1. Dilepton Mass. Progress report.
Peter Renkel: Southern Methodist Uni.
dileptoners

2. Contents L+track selection (frosen in January) NuWt reminder
PDH (around August for the ICHEP)
Pros.
PDF+PDH combination in review for p17/PRD
Talk at TOP2008 at Elba. May 22

3. l+track selection Dimuon and lepton+tau vetoes. Trigger ORing.
Final JES.
Require:
Lepton, track, at least 2 jets
Leading jet pT>40 GeV
Second jet pT>20 GeV
Met, ZFitMet<20 inside the GeV windown and Met, ZFitMet<15 outside this window. For getting Kz factors.
Invert cuts for the Control Plots.

4. Final selection. 7 8 6 Require:
With previous
selection
This selection (veto+trigger Oring)
E+track 7 8
Mu+track 6
Require:
Met, ZFitMet>35(e+track)40(mu+track) inside the GeV window and Met, ZFitMet>25(both channels) outside this window.
NN medium b tag. At least one tag is required.

5. Here should be plots, but you have them in the note/PRD

6. 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

7. Templates or PDH Event Weight Distribution Mean=200 GeV RMS=25 GeV
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)

8. Fit procedure
We fit our histograms in NuWt to smooth functions to avoid local fluctuations
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)
PDH
PDF

9. 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
smoothed function (PDF)
templates MC
DATA
fixing, taking a slice
meani, rmsi

10. 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

11. 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.

12. ! PDH method Use UNSMOOTHED histograms (PDH) as templates Modify:
No fitting
When reconstructing mass, get non analytic function, which we have to fit (simple parabolic fit).
Non analytic
function – parabolic fit
smoothed function
templates ! MC
DATA
fixing, taking a slice
meani, rmsi

13. Simple check. 3 random ensembles
PDF method
PDH method

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

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

16. Improvements. Extended range of top masses.
new points
new points
Added: 110, 125, 140, 215, 230 GeV samples

17. Ensemble tests PDF PDH before PDH after Stat error Pull distribution
5.82
12.95
5.15
Stat error
Pull distribution

18. 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.

19. PDF – PDH.
GeV
85% correlation
<PDFi PDHi> r=
=85%
σPDF σPDH

20. Results
Gain – 100% (299 out of 300) ensembles have fit (compared to 90% before)
Slopes and offsets are better.
Results. Fixed systematic for the PDH
Combined result (BLUE method)
PDF
PDH
We received comments from Ulrich. Thank you! Looking at them.

21. Combination error [GeV] PDF PDH PDF+PDH expected 5.3 5.1
4.7 (~10% improvement)
observed
4.9
4.8

22. Conclusions Alternative method is designed
Sensitivity, comparable to PDF
Simpler, automatic, gives some additional information
Combine and get a combination.

23. 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 done.
Gives comparable result and comparable systematic uncertainty

24. Combination Combination Minimum mean=4.8 GeV mean=4.7 GeV
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.
Combination
Minimum
mean=4.8 GeV
mean=4.7 GeV

25. Empty bins A 1d slice at fixed mean0 PDH PDH in mt/mean plane
mean0 from data
mean1 from data mt
180
175
160
165
170
175
180 mt
170
A 1d slice at fixed mean1
165
PDH
160
mean
160
165
170
175
180 mt

26. Smoothing empty bins. Default approach
PDH
123
PDH 61
coorected bins 35 12 mt mt

27. 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 mt

28. Future
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)
improved
PDH h
PDH1 = h1
IMPROVED_PDH~(h0+h1+h2)/3
PDH 1 2