Dilepton Mass. Progress report.
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Transcript of Dilepton Mass. Progress report.
Dilepton Mass. Progress Dilepton Mass. Progress report.report.
Peter Renkel: Southern Methodist Uni.dileptoners
ContentsContents
L+track selection (frosen in January)L+track selection (frosen in January)
NuWt reminderNuWt reminder
PDH (around August for the ICHEP)PDH (around August for the ICHEP) Pros.Pros.
PDF+PDH combination in review for PDF+PDH combination in review for p17/PRDp17/PRD
Talk at TOP2008 at Elba. May 22Talk at TOP2008 at Elba. May 22
l+track selectionl+track selection
Dimuon and lepton+tau vetoes.Dimuon and lepton+tau vetoes.Trigger ORing.Trigger ORing.Final JES.Final JES.
Require: Require: Lepton, track, at least 2 jetsLepton, track, at least 2 jets
Leading jet pT>40 GeVLeading jet pT>40 GeVSecond jet pT>20 GeVSecond jet pT>20 GeV
Met, ZFitMet<20 inside the 70-110 GeV windown and Met, Met, ZFitMet<20 inside the 70-110 GeV windown and Met, ZFitMet<15 outside this window. For getting Kz factors.ZFitMet<15 outside this window. For getting Kz factors.
Invert cuts for the Control Plots.Invert cuts for the Control Plots.
Final selection.Final selection.
Require: Require: Met, Met,
ZFitMet>35(e+track)40ZFitMet>35(e+track)40(mu+track) inside the (mu+track) inside the 70-110 GeV window 70-110 GeV window and Met, and Met, ZFitMet>25(both ZFitMet>25(both channels) outside this channels) outside this window. window.
NN medium b tag. At NN medium b tag. At least one tag is least one tag is required.required.
With With previousprevious
selectionselection
This This selection selection (veto+trigger (veto+trigger Oring)Oring)
E+trackE+track 77 88
Mu+tracMu+trackk
88 66
Here should be plots, but you Here should be plots, but you have them in the note/PRDhave them in the note/PRD
Reminder. Neutrino Weighting (NuWt)Reminder. Neutrino Weighting (NuWt)
-1C fit underconstrained fit – Assume top mass – can solve event-1C fit underconstrained fit – Assume top mass – can solve eventAssign a weight to each event:Assign a weight to each event:
Omit the information on missing momentaOmit the information on missing momenta Sample from expected neutrino rapidity spectrumSample from expected neutrino rapidity spectrum Compare calculated and observed ECompare calculated and observed Ett
missmiss and assign a weight: and assign a weight:
Repeat for all test massesRepeat for all test massesGet a weight distribution per eventGet a weight distribution per event
Templates or PDHTemplates or PDHSingle Event Weight Distribution
Mean=200 GeV
RMS=25 GeV
For each event record two first moments: mean and rms. Create a 2Dim histoFor each event record two first moments: mean and rms. Create a 2Dim histo
Probability Distribution Histogram (PDH)
Event
Weight Distribution
PDH (templates)
Fit procedureFit procedure
We fit our histograms in NuWt to smooth functions to avoid local We fit our histograms in NuWt to smooth functions to avoid local fluctuationsfluctuations
3Dim signal (input top mass, mean, rms) 3Dim signal (input top mass, mean, rms) 3Dim analytical function 3Dim analytical function 2Dim background (mean, rms) 2Dim background (mean, rms) 2Dim analytical function 2Dim analytical function
A mean vs. rms slices of the 2d plot (PDH) and fit function (PDF)
PDH
Likelihood distributionLikelihood distribution
Get a likelihood distribution by fixing moments obtained Get a likelihood distribution by fixing moments obtained from data in the 3-Dim/2-Dim distributionsfrom data in the 3-Dim/2-Dim distributions
The moments are taken from dataThe moments are taken from data
MC
DATA meani, rmsi
templates smoothed function (PDF)
fixing, taking a slice
PDF related questionsPDF related questionsVery difficult to fitVery difficult to fit
Signal: 3 – dimensional functional form (mSignal: 3 – dimensional functional form (mt, t, mean, rms)mean, rms)
13 parameters in the fit13 parameters in the fit BG: All BG have different shapes/functional forms. BG: All BG have different shapes/functional forms.
Can approximate with gaussians each, but if there are several of Can approximate with gaussians each, but if there are several of them – many gaussians, quite complicated.them – many gaussians, quite complicated.
Lots of time/resourcesLots of time/resources
Is our fit function (PDF) the optimal one? Does it create any bias?Is our fit function (PDF) the optimal one? Does it create any bias? Yes, ensemble tests are Ok, but anyway it’s good to checkYes, ensemble tests are Ok, but anyway it’s good to check
PDH methodPDH method
Why not to use PDH for check?Why not to use PDH for check?
Seems as drawback, since we invented Seems as drawback, since we invented PDF method to smooth local fluctuationsPDF method to smooth local fluctuations
Are these fluctuations important?Are these fluctuations important?
Let’s check.Let’s check.
PDH methodPDH methodUse UNSMOOTHED histograms (PDH) as templatesUse UNSMOOTHED histograms (PDH) as templates
Modify:Modify: No fittingNo fitting When reconstructing mass, get non analytic function, When reconstructing mass, get non analytic function,
which we have to fit (simple parabolic fit).which we have to fit (simple parabolic fit).
