factorizable at Low ΔR?   Study conducted by D. Bloch at my request Looked at b-tagging efficiency scale factors in dijet events    D. Bloch, b tag meeting, 12th Dec. 2012 Mu-jet tagged by TCHEM Non-mu-jet (“away- jet”) tagged by TCHPT Conclude scale factors are factorizable at low ΔR D. Bloch, b tag meeting, 12th Dec. 2012 Brian L. Dorney 07/03/13 Dissertation Defense 61
  62. 62. PYTHIA Hard QCD Process  All hard scattering processes of the form:   qi qi  q j q j  qi qi  g g  qi g  qi g  g g  qi qi   q i q j  qi q j gg gg Where q is any flavor quark (top excluded) and g is a gluon Brian L. Dorney 07/03/13 Dissertation Defense 62
  63. 63.  p T in PYTHIA Mandelstam Variables  Where pi are 4-vectors s =  p A p B  t =  p A − pC  2 u =  p A− p D   2 2 pC pD time  pA pB  Form pT  1  pT =  t u −  m3 m4   s Brian L. Dorney 07/03/13 Dissertation Defense 63
  64. 64. Infrared & Collinear Safe Jet Algorithms   Jet definition is insensitive to “infrared and collinear divergences” What does this Mean?   Theoretical predictions of the inclusive jet cross section must be finite at all orders Experimentally the jet definition does not drastically change in the presence of additionally emitted collinear or soft particles  i.e. Event topology/jet multiplicity is relatively constant Brian L. Dorney 07/03/13 Dissertation Defense 64
  65. 65. Jet Matching  Before the Selection record the ΔR of all possible reconstructed and generator-level jet pairings    For conservative measure apply ΔR matching criterion of 0.25 For reco jets with pT > 10 GeV    First inflection point at ΔR ≈ 0.3 1.19% remain unmatched 0.01% have two possible matches, no jet with three possible matches Fraction of unmatched reco jets with pT > 30 GeV is ≈0.1% Brian L. Dorney 07/03/13 Dissertation Defense 65
  66. 66. Assignment of True Flavor to Jets in Simulated Samples   True flavor of a generator-level jet is determined from the jet's three highest generator-level constituents Heaviest-flavor hadron ancestor in the decay chain of these three particles is assigned as the generator-level jet's flavor   Occurrence of a generator-level particle having more than one mother in a decay chain was found to be negligible (≈0.03%) True flavor of a reconstructed jet is taken from its matched generator-level jet  True flavor of unmatched reconstructed jets assigned as light Brian L. Dorney 07/03/13 Dissertation Defense 66
  67. 67. Tight Muon Selection  Muon is both a global muon and a tracker muon.  Global track  Global track has at least one muon chamber hit.   2 Tracker track required to be matched to muon segments in at least two muon stations. Tracker track has nhits ≥ 10.   fit's  / n.D.o.F.  10. At least one of these hits is in the pixel detector Transverse impact parameter w.r.t. PV ∣d xy∣  2 mm. Brian L. Dorney 07/03/13 Dissertation Defense 67
  68. 68. Loose PFJetID  Neutral hadron energy fraction < 0.99  Neutral EM energy fraction < 0.99  Number of pfConstituents > 1  Charged hadron energy fraction > 0  Charged EM energy fraction < 0.99  Charged multiplicity > 0 Brian L. Dorney 07/03/13 Dissertation Defense 68
  69. 69. Trigger Muon Object Matching   Offline tight muons are matched to HLT_Mu7 trigger objects Matching Criteria  Only HLT_Mu7 trigger objects  ΔR between the tight muon and trigger object is less than 0.5  Matching is one-to-one   i.e. trigger objects matched to one tight muon are not considered for other matches, and vice versa Trigger object match candidates ordered by increasing ΔR  Tight muon-trigger object match with lowest ΔR is taken as the matched pair Brian L. Dorney 07/03/13 Dissertation Defense 69
