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

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

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 70-110 GeV windown and Met, ZFitMet<15 outside this window. For getting Kz factors. Invert cuts for the Control Plots.

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 70-110 GeV window and Met, ZFitMet>25(both channels) outside this window. NN medium b tag. At least one tag is required.

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 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)

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

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

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 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

Simple check. 3 random ensembles PDF method PDH 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 PDF PDH before PDH after Stat error Pull distribution 5.82 12.95 5.15 Stat error Pull distribution

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. GeV 85% correlation <PDFi PDHi> r= =85% σPDF σPDH

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.

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

Conclusions Alternative method is designed Sensitivity, comparable to PDF Simpler, automatic, gives some additional information 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 done. Gives comparable result and comparable systematic uncertainty

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

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

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

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