# Presentation: 678378

## Measurement of the ttbar Cross Section Using Kinematics 

**Blessing– Aug. 07, 2003**
*RDE, Presenting for the OSU/Fermilab/Rutgers Group*

**Richard Hughes, Radu Marginean, Evelyn Thomson, Brian Winer**
*The Ohio State University*
**Robin Erbacher, Rob Roser**
*Fermilab*
**John Conway**
*Rutgers University***   **

## Questions from Preblessing

**The ratio of electrons/muons is different for njet=1,2 vs 3,4. **
** ****Is this caused by the ******** cut?**
**NO.  The ratio is slightly modified by the ******** cut since this cut removes **
**  ****more electrons than muons (more background in the electrons).**
**The ******** cut seems to remove more events than you would expect.**
**  ****Is this true?**
**NO.  Using the efficiency of the ******** cut for signal (W’s) and background, **
**and the predicted amount of background in each jet multiplicity bin, **
**we can predict how many events should pass the ******** cut.  Things are as **
**expected.**

**Questions from Preblessing**

| Njet | Obs Muons | Pred Muons | Obs Elec | Pred Elec |
| --- | --- | --- | --- | --- |
| 1 | 4474 | 4469.2 | 6105 | 6026.7 |
| 2 | 704 | 635.1 | 913 | 944.0 |
| 3 | 80 | 92.1 | 153 | 162.2 |
| 4 | 22 | 23.7 | 53 | 52.8 |

## Questions from Preblessing

**To make sure we are doing this correctly, we have exchanged extensive emails with te jet corrections group (Anwar and Beate)**
**The dominant effects come from the Relative, Scale and Absolute corrections.  True in both the 3 and the 4 jets samples.**
**These dominant effects all contribute about equally to the final results of approximately 30%.**

**Questions from Preblessing**

## Questions from Preblessing

**It was flawed.  We fixed this by using pseudo-experiments (PEs), following the suggestion of Igor Volobouev.  We compared the KS distance observed in our data fit to that expected from PEs using the fitted mix of signal plus background.  See tables later in talk.  Conclusions reached previously still hold: fits look poor in W+1 jet, but look good in W+2 and W+3 jet cases.**
**Fit questions:**
**Let the QCD float****:  Done, answer hardly changes.**
**Remove ttbar from signal fits:**** Done: KS goodness of fit indicates poorer fit without ttbar in both 3 and 4 jet cases.**

**Questions from Preblessing**

## Questions from Preblessing

**Done.  Used method for W->enu cross section.**
**Add a systematic for Q**2**
**Done.  Used ALPGEN Mw**2 (instead of default Mw**2+Sum(Pt**2)).  **
**A large effect in the W+>3 jet bvin (14% systematic), much smaller in the W+>=4 jet bin (0.31%).  Expected fraction of ttbar is approximately twice as large in >=4 jet sample.**
**Smear Jet Et’s.**
**Did not do this for lack of time.  Remember that the comparisons of Ht, Et(jet 1,2,3), Met, etc look good in the W+2,3 jet bins with the default MC, and we include a substantial systematic for th Jet Et scale already.  However, we will investigate this in the near future.**

**Questions from Preblessing**

## Changes Since Preblessing

_**List of improvements**_

**Changes affecting fit results:**
**Full *****final***** good run list used (added 2 pb****-1****)**
**Fix typo in curvature correction**
**Include all the EWK backgrounds in the shape for fit**
**Cross Checks:**
**Use modified KS test to compare data to MC**
**Correct MET v. Iso for W-like events, obtain **
**  ****normalization systematic**
**Divide jet correction systematic into components**
**Estimate the uncertainty due to Q****2**** scale**
**Estimate the shape uncertainty due to PDFs**

- We have a document detailing answers to
- questions raised during preblessing.  Answers
- are also included throughout updated **CDF6206**

## Measurement Approach

**Measure top cross section using kinematic and event shape variables to discriminate ttbar from background**
**Initially: use a single variable to fit data to W+jets, QCD, and  ttbar.  H****T**** is our main discriminator but have examined others.**
**Eventually: More sophisticated method using multivariate techniques and neural networks.**
**Determine the tt fraction, then extract the top cross section**