  70. 70. Online Efficiency SFOnline SFOnline Online Efficiency Trigger Efficiency Weighting Comparison  Online efficiency scale factor SFOnline flat for muon pT > 8 GeV  Noticeable variation w.r.t. muon η Brian L. Dorney 07/03/13 Dissertation Defense 70
  71. 71. Trigger Efficiency Weighting Comparison  Performed analysis using simulated trigger information  Event-by-event weighting: SF Online   high    high is from the highest p muon, having a HLT_Mu7 trigger matched object,   associated to a jet  T Observe that data trigger efficiency weighting is equivalent to online efficiency scale factor weighting Brian L. Dorney 07/03/13 Dissertation Defense 71
  72. 72. Determination of Online Efficiency   Data collected by single-jet and mutlijet triggers provides statistically independent sample for online efficiency measurement Event Selection  Only one offline reconstructed muon present  Muon is associated to a jet    Association uses the jet's particle-flow constituents Jet passes TCHEM operating point (i.e. TCHE > 3.3) Object Selection  Jet with muon must have pT > 30 GeV  Muon must pass the Tight Muon Selection with |η| < 2.1 Brian L. Dorney 07/03/13 Dissertation Defense 72
  73. 73. Determination of Online Efficiency – Results   Efficiency defined as  Online = N matched / N all Nmatched → # of tight muons in a given p  or   bin, associated to a b-tagged jet, T matched with an HLT_Mu7 trigger object    Nall → # of tight muons in a given pT or  bin that are associated to a b-tagged jet  Online efficiency  Online = 85.5±1.1 stat.−1.5  syst. % 3.9 Brian L. Dorney 07/03/13 Dissertation Defense 73
  74. 74. Determination of Online Efficiency – Systematic Uncertainties  Methodology taken from CMS PAS-MUO-10-004  Independently varied the following  Increased selection beyond Tight Muon Selection  Jet b-tagging operating point changed to TCHPT   Muon's track was required to be the track that determined the jet's TCHE value With and w/o the b-tagging requirement under both the Tight Muon Selection and the more stringent muon selection Brian L. Dorney 07/03/13 Dissertation Defense 74
  75. 75. Online Efficiency Online Efficiency Determination of Online Efficiency – Systematic Uncertainties  Black: nominal distribution  Red: increased selection beyond Tight Muon Selection Brian L. Dorney 07/03/13 Dissertation Defense 75
  76. 76. Online Efficiency Online Efficiency Determination of Online Efficiency – Systematic Uncertainties  Black: nominal distribution  Blue: jet passes TCHPT operating point Brian L. Dorney 07/03/13 Dissertation Defense 76
  77. 77. Online Efficiency Online Efficiency Determination of Online Efficiency – Systematic Uncertainties  Black: nominal distribution  Green: muon's track determines jet's TCHE value Brian L. Dorney 07/03/13 Dissertation Defense 77
  78. 78.   Red: increased selection beyond Tight Muon Selection w/b-tagging Blue: increased selection beyond Tight Muon Selection w/o b-tagging Brian L. Dorney 07/03/13 Online Efficiency Purple: using tight muon selection w/o b-tagging Online Efficiency  Black: nominal distribution Online Efficiency  Online Efficiency Determination of Online Efficiency – Systematic Uncertainties Dissertation Defense 78
  79. 79. Determination of Online Efficiency – Systematic Uncertainties  Effect on online efficiency With & w/o B-tagging under Normal & Increased Selection 0.00% Increase B-Tagging -0.1% 0.00% Increased Muon Sel 0.0% +3.9% Muon's track determines TCHE 0.0% +0.6% Total  -1.5% -1.5% +3.9% 3.9 −1.5 Online efficiency  Online = 85.5±1.1 stat. Brian L. Dorney 07/03/13 Dissertation Defense  syst.% 79
