Progress by ewghwehws


									Dilepton Mass. Progress

            Peter Renkel: Southern Methodist Uni.
L+track selection (frosen in January)
NuWt reminder
PDH (around August for the ICHEP)
   Pros.
PDF+PDH combination in review for

Talk at TOP2008 at Elba. May 22
                l+track selection
Dimuon and lepton+tau vetoes.
Trigger ORing.
Final JES.

   Lepton, track, at least 2 jets
       Leading jet pT>40 GeV
       Second jet pT>20 GeV
   Met, ZFitMet<20 inside the 70-110 GeV windown and Met,
    ZFitMet<15 outside this window. For getting Kz factors.
   Invert cuts for the Control Plots.
             Final selection.
                                 With        This
Require:                         previous    selection
                                 selection   (veto+trigger
   Met,                                     Oring)
    (mu+track) inside the E+track 7          8
    70-110 GeV window
    and Met,
    channels) outside this
    NN medium b tag. At Mu+trac
    least one tag is              8          6
    required.              k
Here should be plots, but you
 have them in the note/PRD
     Reminder. Neutrino Weighting (NuWt)

-1C fit underconstrained fit – Assume top mass – can solve event
Assign a weight to each event:
    Omit the information on missing momenta
    Sample from expected neutrino rapidity spectrum
    Compare calculated and observed Etmiss and assign a weight:

Repeat for all test masses
Get a weight distribution per event
                       Templates or PDH
                             Single Event Weight Distribution

Weight Distribution
                                                                 Mean=200 GeV

                                                                 RMS=25 GeV

          For each event record two first moments: mean and rms. Create a 2Dim histo

                      Probability Distribution Histogram (PDH)

 PDH (templates)
                        Fit procedure
We fit our histograms in NuWt to smooth functions to avoid local
    3Dim signal (input top mass, mean, rms)  3Dim analytical function
    2Dim background (mean, rms)  2Dim analytical function

          A mean vs. rms slices of the 2d plot (PDH) and fit function (PDF)

                   PD                       PDF
        Likelihood distribution
Get a likelihood distribution by fixing moments obtained
from data in the 3-Dim/2-Dim distributions
The moments are taken from data

                 templates      smoothed function (PDF)


                                                     fixing, taking a slice
DATA                   meani, rmsi
             PDF related questions
Very difficult to fit
  Signal: 3 – dimensional functional form (mt, mean, rms)
        13 parameters in the fit
  BG: All BG have different shapes/functional forms.
        Can approximate with gaussians each, but if there are several of
        them – many gaussians, quite complicated.
  Lots of time/resources

Is our fit function (PDF) the optimal one? Does it create any bias?
   Yes, ensemble tests are Ok, but anyway it’s good to check
           PDH method
Why not to use PDH for check?
Seems as drawback, since we invented
PDF method to smooth local fluctuations
Are these fluctuations important?

Let’s check.
               PDH method
Use UNSMOOTHED histograms (PDH) as templates
  No fitting

  When reconstructing mass, get non analytic function,

   which we have to fit (simple parabolic fit).
                                                         Non analytic
                                    smoothed function    function – parabolic fit


                                                        fixing, taking a slice
DATA                  meani, rmsi
Simple check. 3 random
   PDF methodPDH method
      Improvements. Filling zero bins.
      PDH(mean,rms)=0   -logL=inf                    bad fits

PDH                           PDH

                                    coorected bins

                        mt                                      mt
      Improvements. Filling zero bins.
      PDH(mean,rms)=0   -logL=inf                    bad fits

PDH                           PDH

                                    coorected bins

                        mt                                      mt
Improvements. Extended range of
         top masses.
        new points               new points

       Added: 110, 125, 140, 215, 230 GeV samples
                         Ensemble tests


PDH                                             5.82
after                                           12.95

         Pull distribution         Stat error
              PDF vs. PDH
PDF smoothes local fluctuations.
PDH from the other side is sensitive to the
local fluctuations.
   But it can catch peculiarities of the signal,
    smoothed out by the PDF.

PDF and PDH add some information to
each other.
  PDF – PDH.

        85% correlation

   <PDFi PDHi>
r=             =85%
    σPDF σPDH
Gain – 100% (299 out of 300) ensembles
have fit (compared to 90% before)
Slopes and offsets are better.

Results. Fixed systematic for the PDH
  PDF                                PDH

Combined result (BLUE method)

 We received comments from Ulrich. Thank you! Looking at them.
error    PDF      PDH   PDF+PDH
expected 5.3      5.1   4.7 (~10%
observed 5.3      4.9   4.8
Alternative method is designed
Sensitivity, comparable to PDF
Simpler, automatic, gives some additional

Combine and get a combination.
             PDH Status now

Method implemented in 2 weeks! Compared to half a
year for the fits in PDF. Automatic!
Was easy to run with just one variable mean and show,
that mean + rms 2d templates give ~16% improvement
compared to 1d mean templates.
   Similar fits for PDH would take several months of work

Started as a simple cross-check, eventually all chain is
   Gives comparable result and comparable systematic uncertainty
85% correlation
    For some of ensembles PDF and PDH errors are equal.
          The combination gives 5% improvement
    For the bulk of ensembles, the errors vary by ~ 10% difference
          the ‘combination’ is very close to the Min(PDF,PDH).
    ~10% improvement in mean over all ensembles.

If take minimum of two measurements.

     Minimum                                                     Combination
 mean=4.8 GeV
                                                                 mean=4.7 GeV
                          Empty bins
                                                 A 1d slice at fixed mean0

 PDH in mt/mean plane

  mean0 from data       mean1 from data

175                                                160 165 170 175 180 mt
170                                          A 1d slice at fixed mean1
165                                       PDH

                                                160 165 170 175 180 mt
      Smoothing empty bins. Default approach

123                        PDH


                                 coorected bins


                      mt                          mt
      Smoothing empty bins. Comparison with default approach
       Uncertainty due to smoothing of empty bins in PDH.
              If several empty bins at the edge, normalize to their number.
              If several empty bins are surrounded by non – empty bins, then:
                   If at least one of them has exactly 1 entry, normalize to their number.
       Shift of 0.1 GeV observed

 PDH                                                                PDH

       1                                                                  1

PDH                                                              PDH                          mt

                                mt                                                           mt
    Should smooth PDH, but not with analytic functions. Taking a bin,
    account for neighbors (also automatic).
        Reason – more stable fits
    Should be easy ( change one line of code – see below)

h                     PDH
                                              PDH1 = h1
                        PDH                   IMPROVED_PDH~(h0+h1+h2)/3

             0           1           2

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