_**Key Analysis Components**_

**Determine QCD contribution using MET v. isolation**
**Validate QCD model, evaluate W+Jets backgrounds**
**Fit signal region for W+********3 Jet and W+********4 Jet events**
**Determine systematic errors using pseudo experiments**
**Extract the top cross section**

## Data and MC Samples

**Data: ****Standard lepton sample from Evelyn**
**Backgrounds:**
**W+Jets Monte Carlo: ****ALPGEN W+n parton**
**QCD**
**Non-isolated (I>0.2) electrons/muons**** **
**Aside from isolation, cuts the same (MET, lepton ID, N jets)**
**Top**
**Pythia MC (175)**
**Herwig MC (175): ****systematic**
**Systematic studies use Pythia for ISR and top mass **
**(170,180GeV/c****2****) studies**

## Event Selection

**Require good run and CEM, CMUP, CMX trigger path**
**Lepton ID requirements:  Standard (CDF Note 6574)**
**Require “N” reconstructed jets with: **
**Corrected E****T**** > 15.0 GeV**
**|Detector ********| < 2.0**
**Require event MET >20.0 GeV (after corrections)**
** ****If 20.0 < MET < 30.0 GeV, also require:**
** ****0.5 < ******** (MET-Leading Jet) < 2.5**
**Signal Samples: ********3 Jets and ********4 Jets **
**Will also investigate 3 (only) Jets sample**

##  v. MET for non-isolated leptons

**For Blessing**

****** ****between **
**MET and lead jet,**
**1 Jet Data**

**electrons **

**muons **

**CDF Preliminary**

##  v. MET ttbar and W+jets MC 

****** ****between **
**MET and lead jet,**
** ********3 Jet events,**
**W+3p and tt MC**

**For Blessing**

**CDF Preliminary**

## Sensitivity to  Cut

**   ****Use PE’s to determine the utility of the ******** cut as well as the sensitivity to it.**
**This cut reduces our background by ~factor of 2**
**Does it help statistical precision?**
**Does it help systematic?**
**We have two models for background: non-isolated leptons and conversions**
**Sample from one, and fit using the other to set the systematic.**

## Sensitivity to and Utility of Cut 

| 
Sample | Observed Data Events (no trigger req.) | Expected ttbar events (7pb xsec) | Expected Precision  on Fit fraction (stat only) | Relative shift of ttbar fraction |
| --- | --- | --- | --- | --- |
| W+3, no    cut | 391 | 71 | 28  8 %
 | 32%
 |
| W+3, with  cut | 346 (predicted)
 | 67 | 28  8 %
 | 16%
 |

**Including the ******** cut in event selection... **
**Has no impact on the expected statistical precision**
**Reduces the systematic effect due to poor background modeling by ~factor of 2.  **

- For Blessing

****** ****PE’s indicate this is an efficient cut choice ******

## Observed/Expected Event Yield 

| 
Jets | Data Electrons | Data Muons | Data Total |  |  |
| --- | --- | --- | --- | --- | --- |
| 0 | 59655 | 44737 | 101663 | 0.2% | 0.2 |
| 1 | 6105 | 4474 | 10359 | 4.0% | 3.4 |
| 2 | 913 | 704 | 1600 | 18.5% | 16.1 |
| 3 | 153 | 80 | 234 | 34.5% | 29.7 |
| 4 | 39 | 18 | 57 | 32.0% | 27.6 |
| 5 | 14 | 3 | 17 | 10.6% | 9.1 |

- For Blessing

## Expected QCD Background Fraction 

| W+”n” jets | Electron bkgnd  | Muon bkgnd  | Total bkgnd |
| --- | --- | --- | --- |
| 1 | 3.8  0.2% | 2.9 0.2% | 3.4  0.3% |
| 2 | 6.1  0.5 % | 2.0  0.2% | 4.3  0.5% |
| 3 | 7.7  1.4 % | 3.1  0.9% | 6.3  1.7% |