  80. 80. Online Efficiency Cross Check  Efficiency of a different low-pT single-muon trigger published in CMS PAS MUO-10-004   Referred to as HLT_Mu9 Measured efficiency of HLT_Mu9 using my technique  Find agreement with published values Brian L. Dorney 07/03/13 Dissertation Defense 80
  81. 81. Preselection: Mu-jet Kinematics Brian L. Dorney 07/03/13 Dissertation Defense 81
  82. 82. Preselection: Non-mu-jet Kinematics Brian L. Dorney 07/03/13 Dissertation Defense 82
  83. 83. Track Counting Discriminators TCHE N=2 Brian L. Dorney 07/03/13 Dissertation Defense TCHP N=3 83
  84. 84. Summary of Event Selection   Number of events passing each stage of the event selection Fraction of events remaining after each stage of event selection w.r.t. previous stage allows for direct comparison of data and simulation Brian L. Dorney 07/03/13 Dissertation Defense 84
  85. 85. Δφ & ΔR Resolution  For all true flavor bb dijet pairs record  A Reco− AGen   ΔA represents Δφ or ΔR RMS of this distribution taken as resolution on ΔA Brian L. Dorney 07/03/13 Dissertation Defense 85
  86. 86. Detector Response – Revisited  Decrease Δφ detector response matrix bin size by 2    Bin size now approximately five times Δφ resolution Observe off diagonal elements in “larger” bin size are actually part of main diagonal Conclusion: bin-to-bin migration is negligible Brian L. Dorney 07/03/13 Dissertation Defense 86
  87. 87. System4 Flavor Vector Efficiency Matrix Dijet Tagging Efficiencies TCHEM  ij =  i Description First (second) letter is the flavor of the mu-jet (non-mu-jet), i, j = B or X. TCHPT j Non-b Tagging Efficiencies all X= nc all Description all Sim.   all c nc  n l Brian L. Dorney 07/03/13 nl all Yields Vector Sim.  all l Efficiency to tag a non-b jet nc n l Dissertation Defense 87
  88. 88. System4 Flavor Vector Efficiency Matrix Beta Factors Both Tag  IJ =  IJ TCHEM I TCHPT J Alpha & Gamma Factors  IJ =  IJ =   Mu Tag IJ  TCHEM I Non Mu Tag IJ TCHPT J  Brian L. Dorney 07/03/13 Yields Vector Description Ratio of dijet efficiency to single jet efficiency Description As above Define κIJ = {αIJ, βIJ, γIJ} As above Dissertation Defense 88
  89. 89. System4 Flavor Vector Efficiency Matrix Beta Factors Description Both Tag  IJ =  IJ TCHEM I TCHPT J Dijet Efficiency Example Tag Both Tag  IJ = N IJ Tag Tag N IJ  N IJ Brian L. Dorney 07/03/13 Yields Vector Ratio of dijet efficiency to single jet efficiency Description Example dijet efficiency, similarly for other two cases Dissertation Defense 89
  90. 90. System4 Flavor Vector Efficiency Matrix Purity Definition P BB =   BB  BB f BB  / f Brian L. Dorney 07/03/13 Yields Vector Description Both First (second) letter is the flavor of the mu-jet (non-mu-jet), i, j = B or X. Dissertation Defense 90
  91. 91. System4 –  IJ Factors, Δφ Brian L. Dorney 07/03/13 Dissertation Defense 91
  92. 92. System4 –  IJ Factors, ΔR Brian L. Dorney 07/03/13 Dissertation Defense 92
  93. 93. System4 –  IJ Factors, Shape Investigation    Factors generally increase with decreasing angular separation between two jets Investigated whether factor behavior is due to differing kinematic behavior Investigated shape of factors in bins of jet transverse momentum and absolute pseudorapidity Brian L. Dorney 07/03/13 Dissertation Defense 93
  94. 94. System4 –  IJ Factors, Binned by Mu-Jet pT  Approximately uniform shape over all pT bins Brian L. Dorney 07/03/13 Dissertation Defense 94
  95. 95. System4 –  IJ Factors, Binned by Jet pT  Approximately uniform shape over all pT bins Brian L. Dorney 07/03/13 Dissertation Defense 95
  96. 96. System4 –  IJ Factors, Binned by Non-Mu-Jet pT  Approximately uniform shape over all pT bins Brian L. Dorney 07/03/13 Dissertation Defense 96
  97. 97. System4 –  IJ Factors, Binned by Jet |η|  Uniform shape over all |η| bins Brian L. Dorney 07/03/13 Dissertation Defense 97
