# Single-top Analysis with Early Data

The early data are characterized simply by low luminosity levels, below 1 fb-1, and the larger impacts of certain systematics, particularly jet energy scale and b-tagging systematics. The purpose of this analysis is to detect single top events, and thus an emphasis is placed on reaching a discovery sigma level at very low luminosities. The analysis attempts to determine cuts that will raise the sigma level further and allow this discovery level at lower luminosities. It should also be noted that this analysis is not divided into separate channels, but rather looks at the combined single top signal, and is based totally on Monte Carlo, as data is not yet available.

## Event selection

The typical preselection cuts discussed in previous sections were applied here, although because this is a low luminosity study, the second jet pt cut was adjusted to 25 GeV, the lepton Pt cuts were adjusted to 20 GeV for electrons and 25 GeV for muons,and the early data b-tagger, TRFIP2D, was used. Additionally, the trigger cuts could not be applied to the W+jets samples (not including Wbb+jets), since these were FastSim files, so these events were weighted based on the trigger turn-on curves instead. After applying these cuts, the events were separated into groups according to the number of b-tagged jets, specifically looking at 1 or 2 b-tagged jet events, effectively introducing a maximum tagged jet cut. The event yields, weighted to 100 pb-1, can be found in the table below for samples containing 1 or 2 b-tagged jets, and muons or electrons.

processes muon (1 b-jet) muon (2 b-jet) electron (1 b-jets) electron (2 b-jets)
s-channel 13.91 8.37 9.95 6.44
t-channel 336.16 107.23 247.76 93.56
W+t channel 99.78 28.23 76.6 23.78
ttbar to l+jets 899.45 547.42 729.48 444.69
ttbar to l+l 411.01 270.28 316.85 205.73
Wjets to 0 jets 78.42 8.88 2.58 6.26
Wjets to 1 jets 84.31 8.27 55.73 11.15
Wjets to 2 jets 824.95 51.56 533.97 32.9
Wjets to 3 jets 435.15 45.28 286.43 28.83
Wbbjets to 0 jets 11.72 7.61 6.51 4.81
Wbbjets to 1 jets 20.0397 11.81 13.65 7.74
Wbbjets to 2 jets 11.1720 5.19 6.86 3.23
Wbbjets to 3 jets 3.05 1.11 2.22 1.02
WW 23.08 3.27 17.86 1.96
WZ 7.26 2.85 5.43 2.15

## Sigma and Luminosity

The sigma values for several different low luminosity levels were examined without the addition of systematics and, at 100 pb-1 without systematics anticipated sigma levels were estimated at 11.3 for the 1 tagged jet sample and 6.5 for the 2 tagged jet sample, even without cuts beyond the preselection cuts. A much more realistic estimate including systematics drops the anticipated sigma levels at 100 pb-1 to 0.8 for the 1 b-tag sample and 1.0 for the 2 b-tag sample. The figure below shows the sigma value (Signal/sqrt(Background)) for each of the samples, including JES and B-tagging systematics. Here, the electron and muon samples are combined together, so that there are only two samples differentiated by number of tagged jets.

## Systematics Estimation

In the previous section, it was apparent that it is theoretically possible to reach the 5 sigma level at low luminosities. However, these numbers represent an optimal running and understanding of the detector, since these numbers do not include systematics errors. Thus, it is prudent to examine sources of systematic errors and see what cuts can be made to reduce this error and bring us closer to these optimal numbers. The JES (jet energy scale) and b-tagging systematics were emphasized, because of their expected impact on early data.

To examine the JES systematic, the JES error was taken as 10 percent. The jet energies in the events were then scaled up and down by this percentage and the overall change in events from an unscaled sample was noted. The b-tagging efficiency was also altered up and down to determine the average effect of this systematic. These systematics were then squared and added to the number of background events in the Signal/sqrt(Background) (sigma) calculation. In this way, the effect of this error on sigma at a particular luminosity could be estimated. The effects of the JES and b-tagging systematics on the anticipated sigma level at 100 pb-1 can be seen in the table below. This table also includes a brief look at numbers without b-tagging cuts, referred to as the no b-tag sample.

