Likelihood Method

Contents

This likelihood method is the same one used in 1-D top mass analysis. The fit function consists of a Gamma and two Gaussian probability density function whose parameters are linearly depended on the top width.

  1. PEs with Width 1.5 GeV
  2. PEs with width 30 GeV
  3. Study on the Tails of the mass distributions
  4. Study on the Top Mass dependency
  5. Study on with and without Top Mass constraint
  6. Systematic Uncertanties on Likelihood

The linear dependency on the top width in the fit function did not adequately capture the shapes of the top mass distribtutions. Thus, we added the quadratic dependency on the top width in the fit funciton.

  1. PEs with fits that has quadratic dependency on the width

  1. Pseudo-experiments for ttopkl (Pythia 175 GeV, Top Width 1.5 GeV, 680 pb-1)

  2. Input top width 30 GeV
  3. 2tag_080250
    width+1sigma(2tag+1tagT)
    55 GeV

  4. Tails of the top mass distributions (Pythia 175 GeV, Top Width 1.5 GeV, 680 pb-1)
  5. We made the fit function based on the shapes of 80-250 GeV, 80-300GeV, and 80-380GeV (full range) distributions. The PE shows that the tails affect our results, but not so significantly.

    1. fit range 80-300 GeV
      1. 2 tag
        2tag_080250
      2. 1 tag Tight
        2tag_080250
      3. 2 tag + 1 tag T
        2tag_080250

    2. fittng range 80-250 GeV
      1. 2 tag
        2tag_080250

    3. Comparisons
    4. Fit Range width+1sigma(2tag) width+1sigma(1tagT)width+1sigma(2tag+1tagT)
      full 18 GeV 18 GeV 13 GeV
      80-300 GeV 20 GeV 19 GeV 13 GeV
      80-250 GeV 21 GeV

  6. Dependency on Top Mass samples for 2tag+1tagT samples (Herwig Top Mass = 170, 172.5, 175, 177.5, 180 GeV)
  7. input mass affects width a little but not much...

    Herwig PE
    Input Top Mass width (GeV) width+1sigma(GeV)
    Herwig 170 GeV 6.6 18 GeV
    Herwig 172.5 GeV 5.1 17 GeV
    Herwig 175 GeV 0.97 12 GeV
    Herwig 177.5 GeV 0.13 12 GeV
    Herwig 180 GeV 2.9 15 GeV

  8. Start the fit from Width=30GeV instead of 1.5 GeV to see if the likelihood is finding a local minimum or not (2tag+1tagT sample).
  9. 2tag_080250
    width+1sigma(2tag+1tagT)
    12 GeV

  10. Top Width at 95% Confidence Level (955pb-1 statistics, 1 b tag T and 2 b tag samples)
  11. These are the psuedo experiments for measured top width (&Gammatopmeas.) using the likelhood method. The &Gammatopmeas. histograms for each input width 0-100 GeV are shown along with the arrows marking the 95% points. On the left (with red arrows) is the output using the massAna with width constraint 1.5 GeV and on the rigth (with blue arrows) is the output using no constraint in the massAna.
    Constraint 1.5 GeV 2tag_080250
    No constraint 2tag_080250

    Confidence Belt
    From these &Gammatopmeas. distributions, we evaluate 95% CL of &Gammatopmeas. for each input top width. These values are plotted in a graph below.
    Constraint 1.5 GeV 2tag_080250
    No constraint 2tag_080250

    The 3rd deg polynomial fit to the confidence belt. The fits aren't so good...
    Constraint 1.5 GeV 2tag_080250
    No constraint 2tag_080250

    For each event in the psuedo experiments for &Gammatopmeas., a true top width, &Gammatoptrue, is extracted using the fitted polynomial to the confidence belt.
    Constraint 1.5 GeV, &Gammatopinput=1.5GeV 2tag_080250
    No constraint, &Gammatopinput=1.5GeV 2tag_080250

    Constraint 1.5 GeV, &Gammatopinput=30 GeV 2tag_080250
    No constraint, &Gammatopinput=30 GeV 2tag_080250
    Limits at 95% CL
    &Gammatopinput 1.5GeV constraintNo constraint
    1.5 GeV 16 GeV 18 GeV
    30 GeV 77 GeV 82 GeV

  12. Systematic Uncertainties on the Likelihood
    1. Our Template for Input Top Width 1.5 GeV. MC sample is generated by Pythia using the leption filter.
    2. 2tag_080250
      Output of Liklihood PE. (X axis are measured top width).

    3. JES
    4. 2tag_080250

    5. ISR
    6. 2tag_080250

    7. FSR
    8. 2tag_080250

    9. Generator
    10. Pythia vs Herwig for the input mass of 175 GeV.
      Herwig
      2tag_080250
      Pythia (no lepton filter)
      2tag_080250

    11. Background
    12. PE with twice as much and half as much background. These are the widths from the fits with no background constraint. This is an order of magnitude estimate.
      Twice as much background
      2tag_080250
      Half as much background
      2tag_080250

    13. Jet Resolution
    14. Smear things by another 5% by setting the jetEnergyScale to 10005 in the control file when running massAna. This is also a way to get an idea of the systematics.
      2tag_080250

    15. Summary
    16. Here, our default sample is ttop6w, a sample generated by Pythia for 1.5 GeV input top width with lepton filter for our analysis.
      &Gammatopmeas - &Gammatopmeas(ttop6w) &Gammatopmeas 1 sigma
      JES 2~3 GeV -1: 5 / +1: 0.5 -1: 8 / +1: 8
      ISR 1 GeV less: 2 / more: 3 less: 8 / more: 8
      FSR ~0.5 GeV less: 3 / more: 3 less: 8 / more: 8
      Generator 1~2 GeV Herwig: 1.5 / Pythia: 1.8 Herwig: 7.7 / Pythia: 7.8
      Background 1~2 GeV twice: 3 / half: 2 twice: 10 / half: 9
      Jet resolution 1 GeV 4 GeV 8 GeV
      Top Mass 6 GeV
      Modeling 4 GeV
      Modeling: dependence on tails of the mass distributions since we do not model events at the tails well.


  13. Added the quadratic dependency on the width in the fit function
  14. Output of the L-machinery for input top width 1.5, 15, 30, 50, 70 GeV. Due to the quadratic dependency, the number of parameter is 27 (instead of 18). No peak at 120 GeV!
    PE distribution
    2tag_080250
    Asymmeric pull for these distributions
    2tag_080250

    Measured top width

    This is the output of the Likelihood using quadratic dependency on the top width
    2tag_080250