  98. 98. System4 –  IJ Factors, Binned by Jet |η|  Uniform shape over all |η| bins Brian L. Dorney 07/03/13 Dissertation Defense 98
  99. 99. System4 –  IJ Factors, Binned by Jet |η|  Uniform shape over all |η| bins Brian L. Dorney 07/03/13 Dissertation Defense 99
  100. 100. System4 –  IJ Factors, Track Mismatching   Investigated possibility of track mismatching as a contributor to shapes of κIJ factors For each mu-jet (non-mu-jet) track that determines jet's TCHE (TCHP) referred to as the b-tagging track   ΔR between parent mu-jet (non-mu-jet) and b-tagging track plotted against the ΔR between the adjacent non-mu-jet (mu-jet) and the b-tagging track   Symbolically referred to as trackTCHE (trackTCHP) for the mu-jet (non-mu-jet) Here “adjacent” refers to the other member of the dijet object In O(107) events, O(10) events have instances of track mismatching  i.e. Negligible, too rare to describe shapes of κIJ factors Brian L. Dorney 07/03/13 Dissertation Defense 100
  101. 101. System4 – Track Mismatching Mu-Jet Passes TCHEM, b-tagging = trackTCHE    Imagine y=x line Entries falling below line indicate track mismatching i.e. mu-jet's b-tagging track is closer in ηφ-plane to the non-mu-jet Brian L. Dorney 07/03/13 Dissertation Defense 101
  102. 102. System4 – Track Mismatching Non-Mu-Jet Passes TCHPT, b-tagging = trackTCHP    Imagine y=x line Entries falling above line indicate track mismatching i.e. non-mu-jet's b-tagging track is closer in ηφ-plane to the mu-jet Brian L. Dorney 07/03/13 Dissertation Defense 102
  103. 103. System4 – Track Mismatching Both Jets Pass Operating Pts, b-tagging = trackTCHE    Imagine y=x line Entries falling below line indicate track mismatching i.e. mu-jet's b-tagging track is closer in ηφ-plane to the non-mu-jet Brian L. Dorney 07/03/13 Dissertation Defense 103
  104. 104. System4 – Track Mismatching Both Jets Pass Operating Pts, b-tagging = trackTCHP    Imagine y=x line Entries falling above line indicate track mismatching i.e. non-mu-jet's b-tagging track is closer in ηφ-plane to the mu-jet Brian L. Dorney 07/03/13 Dissertation Defense 104
  105. 105. System4 – Minimum ΔR Separation  Spike in first bin of ΔR of κIJ factors   Could be caused by poorly reconstructed and/or fake jets being used in System4 dijet pair Investigated requiring minimum ΔR separation between jets used in dijet pair Brian L. Dorney 07/03/13 Dissertation Defense 105
  106. 106. System4 – Minimum ΔR Separation   Reduction in spiking κIJ behavior when going from ΔR > 0.5 to ΔR > 0.6 Values of κIJ don't vary substantially when moving from ΔR > 0.6 to ΔR > 0.7 Brian L. Dorney 07/03/13 Dissertation Defense 106
  107. 107. System4 – Correlation of  IJ Factors  Order pairs of κIJ's made from all bin of ΔA   i.e. { { (αIJ, βIJ) }, { (αIJ, γIJ) }, { (γIJ, βIJ) } } Correlation coefficients ρ determined from each set of ordered pairs  αIJ weakly correlated with βIJ and γIJ  βIJ and γIJ strongly correlated Brian L. Dorney 07/03/13 Dissertation Defense 107
  108. 108. System4 – Event Rejection Concerns mu-jet multi.  Fraction of events that would be rejected for System4 is negligible    non-mu-jet multi. In data (sim.) for cut stage 2, TCHPT applied to non-mu-jet, have 0.8% (0.7%) events with two or more non-mu-jets passing TCHPT In data (sim.) for cut stage 3, TCHEM applied to mu-jet, have 0.14% (0.15%) events with two or more mu-jets passing TCHEM Note: the event rejection is not used for cut cases of System4 Brian L. Dorney 07/03/13 Dissertation Defense 108