 Systematics 1 b-jet 2 b-jets *no b-jet None 11.3 6.5 9.3 JES 0.9 2.2 0.3 B-tagging 1.8 1.2 N/A JES and B-tagging 0.8 1.0 N/A

## Additional Variable Selection

Extra requirements were then examined to help reduce the systematic effects and increase the anticipated significance levels. All the considered variables were scanned one at a time over the possible ranges of cut values to determine what cut value would result in the highest significance value for a particular variable at a given luminosity. The best cut and corresponding significance value for each variable were examined to determine an optimal first cut (after preselection) to allow a higher potential significance value at a given luminosity. This initial study was done only looking at cuts on individual variables, which include:

• Ht refers to the sum of the Pt of the particles indicated (except for MET, for which we used Et)
• DeltaR refers to sqrt{(Delta Eta)2 + (Delta Pt)2 } for the particles in question
• H is the sum of the P (momentum) of the particles
• lepton refers to the leading lepton
• centrality is (sum Pt/sum P)
• Transverse W mass is sqrt{(leptonPt + MET)2 - (leptonP_x + MEX)2 - (leptonP_y + MEY)2 }

The variables considered were:

• Ht(jet1, jet2), Ht(all jets), Ht(lepton, MET)
• Ht(jet1, jet2, lepton, MET), Ht(all jets, lepton, MET)
• Delta Pt(jet1, jet2), Delta Pt(btaggedjet1, untaggedjet1)
• DeltaR(btaggedjet1, lepton), DeltaR(untaggedjet1, lepton), DeltaR(jet1, lepton)
• DeltaR(btaggedjet1, btaggedjet2), DeltaR(jet1, jet2)
• H(all jets), H(jet1, jet2)
• Pt(jet1), Pt(btaggedjet1), Pt(untaggedjet1), Pt(untaggedjet2), Pt(lepton)
• Pt(jet1) + Pt(jet2)
• Eta(btaggedjet1), Eta(untaggedjet1)
• Maximum jet eta in event
• Minimum jet eta in event
• Mass of jet1 + mass of jet2
• Missing Et, also written MET
• Number of jets, Number of untagged jets
• Transverse mass of W
• Mass of the b-tagged top
• Centrality(all jets, lepton),Centrality(jet1, jet2)

Additionally, normalized and unnormalized plots are shown for a selection of variables, Ht, top mass, leading untagged jet eta, and leading lepton pt below. The plots are shown for the 1 b-tag sample and do not include systematic effects.

In the case of the number of jets variable, a jet number cut of 2 is not indicated for our combined signal sample, unlike the individual channel analyses done at higher luminosities. For example, looking at the 1 b-tag sample, the jet number plot below shows a peak in s-channel signal in the 2-jet bin with a relatively small background, whereas the signal is much lower in the 3 and 4-jet bins compared to background, so an analysis in this channel would require number of jets equal to two. However, the combined signals and the square root of the combined backgrounds do not vary much relative to each other. Thus, the combined signal and background study sees no useful cut to increase sigma here, in terms of improving statistical systematics, even though it may be very useful in a single channel analysis. If other systematics are also considered, then a jet number cut of 4 might be useful to reduce some of the effects of systematics, particularly JES systematics for the 1 b-tag sample.

In the one and two b-tagged samples, including both JES and b-tagging systematics, certain cuts seemed useful, as can be seen in the table below. This analysis supported a cut requiring Jet Number = 4 for the 1 b-tagged sample, which increase the potential sigma level to 1.4 at 100 pb-1. Also, a cut on the 2 b-tagged sample at Leading Untagged Jet Eta > 3.35 raised the expected sigma level to 2.4 at 100 pb-1. Of course, we may not understand the detector well enough in early data to make a cut to keep such forward jets. In this case, the next best cut (of which there are several) has an anticipated sigma of about 1.1 at 100 pb-1. For early data, then, the 2 b-tagged sample, may require more complicated cuts.
samples 1 b-jet 2 b-jets
Preselection cuts 0.8 1.0
Preselection and best cut 1.4 2.4

## Results

Thus, at 100 pb-1 without the inclusion of systematics, the estimated significance levels are above discovery level. These are the optimum levels however, and including the jet energy scale and b-tagging systematics at $\rm 100$ \PB\ results in much lower anticipated significances. For the no b-tagging cut sample, the JES systematic resulted in a drop to an expected sigma of 0.3. For the other two samples, including JES and B-tagging systematics, we anticipate sigma levels of 0.8 for a sample containing events with 1 b-tagged jets and 1.0 for a sample containing events with 2 b-tagged jets. Initial work indicates that there may be cuts that can reduce the effect of these systematics. However, the large impact of these JES and B-tagging systematics shows that understanding them and finding additional cuts to lessen their impact will certainly play a large role in the analysis of early data.