- For Blessing

**Determine QCD background normalization using      MET vs Isolation**

## Discriminating Variables 

**Use a single input neural network to discriminate ttbar from W+jets. **
_**Table**_**:  % of correct classifications possible using  each variable.**
**E.g:  For E****T ****of the 3****rd**** leading jet, its possible to correctly classify 74.4%  of a sample of W+jets and ttbar. For sphericity, only 60% can be correctly classified.**
**Many variables were studied.  Shown are just the best E****T**** based and shape-based variables.**

|   | HERWIG tt
ALPGEN W+jets | PYTHIA tt
ALPGEN W+jets |
| --- | --- | --- |
| ET(jet 3) | 74.4 ± 0.5 | 73.7 ± 0.5 |
| HT | 73.9 ± 0.5 | 72.5 ± 0.5 |
| ET(jet 2 + jet 3) | 73.9 ± 0.5 | 73.4 ± 0.5 |
| ET(jet 2) | 73.7 ± 0.5 | 71.8 ± 0.5 |
| min(mjj) | 72.3 ± 0.6 | 71.0 ± 0.6 |
| ET(jet 1 + jet 2) | 71.0 ± 0.6 | 71.0 ± 0.6 |
| event inv. mass | 70.8 ± 0.6 | 70.1 ± 0.6 |
| ET(jet 4) | 69.4 ± 0.6 | 69.5 ± 0.6 |
| ET(jet 1) | 67.7 ± 0.6 | 67.1 ± 0.6 |
| sum dijet mass | 66.6 ± 0.6 | 64.9 ± 0.6 |
| Ez/ ET | 63.3 ± 0.6 | 64.0 ± 0.6 |
| aplanarity | 59.2 ± 0.6 | 60.2 ± 0.6 |
| min jet sep. | 60.3 ± 0.6 | 60.6 ± 0.6 |
| sphericity | 60.0 ± 0.6 | 59.6 ± 0.6 |
| missing ET | 57.7 ± 0.6 | 55.7 ± 0.6 |

## Kinematic Variables: ttbar v. W+3p MC 

- For Blessing

## More Kinematics: ttbar v. W+3p MC 

- For Blessing

## Event Shape Variables: ttbar v. W+3p MC 

- For Blessing

## Sensitivity to Various Event Variables 

- For Blessing

**Points are the mean returned uncertainties from fitting the PE’s. Error bars represent the 1 sigma range of possible returned uncertainty from the fit.**

**Sensitivity to Various Event Variables**** **

- 3 or more jets

## Sensitivity to Various Event Variables

- For Blessing

- 4 or more jets

**Points are the mean returned uncertainties from fitting the PE’s. Error bars represent the 1 sigma range of possible returned uncertainty from the fit.**

## Validating the Background MC

_**Main background**_**: **
**W+Jets, modeled by ALPGEN**
**W+n parton Monte Carlo.**
**Validate this MC in a top-depleted region: W+1,2 jet data.**
**  **
** **_**Upper plot**_**: observed W+jets data**
** ****(red)**** along with a ****prediction ****for**
** ****the amount of ttbar ****(blue),**** as a**
** ****function of jet multiplicity. **
** **_**Lower plot**_**: The top/W ratio is about**
**1:1 in the 4 and 5 jet bins, but only**
** ****about 12% in the W+3 jet bin.**

- For Blessing

## Testing the Model

**In the W+1 jet sample we fit using:**
**ALPGEN W+1 parton, plus non-isolated leptons**** **
**In W+2 jet sample:**
**ALPGEN W+2 parton**
**In the W+3 jet sample, we fit using:**
**ALPGEN W+3 parton, Herwig ttbar, plus non-isolated leptons****  **
**In the W+********3 jets and W+********4 jets fits, the ******** cut is imposed.**

## Data/ MC Comparisons

_**Problem**_**: Examining the H****T**** distribution in the W+1 jet data: the fit undershoots H****T**** in the low end, and overshoots H****T**** at the high end. **
** **
**How to quantify the difference?**
**Kolmogorov-Smirnov statistic is biased in ROOT**
_**Modify procedure**_**: **
**Flatten KS distribution using**
**      ****integral distribution.**