  109. 109. System4 – Closure Test  Split Simulated PYTHIA sample into two statistically independent datasets     Efficiency matrix taken from even events Yields vector taken from odd events System4 solution obtained from toy MC method in odd events compared to the true solution in odd events Four closure tests performed  Nominal  Using κIJ = 1  Reweighting gluon splitting events by factor of ½  Reweighting gluon splitting events by factor of 2 Brian L. Dorney 07/03/13 Dissertation Defense 109
  110. 110. System4 – Closure Test, ΔR   Better agreement using κIJ Behavior of attributed to small statistics of XB dijet case Brian L. Dorney 07/03/13 Dissertation Defense 110
  111. 111. System4 – Closure Test, ΔR   With GSP events reweighted by factor of ½ Behavior of attributed to small statistics of XB dijet case Brian L. Dorney 07/03/13 Dissertation Defense 111
  112. 112. System4 – Closure Test, ΔR   With GSP events reweighted by factor of 2 Behavior of attributed to small statistics of XB dijet case Brian L. Dorney 07/03/13 Dissertation Defense 112
  113. 113. System4 – Closure Test, Δφ   Better agreement using κIJ Behavior of attributed to small statistics of XB dijet case Brian L. Dorney 07/03/13 Dissertation Defense 113
  114. 114. System4 – Closure Test, Δφ   With GSP events reweighted by factor of ½ Behavior of attributed to small statistics of XB dijet case Brian L. Dorney 07/03/13 Dissertation Defense 114
  115. 115. System4 – Closure Test, Δφ   With GSP events reweighted by factor of 2 Behavior of attributed to small statistics of XB dijet case Brian L. Dorney 07/03/13 Dissertation Defense 115
  116. 116. System4 – Results From Data, ΔR  Behavior of fXB attributed to small statistics of XB dijet case Brian L. Dorney 07/03/13 Dissertation Defense 116
  117. 117. System4 – Results From Data, Δφ  Behavior of fXB attributed to small statistics of XB dijet case Dissertation Defense Δφ Δφ Brian L. Dorney 07/03/13 Δφ Δφ 117
  118. 118. B Jet Transverse Momentum Residuals Post Preselection  Post Final Selection Post Final Selection Reco Gen For true flavor b jets and their matched generator-level jets, studied: p T − pT    Means of distributions slightly positive with large RMS Conclude that the residuals are consistent with zero within their statistical uncertainties A small fraction of final selected true flavor b jets with pT > 30 GeV are matched with generator-level jets with pT < 30 GeV  Vast majority of these cases are within one standard deviation of 30 GeV Brian L. Dorney 07/03/13 Dissertation Defense 118
  119. 119. Shape of Jet pT in Final Event Sample, Binned by Δφ  Highest pT jet in bb dijet candidate 0   4 Highest pT Jet    4 2 Highest pT Jet  3  2 4 Highest pT Jet Brian L. Dorney 07/03/13 Dissertation Defense 3   4 Highest pT Jet 119
  120. 120. Shape of Jet pT in Final Event Sample, Binned by Δφ  Lowest pT jet in bb dijet candidate 0   4 Lowest pT Jet    4 2 Lowest pT Jet  3  2 4 Lowest pT Jet Brian L. Dorney 07/03/13 Dissertation Defense 3   4 Lowest pT Jet 120
  121. 121. Shape of Jet pT in Final Event Sample, Binned by ΔR 0.6 R1.4 1.4 R2.3 2.3 R3.2 Leading Jet pT Leading Jet pT Leading Jet pT 3.2 R4.1  Highest pT jet in bb dijet candidate Brian L. Dorney 07/03/13 Leading Jet pT Dissertation Defense 4.1 R5.0 Leading Jet pT 121
  122. 122. Shape of Jet pT in Final Event Sample, Binned by ΔR 0.6 R1.4 1.4 R2.3 2.3 R3.2 Leading Jet pT Leading Jet pT Leading Jet pT 3.2 R4.1  Lowest pT jet in bb dijet candidate Brian L. Dorney 07/03/13 Leading Jet pT Dissertation Defense 4.1 R5.0 Leading Jet pT 122
  123. 123. Systematic Uncertainty, Shape of Online Plus Offline Eff.    Differing kinematic behavior between data and simulation could adversely affect cross section Affect would be most pronounced in uncertainties in the shape of the online plus offline selection efficiency Investigated in similar manner to what was presented in JHEP03(2011)136.  However analysis performed in three jet |η| bins Brian L. Dorney 07/03/13 Dissertation Defense 123
