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

PDF

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

PDF

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