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A Measurement of Top Quark Mass in lepton + jets channel

A Measurement of Top Quark Mass in lepton + jets channel. Vivek Parihar. Overview. General picture of Top Quark Top quark Production & motivation for precise mass measurement. Experimental Setup : Fermilab Chain of Accelerators Various components of the DZero detector

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A Measurement of Top Quark Mass in lepton + jets channel

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  1. A Measurement of Top Quark Mass in lepton + jets channel Vivek Parihar

  2. Overview • General picture of Top Quark • Top quark Production & motivation for precise mass measurement. • Experimental Setup : Fermilab Chain of Accelerators • Various components of the DZero detector • Top Quark Signature through its decay • Template Method • Simultaneous template fits and uncertainty predictions.

  3. General Picture of Top Quark • Top quark is an elementary particle in the Standard Model characterized by a heavy mass (~170 GeV) and a very small lifetime (~10-25 sec) • Precision electroweak data requires a weak isospin partner of b-quark ( with charge +2/3 and large mass.) • Short lifetime => decays immediately before ‘hadronizing’ (forming bound states of mesons/baryons), which facilitates study of a ‘free bare’ quark.

  4. Top Quark Production • Tevatron is the only existing top production machine. • Run II (since 2001): s =1.96 TeV • Run II goal is to have 4-8 fb-1 of integrated luminosity on tape • Top quarks are mainly produced in pairs via strong interaction • tt (1.96 TeV)~ 6.8 pb • One top quark pair is produced in every 1010 inelastic collisions.

  5. Most recent Top mass measurements at DZero • The best measurement in lepton + jets • channel has an uncertainty of ~ 1.5 GeV at an integrated luminosity of 1 fb-1

  6. A fundamental parameter of Standard Model One loop heavy fermion and Higgs-boson correction to W self-energy • At the tree level in Standard Model, there are mainly 3 parameters • (appearing in the prefactor of MW) that are known to a great precision : GF is • the Fermi constant, cosW = MW/MZ and  being the electromagnetic coupling • constant. • r contains the radiative corrections with the following contributions : Hence, precision measurements of Mtop alongwith MW constrains the, yet eluded, Higgs-boson mass.

  7. Higgs Mass Prediction • The gauge theory of particle physics • predicts all particles to be massless. The theory is inducted with a “Higgs” field which permeates all space and to which the particles couple and appear massive. • Standard Model predicts a lighter, yet eluded, Higgs Boson, whose mass through r is constrained by the Mtop & the MW . Such constraints on MH can help direct and future Higgs searches and constitutes another stringent test of SM when compared to limits from direct searches or mass measurements from an eventual discovery. Predicted Higgs mass from global electroweak data: mH =80+36-26 GeV (< 153 GeV at 95% CL) Direct search from LEP II: mH > 114.4 GeV at 95% CL

  8. Experimental Setup (Fermilab Chain of accelerators)

  9. The DZero Detector Tracking sys. EM cal. Had cal. Muon sys. jets muons electrons photons Tracking: Silicon vertex detector (SMT) Central Fiber Tracker (CFT) 2 T Superconducting Solenoid. Preshowers EM/HAD Calorimeter: Central, |h|<1.1 Forward, |h|<4.2 Muon system: 1.8 T iron toroid. 9

  10. Detector Effects & Challenges • From all the detector components, • what escapes is a neutrino which can be conferred only indirectly. Since initially, • All the momentum is in the longitudinal • direction, the final momenta in the transverse plane should add up to zero. • Any momentum imbalance in the transverse plane indicates the same carried by a neutrino. • Quarks, anti-quarks and gluons produced in a process undergo ‘fragmentation’ process to form particle JETS, these undergo nuclear interactions • in hadronic calorimeter to deposit energy in cluster that is termed as ‘calorimeter jet’.

  11. Top Quark Decay & Signature • SM top quark decays weakly through • a mediating W boson, before hadronization • W decay determines the experimental signature • DZerohas vertex detectors to find • displaced vertices from decay of long-lived • b-hadrons (~3mm for a 40 GeV b-quark) • …..crucial to reduce physics background !

  12. Lepton + Jets Channel • “Golden Channel” • Branching ratio ~ 30% • Signal/Background = ¼ - 11/1 • (depending on the b-tag) • 1 e/µ with large pT + Energy imbalance, high missing ET • 4 jets with large ET + 0,1 or 2 b-tags

  13. Backgrounds & ambiguities • Combinotorial quark/jet ambiguity : 12 (0 b-tag), 6 (1 b-tag), 2 (2 b-tags) • Well defined kinmatics : neutrino momentum partly derived from missing ET • Dominant background types: • - Wbb, Wcc, Wc • - W + light quarks • -non-W + light quarks • (fake b-tags)

  14. Template Method • Calculate a per-event observable correlated with Mtop . • Compare simulated distributions (Signal+background) • with varying Mtop with data to obtain Mtop Eg. The “reconstructed” top mass could be used as per-event observable by minimizing the above 2 with various kinematic constraints.

  15. Thesis Plan • Tevatron (CDF & DZero) have a combined precision of 1.2 % on the top mass Mtop = 171.4  1.9 GeV / c2 • With the new data (~5 fb-1), a 1% precision could be reached to push mtop~1 GeV • In this effort, a raw study was done to have a framework of measurement (unbiased and efficient in time) ready for the new data.

  16. Overview • OBJECTIVE: develop a fast algorithm for the measurement of the top quark mass in l + jets channel to complement the computing intensive matrix element technique. • currently studied a template fit method using only ttbar signal MC in the e + jets channel • results shown here are based on the output of a kinematical fitter package. • event selection was done on the Monte Carlo files corresponding to 1 fb-1. • templates are constructed using the mass for each event for which the Kinematical Fitter obtains the lowest chi-squared.