  124. 124. Systematic Uncertainty, Shape of Online Plus Offline Eff.    Top: difference between data and simulation in the average pT of the highest pT jet in the bb dijet candidate Bottom: online plus offline selection efficiency w.r.t. pT of highest jet in bb dijet candidate All plots from final selected events Brian L. Dorney 07/03/13 Dissertation Defense 124
  125. 125. Systematic Uncertainty, Shape of Online Plus Offline Eff.  Differences btw data and sim. used to modify  Sel via:   Prime Sel   〈 pT 〉 Sim.   Performed in three |ηjet| bins    =  Sel⋅ 1   〈 pT 〉 Data  −  〈 pT 〉 Sim.  { [0,2.4),[0.0.9),[0.9,2.4)} Performed using highest and lowest pT jet in the bb dijet candidate  Six variations in total Brian L. Dorney 07/03/13 Dissertation Defense 125
  126. 126. Systematic Uncertainty, Shape of Online Plus Offline Eff.  Differences btw data and sim. used to modify  Sel via:   Prime Sel   〈 pT 〉 Sim.   Performed in three |ηjet| bins    =  Sel⋅ 1   〈 pT 〉 Data  −  〈 pT 〉 Sim.  { [0,2.4),[0.0.9),[0.9,2.4)} Performed using highest and lowest pT jet in the bb dijet candidate  Six variations in total Brian L. Dorney 07/03/13 Dissertation Defense 126
  127. 127. Systematic Uncertainty, Shape of Online Plus Offline Eff.  Differences btw data and sim. used to modify  Sel via:   Prime Sel   〈 pT 〉 Sim.   Performed in three |ηjet| bins    =  Sel⋅ 1   〈 pT 〉 Data  −  〈 pT 〉 Sim.  { [0,2.4),[0.0.9),[0.9,2.4)} Performed using highest and lowest pT jet in the bb dijet candidate  Six variations in total Brian L. Dorney 07/03/13 Dissertation Defense 127
  128. 128. Systematic Uncertainty, Shape of Online Plus Offline Eff.   Brian L. Dorney 07/03/13 Modified online plus offline selection efficiencies used to recompute the cross section Maximum difference, for each bin of ΔA, between nominal cross section and the six new cross sections taken as systematic uncertainty Dissertation Defense 128
  129. 129. Systematic Uncertainty, Shape of Online Plus Offline Eff.   Brian L. Dorney 07/03/13 Modified online plus offline selection efficiencies used to recompute the cross section Maximum difference, for each bin of ΔA, between nominal cross section and the six new cross sections taken as systematic uncertainty Dissertation Defense 129
  130. 130. Systematic Uncertainty, Signal Purity  Mismodeling of the shapes of kIJ factors    System4 was solved using varied αIJ and using simultaneously varied βIJ and γIJ true Closure Difference f BB − f BB between System4 solution and the true solution obtained in the nominal closure test    Varied shapes of efficiencies in the numerators of the kIJ equations in identical fashion to what was done for the shape of the online plus offline selection efficiency prime true Closure Solution in data modified by f BB = f BB   f BB − f BB  prime Purity in data recalculated using f BB Possible differences in relative fraction of charm and light jets between data and simulation The value of n c  n l  is varied up and down by a factor of two while holding the value n all  n all  of fixed. l c all   all Cross section recalculated for each of the above variations  Differences between nominal and varied cases are added in quadrature and assigned as the systematic uncertainty for signal purity Brian L. Dorney 07/03/13 Dissertation Defense 130