- For Blessing

## Distributions for 1 Jet Bin

- For Blessing

**CDF Preliminary**

## Distributions for 2 Jet Bin

- For Blessing

**CDF Preliminary**

## Distributions for 3 Jet Bin

- For Blessing

**Sum Et; Njets=3 only**

**CDF Preliminary**

## Comparison Results: 1,2,3  Jet Bins

**Results of the modified KS test for a subset of the variables in the W+1,**
**W+2, and W+3 jet bins are shown above. “QCD” Background in these**
**fits is the non-isolated lepton sample.**
_**Conclusions**_**:  ****While the KS tests shown at preblessing to attempt to quantify agreement between data and MC were skewed, conclusions remain the same:  **
**Although the fits look poor in the W+1 jet sample, in the W+2 and W+ 3 jet bins**
** ****a mixture of W+np MC, ttbar MC, and non-isol leptons describe the data well.**** **

| Variable | 1 Jet Bin | 2 Jet Bin | 3 Jet Bin |
| --- | --- | --- | --- |
| Ht | 0% | 42.4% | 47.6% |
| LeptonEt | 0% | 65.8% | 71.4% |
| MET | 0% | 24.0% | 86.3% |
| Et Jet 1 | 11.4% | 14.1% | 45.1% |
| Et Jet 2 | N/A |  90.0 % | 98.9% |
| Et Jet 3 | N/A | N/A | 74.5% |

## Fitting the Signal Region

**Now we fit in the W+********3 and W+********4 jet sample:**
**The fit uses**** **
**Pythia ttbar 175 to model the top contribution (float)**
**ALPGEN W+3p MC to model W+jets for the W+********3 jet sample (float)**
**ALPGEN W+4p MC to model W+jets for the W+********4 jet sample (float)**
**non-isolated leptons as the QCD background**
**Fix QCD bkgnd to expectation from MET vs Iso (6.3%)**
**Other backgrounds in fit:   ****WW+1p,  W********+2p, Z********ee/********/********+2p, WZ+0p, W****l********bb+1p, single top****.  **
**These bkgnds add to ~11% and have similar shape to W+jets       (at least for H****T****).**
**We fix this shape within the W+3p shape**
**Our primary variable is H****T****, but we investigate the fit fraction stability for the other kinematic variables.**

## HT Fit to Signal Region, 3 Jets

**Plot showing shapes**
**of contributing components**

**Plot showing stacked conrib-**
**ution from each component **

- For Blessing

## ET(2) + ET(3) Fit, 3 Jets

- ET(2) + ET(3) Fit, 3 Jets

- For Blessing

**CDF Preliminary**

## Min(DeltaR jj) Fit, 3 Jets

- Min(DeltaR jj) Fit, 3 Jets

- For Blessing

**CDF Preliminary**

## Aplanarity Fit, 3 Jets

- For Blessing

**CDF Preliminary**

## Fit Results for the W+3 Jets Sample

- Fit Results for the W+3 Jets Sample

- For Blessing

**CDF Preliminary**

## HT Fit to Signal Region, 4 Jets

- For Blessing

**Plot showing shapes**
**of contributing components**

**Plot showing contribution**
**amt. from each component**

## ET(2) + ET(3) Fit, 4 Jets

- For Blessing

**CDF Preliminary**

## Min(DeltaR jj) Fit, 4 Jets

- For Blessing

**CDF Preliminary**

## Aplanarity Fit, 4 Jets

- For Blessing

**CDF Preliminary**

## Fit Results for the W+4 Jets Sample

- Fit Results for the W+4 Jets Sample

- For Blessing

**CDF Preliminary**

## Summary of Fit Fraction Results

**ttbar fraction taken from the H****T**** fits.**

**fraction of ttbar in W+********3 Jets****	**
**Fraction = ****0.148 ******** 0.053**
**fraction of ttbar in W+********4 Jets****	**
**Fraction = ****0.510 ******** 0.164**

**CDF Preliminary**

- For Blessing

## Determination of the Cross Section

| Sample | Data Observed | Fraction | Cross Section |
| --- | --- | --- | --- |
| W+3 Jets | 308 | 0.148  0.053 | 5.1  1.8 pb |
| W+4 Jets | 75 | 0.510  0.164 | 7.7  2.4 pb |