MC
DATA meani, rmsi
templates smoothed function
fixing, taking a slice
Non analyticfunction – parabolic fit
!
Simple check. 3 random ensemblesSimple check. 3 random ensemblesPDF method PDH method
Improvements. Filling zero bins.Improvements. Filling zero bins.PDH(mean,rms)=0 -logL=inf bad fits
PDH PDH
mt mt
coorected bins
Improvements. Filling zero bins.Improvements. Filling zero bins.PDH(mean,rms)=0 -logL=inf bad fits
PDH PDH
mt mt
coorected bins
Improvements. Extended range of Improvements. Extended range of top masses.top masses.
new points new points
Added: 110, 125, 140, 215, 230 GeV samples
Ensemble testsEnsemble tests
PDH before
PDH after
Pull distribution Stat error
12.95
5.82
5.15
PDF vs. PDHPDF vs. PDHPDF smoothes local fluctuations.PDF smoothes local fluctuations.PDH from the other side is sensitive to the PDH from the other side is sensitive to the local fluctuations. local fluctuations. But it can catch peculiarities of the signal, But it can catch peculiarities of the signal,
smoothed out by the PDF.smoothed out by the PDF.
PDF and PDH add some information to PDF and PDH add some information to each other.each other.
PDF – PDH.PDF – PDH.
85% correlation
GeV
r=<PDFi PDHi>
σPDF σPDH
=85%
ResultsResultsGain – 100% (299 out of 300) ensembles Gain – 100% (299 out of 300) ensembles have fit (compared to 90% before)have fit (compared to 90% before)Slopes and offsets are better.Slopes and offsets are better.
Results. Fixed systematic for the PDHResults. Fixed systematic for the PDH
Combined result (BLUE method)Combined result (BLUE method)
PDF PDH
We received comments from Ulrich. Thank you! Looking at them.
CombinationCombinationerror error [GeV][GeV]
PDFPDF PDHPDH PDF+PDHPDF+PDH
expecteexpectedd
5.35.3 5.15.1 4.7 (~10% 4.7 (~10% improvement)improvement)
observeobservedd
5.35.3 4.94.9 4.84.8
ConclusionsConclusions
Alternative method is designedAlternative method is designed
Sensitivity, comparable to PDFSensitivity, comparable to PDF
Simpler, automatic, gives some additional Simpler, automatic, gives some additional informationinformation
Combine and get a combination.Combine and get a combination.
PDH Status nowPDH Status now
Method implemented in 2 weeks! Compared to half a Method implemented in 2 weeks! Compared to half a year for the fits in PDF. Automatic!year for the fits in PDF. Automatic!Was easy to run with just one variable mean and show, Was easy to run with just one variable mean and show, that mean + rms 2d templates give ~16% improvement that mean + rms 2d templates give ~16% improvement compared to 1d mean templates.compared to 1d mean templates.
Similar fits for PDH would take several months of workSimilar fits for PDH would take several months of work
Started as a simple cross-check, eventually all chain is Started as a simple cross-check, eventually all chain is done.done.
Gives comparable result and comparable systematic uncertaintyGives comparable result and comparable systematic uncertainty
CombinationCombination85% correlation85% correlation
For some of ensembles PDF and PDH errors are equal.For some of ensembles PDF and PDH errors are equal. The combination gives 5% improvementThe combination gives 5% improvement
For the bulk of ensembles, the errors vary by ~ 10% differenceFor the bulk of ensembles, the errors vary by ~ 10% differencethe ‘combination’ is very close to the Min(PDF,PDH). the ‘combination’ is very close to the Min(PDF,PDH).
~10% improvement in mean over all ensembles.~10% improvement in mean over all ensembles.
If take minimum of two measurements.If take minimum of two measurements.
Minimum Combination
mean=4.8 GeVmean=4.7 GeV
Empty binsEmpty bins
mt
mean
mean0 from data
160165170
175
180
mt
PDH
160 165 170 175 180
PDH in mt/mean plane
A 1d slice at fixed mean0
mt
PDH
160 165 170 175 180
A 1d slice at fixed mean1
mean1 from data
Smoothing empty bins. Default approachSmoothing empty bins. Default approach
PDHPDH
mt mt
coorected bins
12
35
61
123
Smoothing empty bins. Comparison with default approachSmoothing empty bins. Comparison with default approach
Uncertainty due to smoothing of empty bins in PDH.Uncertainty due to smoothing of empty bins in PDH. If several empty bins at the edge, normalize to their number.If several empty bins at the edge, normalize to their number. If several empty bins are surrounded by non – empty bins, then: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.If at least one of them has exactly 1 entry, normalize to their number.
Shift of 0.1 GeV observedShift of 0.1 GeV observed
mt
PDH
1
mt
PDH
1
mt
PDH
mt
PDH
FutureFutureShould smooth PDH, but not with analytic functions. Taking a bin, Should smooth PDH, but not with analytic functions. Taking a bin, account for neighbors (also automatic).account for neighbors (also automatic).
Reason – more stable fitsReason – more stable fits
Should be easy ( change one line of code – see below)Should be easy ( change one line of code – see below)
PDH
improvedPDHh
0 1 2
PDH1 = h1
IMPROVED_PDH~(h0+h1+h2)/3