  17. mtop=170 GeV Templates mtop=155 GeV mtop=195 GeV Each template is fitted with Landau convoluted with Gaussian + Pure Gaussian with a total of 7 parameters

  18. Fit Function : Landau Convolution Gaussian Distribution

  19. Fit Parameters • show that parameters vary smoothly with mtop • Landau * Gauss

  20. Fit Parameters Gaussian

  21. 2 D Simultaneous Fit • express the 7 parameters as functions of mtop • fit all templates simultaneously Function used : Landau*Gaussian + Gaussian with total 7 internal parameters.

  22. 2 D Simultaneous Fit • results Landau* gauss parameters Width of Landau      a0 - a1*(mtop-175) Most Probable         a2 + a3*(mtop-175) Area                       a4*(1- a7) GSigma                   a5+ a6*(mtop-175) Pure Gaussian Norm                     a4*a7 Most Probable        a8+ a9*(mtop-175) Sigma                      a10 a0 = 8.82   ;    a1= 0.02    ;  a2 = 162.82    ;  a3 = 0.49   ; a4 = 4.69 ;   a5 = 19.16  ;   a6 = 0.17   ; a7 = 0.14 ;   a8 = 175.32 ;   a9 = 0.96  ;    a10 = 11.6

  23. 2 D Simultaneous Fit • superimpose template parametrizations

  24. PART II : Ensemble Tests • To check whether the method gives a measurement consistent within its resolution, we perform Ensemble Tests. • Testing requires a series of ‘mock’ experiments to be caried out by producing pseudo-data sets from MC. -> 1000ensembles with 200 ttbar events each, randomly picked from the data (MC signal) files. -> parametrized templates used to calculate the negative log likelihood for each ensemble of 200 events.

  25. Ensemble tests • - log likelihood plot and quadratic fit for a sample ensemble (mtop = 155 GeV) The fit procedure, determines the measured top mass by, finding the minimum of the Log likelihood curve. Assuming a Gaussian Likelihood curve near the minimum, the statistical error is taken as the interval that contains 68% of its integral =>  Ln(L) = 0.5

  26. Ensemble tests (Expectations) • Does the estimator have a bias? Unbiased => Avg. of measured masses  consistent with known input value for a range of hypothetical mtop. • Expected resolution on measurement ? The spread of the measurements from the mock experiments. • Errors consistent with stat. spread? Large # ensembles => Pull should be a Gaussian with mean = 0 and RMS = 1

  27. Input Mass = 175 GeV Pull distribution Mean measured 0.2527 (1.03) 174.2 (3.289)

  28. Calibration Plots :

  29. Conclusion & Future Plans • using 200 ttbar signal events • measure the top quark mass without bias • expected statistical uncertainty  3.2 GeV With 5 fb-1 data, we expect roughly 1000 events and the statistical uncertainity to scale down by a factor of ~ sqrt(5) • At a preliminary stage, the signal studies show promising results and the method is expected to evolve with inclusion of background studies.

  30. BACK UP SLIDES

  31. Matrix element • Calculate a per-event probability density from ME for sig + back as a fn of mtop • Multiply all the probabilities to construct likelihood to get mtop

  32. 165 GeV (2.919) 159.9 GeV(2.986) 154.4 GeV (3.31) 0.0394 (1.002) 0.2046 (1.116) 0.0171 (0.974)

  33. 185.2 GeV(4.467) 190.4 GeV (3.108) 193.8 GeV (4.488) 0.378 (1.292) -0.1098 (0.9465) -0.0299 (1.377)

  34. One top pair is produced every 1010 inelastic Collision at D0. 0.1 b Top Quark Produced at Fermilab x100 At the Tevatron, top quarks are primarily produced in pairs via the strong interaction. The top quark almost always decays to Wb.The top quark is the only quark that decays before hadronizing (production of jets of particles). 15% of the time top is produced by a fusion of two gluons instead of qq anhiliation. Preliminary Oral Exam 35

  35. Template method – data are compared with signal and background MCs • Reconstruct invariant top mass in each event. For example • Compute 2as follows: • Use kinematic constraints • Minimize with MT= mfit as a free parameter

  36. Create templates (Prob. Density Functions): • plot mfitfor the minimal2 and create PDFs • signal distributions for different simulated top masses (mtop) • background distributions • Using the PDFs perform maximum likelihood fit to obtain the most probable value from the data Signal templates for mtop = 155,170 and 195 GeV

  37. b-jet b b p p jet b-jet jet E Tmis   38

  38. Consistency Check The knowledge of top quark mass is necessary to compare as precisely as possible, the theoretical predictions and measurements of ttbar cross sections. An eventual discrepancy could be a sign of new physics. Cross Section of ttbar production as a function of center of mass energy for the theoretical predictions.

  39. Measuring the Energy Scale of Jets in Top Events The jet energy scale represents the dominant source of systematic uncertainty: Extend the Matrix Element method by one additional parameter: JES: global scale factor relative to the reference scale. Overall JES is a free parameter in the fit, constrained in situ by the mass of the W decaying hadronically. W -> jj is used to measure JES. The likelihood will present a maximum when the correct W mass is reconstructed. The top quark mass is obtained from a two-dimensional fit which yields both the statistical and systematic jet energy scale uncertainty. l b-jet n W+ t t jet Mjj(W) W- jet b-jet Preliminary Oral Exam 40

  40. Templates mtop=170 GeV mtop=155 GeV 155 mtop=195 GeV

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