-- JennyHolzbauer - 01 Nov 2007 -- JennyHolzbauer - 10 Mar 2008
Topic attachments
I Attachment Action Size Date Who Comment
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gif Add_earlydata_ht_tag2.gif manage 23.1 K 10 Mar 2008 - 16:16 JennyHolzbauer Ht, 2tag
gif Add_earlydata_lep1pt_tag1.gif manage 23.8 K 10 Mar 2008 - 16:21 JennyHolzbauer lep1pt, 1tag
gif Add_earlydata_lep1pt_tag2.gif manage 22.1 K 10 Mar 2008 - 16:21 JennyHolzbauer lep1pt, 2tag
gif Add_earlydata_topmass_tag1.gif manage 29.6 K 10 Mar 2008 - 16:17 JennyHolzbauer topmass, 1tag
gif Add_earlydata_topmass_tag2.gif manage 29.5 K 10 Mar 2008 - 16:17 JennyHolzbauer topmass, 2tag
gif Add_earlydata_unjeteta_tag1.gif manage 26.3 K 10 Mar 2008 - 16:17 JennyHolzbauer leading untagged jet eta, 1tag
gif Add_earlydata_unjeteta_tag2.gif manage 25.9 K 10 Mar 2008 - 16:18 JennyHolzbauer leading untagged jet eta, 2tag
gif Add_earlydata_wtmass_tag1.gif manage 24.3 K 18 Feb 2008 - 19:16 JennyHolzbauer Wtmass, 1tag
gif Add_earlydata_wtmass_tag2.gif manage 25.0 K 18 Feb 2008 - 19:17 JennyHolzbauer wtmass, 2tag
gif Add_event_selection_jetn_tag1.gif manage 24.7 K 10 Mar 2008 - 16:15 JennyHolzbauer JetN, 1tag
gif Add_event_selection_jetn_tag2.gif manage 19.7 K 10 Mar 2008 - 16:15 JennyHolzbauer JetN, 2tag
gif Normalized_earlydata_ht_sig_tag1.gif manage 18.5 K 10 Mar 2008 - 16:18 JennyHolzbauer Ht, 1tag, normalized
gif Normalized_earlydata_ht_sig_tag2.gif manage 19.1 K 10 Mar 2008 - 16:18 JennyHolzbauer Ht, 2tag, normalized
gif Normalized_earlydata_lep1pt_sig_tag1.gif manage 17.3 K 10 Mar 2008 - 16:21 JennyHolzbauer lep1pt, 1tag, normalized
gif Normalized_earlydata_lep1pt_sig_tag2.gif manage 17.3 K 10 Mar 2008 - 16:22 JennyHolzbauer lep1pt, 2tag, normalized
gif Normalized_earlydata_topmass_sig_tag1.gif manage 19.7 K 10 Mar 2008 - 16:19 JennyHolzbauer topmass, 1tag, normalized
gif Normalized_earlydata_topmass_sig_tag2.gif manage 29.5 K 10 Mar 2008 - 16:19 JennyHolzbauer topmass, 2tag, normalized
gif Normalized_earlydata_unjeteta_sig_tag1.gif manage 19.9 K 10 Mar 2008 - 16:19 JennyHolzbauer leading untagged jet eta, 1tag, normalized
gif Normalized_earlydata_unjeteta_sig_tag2.gif manage 21.0 K 10 Mar 2008 - 16:20 JennyHolzbauer leading untagged jet eta, 2tag, normalized
gif Normalized_event_selection_jetn_sig_tag1.gif manage 16.3 K 10 Mar 2008 - 16:15 JennyHolzbauer JetN signal, 1tag, normalized
gif Normalized_event_selection_jetn_sig_tag2.gif manage 16.5 K 10 Mar 2008 - 16:16 JennyHolzbauer JetN signal, 2tag, normalized
gif hLumSiglog_combo_tag1_allcut.gif manage 7.1 K 10 Mar 2008 - 16:13 JennyHolzbauer sigma vs luminosity, 1tag, log
gif hLumSiglog_combo_tag2_allcut.gif manage 7.2 K 10 Mar 2008 - 16:14 JennyHolzbauer sigma vs luminosity, 2tag, log
gif hNJets_LSsqrtB_combo_tag1_allcut.gif manage 8.0 K 10 Mar 2008 - 16:23 JennyHolzbauer JetN, 1tag, left cutopt
gif hNJets_LSsqrtB_combo_tag2_allcut.gif manage 7.5 K 10 Mar 2008 - 16:25 JennyHolzbauer JetN, 2tag, left cutopt
gif hWTransverseMass_LSsqrtB_combo_tag1_allcut.gif manage 7.3 K 02 Nov 2007 - 17:19 JennyHolzbauer wtmass, 1tag, left cutopt
gif hWTransverseMass_LSsqrtB_combo_tag2_allcut.gif manage 7.1 K 02 Nov 2007 - 17:20 JennyHolzbauer wtmass, 2tag, left cutopt
Topic revision: r118 - 16 Oct 2009, TomRockwell

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