- For Blessing

**CDF Preliminary**

## Studies of Systematic Effects

**Systematics are studied to determine impact on:**
**Fit result due to shape difference in H****T**
**Acceptance**
**Systematics examined****:**
**Jet Energy scale: ****method prescribed by Jet Corrections Group**
**Generator for ttbar: ****Determine using Pythia vs Herwig**
**Top Mass: ****Determine using Pythia (170-180 GeV/c****2****)**
**Q****2**** for Background Model: ****AlpGen Q****2****= M****W****2**** v. Q****2**** = M****W****2****+********P****T****2****(Jets)**
**Lepton ID: ****From CDF6574**
**PDF’s: ****From CDF6574 and from shape study**
**Background model: ****conversions vs non-isolated leptons**
**ISR: ****on/off using Pythia ttbar**
**Method: use PE’s**

## Jet Energy Scale Systematics

| Data | Shape Error % | Acceptance Error % | Total Error % |
| --- | --- | --- | --- |
| relative | 0.090 | 0.009 | 0.099 |
| cal stability | 0.046 | 0.004 | 0.049 |
| energy scale | 0.129 | 0.012 | 0.141 |
| MC | Shape Error % | Acceptance Error % | Total Error % |
| Relative | 0.105 | 0.016 | 0.121 |
| energy scale | 0.033 | 0.017 | 0.181 |
| mult. Int. | 0.00 | 0.00 | 0.00 |
| absolute | 0.022 | 0.015 | 0.120 |
| OOC | 0.005 | 0.020 | 0.046 |
| splash out | 0.010 | 0.024 | 0.073 |
| Total | ± 26.4% | ± 4.5% | ± 30.2% |

**Table for**
**NJets ******** 3**

**Result for**
**NJets ******** 4:**
**  ****±**** ****31.5%**

## QCD Background Model Systematic

| HT | double | half | Error |
| --- | --- | --- | --- |
| NJets  3 | 2.0% | 1.4% | 1.7% |
| NJets  4
 | 5.3% | 1.4% | 3.3% |

_**Normalization:**_** ****Use MET v. Iso. technique to estimate quantity **
**of QCD fakes in our sample.  Determine error: vary MET and **
**isolation cuts independently.  See a ~10% shift (see table in note).**
**Re-fit using PE’s and get a negligible shift in the fraction.      **_** **_

**Normalization error**
**obtained but doubling **
**and halving our QCD**

_**Shape:**_** ****Use conversion electron sample for alternate Ht shape.**
** ****Generate PE’s and re-fit data twice: with non-isolated lepton**
**sample and with conversions.  Take mean of difference of fits.**
**Result: 16%**

## Systematic for Q2 Scale

- Systematic for Q2 Scale

| fit | Error |
| --- | --- |
| NJets  3 | 14% |
| NJets  4
 | 0.6% |

** ****Almost all of the MC samples of X+n parton (jet)**
**in the top group are AlpGen with a fairly hard**
**Q****2**** scale:  ****Q****2**** = M****W****2****+********P****T****2****(Jets) **
**We obtained a sample of AlpGen W+3p MC at**
**Q****2**** = M****W****2**** ****, and ran it through simulation/production**

**Performed PE’s with**
**shifted shapes much**
**like with the jet corrections,**
**took difference of fits ********2**

## PDF Shape Systematic

**CTEQ6 with NLO + HERWIG / PYTHIA with LO**
- Eigenvector #15: gluon distribution functions dominate

**Consider largest **
**contributing **
**Eigenvectors:**
**10, 15, 19**
**Create shifted**
**Templates, refit**
**Using PE’s.**
**Systematic Error:**
**Njets ******** 3:  ****3.3%**
**Njets ******** 4:****  ****4.3%**

## Systematic Effects W+3 Jets

| Effect | Shape  | Acceptance | Total |
| --- | --- | --- | --- |
| Energy Scale | 28% | 5.1% | 30% |
| Generator | 0.60% | --- | 0.6% |
| Top Mass | 8.0% | 5.0% | 13% |
| Q2 Choice | 14% | --- | 14% |
| PDF | 3.3% | 5.3% 
(from lepton ID) | 8.6% |
| ISR (Pythia) | 0.56% | 0.78% | 1.3% |
| Luminosity |  |  | 5.9% |
| Background model | 16% | 1.7%
(normalization) | 16% |
| Total |  |  | 40.6% |