  131. 131. Systematic Uncertainty, Muon Reco & ID Eff. Scale Factor    Muon reconstruction and identification scale factor taken from CMS PAS MUO-10-004 Observables obtained from tight muons (or the jets they are found w/in) are weighted muon-by-muon (jetby-jet) with the scale factor For systematic uncertainty  Scale factor is varied up (down) by its total uncertainty resulting in a -1.2% (+1.2%) change in the total cross section Brian L. Dorney 07/03/13 Dissertation Defense 131
  132. 132. Systematic Uncertainty, B-Tagging Eff. Scale Factors  B-tagging scale factors {SF b , SF c , SF l } for TCHEM and TCHPT are varied up and down by their uncertainties   Both scale factors changed at the same time in the same direction Beauty and charm scale factors are correlated, varied simultaneously    Light scale factor uncorrelated, varied independently Results of variations added in quadrature Scale factor variations up (down) resulted in a -3.2% (+6.7%) change in total cross section Brian L. Dorney 07/03/13 Dissertation Defense 132
  133. 133. Systematic Uncertainty, JEC and JER  The jet energy correction is varied up and down by its uncertainty   The up (down) variations of the JEC resulted in a -5.6% (+9.1%) change in the total cross section The JER in the simulation is smeared jet-by-jet via prime Reco p T = p Gen  SF JER⋅ p T − p Gen  T T SFJER =  JM E10 -0 11 SFJER variations resulted in a +1.7% change in the total cross section Brian L. Dorney 07/03/13 Dissertation Defense 133
  134. 134. Systematic Uncertainty, Fragmentation     An additional PYTHIA sample was generated using Peterson/SLAC fragmentation function Generator-level jet pT distributions between two PYTHIA samples are compared Differences are used to modify the reco and generator-level jet pT in the nominal case Same is done for muons Brian L. Dorney 07/03/13 Dissertation Defense 134
  135. 135. Systematic Uncertainty, Fragmentation  The transverse momentum of reconstructed and generator-level jets and muons modified via p   prime T f Lund  pT  − f Peterson  pT  = pT  m Modifications are performed before the selection is applied Effect on total cross section found to be +0.4% Brian L. Dorney 07/03/13 Dissertation Defense 135
  136. 136. Systematic Uncertainty, Proton PDFs   Uncertainty due to proton PDFs assessed by reweighting technique Contribution of PDF to cross section can be assigned a weight wi 1 1  k1 k2    h1 h2  Y  =∫0 dx 1∫0 dx2 ∑ ∑ f k  x 1  f k  x 2   q1  x1 P 1   q 2  x 2 P 2   y k1 1 1 k2 2 1   k  k   h1 h2  Y  =∫0 dx 1∫0 dx2 ∑ ∑ f k  x 1  f k  x 2  w i  q1  x1 P 1   q2  x 2 P 2   y k1 k2 1 2 1 2 f k  x1 ; Si  f k  x2 ; S i  Where wi given by: w i = f  x ; S  f  x ; S  k 1 0 k 2 0 1  1 Brian L. Dorney 07/03/13 2 2 Dissertation Defense 136 
  137. 137. Systematic Uncertainty, Proton PDFs  In practice this means simulated events are reweighted by wi   Three PDF sets were used in reweighting   Maximum deviation per bin of ΔA between the nominal cross section and the reweighted cross sections is taken as the systematic uncertainty CTEQ66m, MSTW2008-nlo, NNPDF2.0 Effect on total cross section found to be -1.0% wi= f k  x1 ; Si  f k  x2 ; S i  1 f k  x1 ; S0  f k  x2 ; S0  1 Brian L. Dorney 07/03/13 2 Dissertation Defense 2 137
  138. 138. Systematic Uncertainty, Summary  Right: systematic uncertainties on total cross section   Uncertainty sources listed under the shape variations and theory headings do not follow standard “down/up” description   Down/upwards headings give direction of parameter variation while the sign of the value gives effect on total cross section Sign of the value again gives effect on total cross section Total systematic uncertainty on total cross section +13.1/-9.8%  Dominat systematics are the JEC and b-tagging scale factors Brian L. Dorney 07/03/13 Dissertation Defense 138

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