- For Blessing

## Systematic Effects W+4 Jets

| Effect | Shape  | Acceptance | Total |
| --- | --- | --- | --- |
| Energy Scale | 20.4% | 13.0% | 32% |
| Generator | 0.60% | --- | 0.6% |
| Top Mass | 8.0% | 5.0% | 13% |
| Q2 Scale | 0.31% | --- | 0.3% |
| PDF | 4.3% | 5.3%
(from lepton ID) | 9.6% |
| ISR | 0.56% | 0.78% | 1.3% |
| Luminosity |  |  | 5.9% |
| Background model | 16% | 3.3%
(normalization) | 16% |
| Total |  |  | 39.5% |

- For Blessing

## Summary

**We’ve measured the top cross section in the lepton + jets**
**channel using H****T  ****.  **
**Requiring 3 or more jets: ******** ****(ttbar)**** = 5.1 ± 1.8 ****(stat)**** ± 2.1 ****(sys)**** **
**Requiring 4 or more jets: ******** ****(ttbar)**** = 7.1 ± 2.4 ****(stat)**** ± 3.0 ****(sys)**

## Backup Slides

## Data/ MC Comparisons

_**Problem**_**: Examining the H****T**** distribution in the W+1 jet data: the fit undershoots H****T**** in the low end, and overshoots H****T**** at the high end.  **
**How to quantify the difference?**
**Kolmogorov-Smirnov statistic *****flawed (biased?) in ROOT***
**Modify procedure****: **
**Fit MC+QCD to data**
**Obtain Kolmogorov distance ‘****D****’**
**Generate PE events according to fitted MC **
** ****Refit random events**
**Obtain Kolmogorov distance ‘****d****’ between random sample and fit**
**Probability of data fit = fraction of time ****D ****< ****d**** **

- For Blessing

## Acceptance

## Expected QCD Background Fraction 

- For Blessing

- Update this!

| W+”n” jets | Electron bkgnd  | Muon bkgnd | Total bkgnd  |
| --- | --- | --- | --- |
| 1 | 9.6  0.3% | 5.1  0.2% | 7.6  0.4% |
| 2 | 12.6  0.8% | 4.0  0.4% | 8.7  0.9% |
|  3 | 15.0  1.9% | 5.6  1.2% | 11.7 2.2% |

| W+”n” jets | Electron bkgnd  | Muon bkgnd  | Total bkgnd |
| --- | --- | --- | --- |
| 1 | 3.8  0.2% | 2.9 0.2% | 3.4  0.3% |
| 2 | 6.1  0.5 % | 2.0  0.2% | 4.3  0.5% |
| 3 | 8.9  1.5 % | 3.4  0.9% | 7.0  1.7% |

- For Blessing

**No ******** cut imposed**

****** ****cut imposed**

- Use MET vs Isolation to determine the
- background normalization and  effect of the ****** cut**

## Determination of Sensitivities

**Use pseudo-experiments (PE’s) to determine expected precision on cross section:**
**Number of ttbar using acceptance, luminosity,  theory ******** (7pb)**
**Number of QCD from MET vs ISO**
**Number of W’s: # observed events minus (expected ttbar + QCD)**
**Each of the above numbers correspond to mean of Poisson**
**Use Ht as the discriminating variable; sample from ttbar and AlpGen MC’s, and conversion data sample. **

## HT Shape Comparison,                               W+3p v. Smaller Backgrounds

## QCD Background Findings(old)

| Njets
(muons) | MET v. Isol |
| --- | --- |
| 1
2
3+4 | 0.111 ± 0.004
0.077 ± 0.005
0.070 ± 0.012 |
| Njets
(electrons) | MET v. Isol |
| 1
2
3+4 | 0.186 ± 0.004
0.159 ± 0.006
0.196 ± 0.017 |

- QCD higher for electrons as expected.  Numbers still
- under study... muon 3-4 jet strange.  Also studying
- shapes from low MET and high “isolation” region.

## Bias in KS

- Note: 50% of PE’s have KS probability>80%

**Bias in KS Probability Due to Fitting**