# Presentation: 886420

## Search for Single Top at CDF

**Bernd Stelzer, **UCLA
- on behalf of the CDF Collaboration
- Fermilab, December 1st 2006**_x0013_**

## Outline

*Outline*

- Single Quark Production at the Tevatron
- Motivation for Single Top Search
- The Experimental Challenge
- Analysis Techniques at CDF
- Likelihood Function Analysis (955 pb-1)
- Neural Network Analysis (700 pb-1)
- Matrix Element Analysis (955 pb-1)
- New Results
- Conclusions

## The Tevatron Collider

*The Tevatron Collider*

- Tevatron produces per day:
- ~ 40 top pair events
- ~ 20 single top events

- Cross Sections at s = 1.96 TeV

## Top Quark Production

- s-channel
- NLO = 0.88±0.07 pb

- t-channel
- NLO = 1.98±0.21 pb

**Observed **
**1995!**

**Wanted!**
**2006/7?**

- B.W. Harris et. al, hep-ph/0207055, Z.  Sullivan hep-ph/0408049

- Quoted cross-sections at Mtop=175GeV/c2

- Vtb

- Directly measure Vtb
-   Single Top ~ (Vtb)2
- Source of ~100%
- polarized top quarks

- NLO = 6.7±0.8 pb

- Mtop = 171.4  2.1 GeV/c2

- Current World average:

## Sensitivity to New Physics

- Single top rate can be altered due to the presence of new Physics
- Heavy *W* boson, charged Higgs H+, Kaluza Klein excited *W*KK (s-channel signature)
- Flavor changing neutral currents: *t-Z/**γ/g**-c *couplings (t-channel signature)

**Tait, Yuan PRD63, 014018(2001)**

- s-channel and t-channel have
- different sensitivity to new physics

- Z

- c

- t

- W,H+

**Experimental**
**Challenge**

## Event Signatures

*Event Signatures*

- Jet2

- MET

- Top Pair Production with decay
- Into Lepton + 4 Jets final state
- are very striking signatures!

- Single top Production with decay
- Into Lepton + 2 Jets final state
- Is less distinct!

## Data Collected at CDF

*Data Collected at CDF*

**Delivered : 2.1 fb****-1**

**Collected : 1.7 fb****-1**

- This analysis: 955/pb
- (All detector components ON)

- CDF is getting faster, too!
- 6 weeks turnaround time to calibrate,
- validate and process raw data

- Tevatron people are
- doing a fantastic job!
- 2fb-1 party coming up!

- Design goal

## Single Top Selection

_**Event Selection:**_
**1 Lepton, **ET >15 GeV, ||< 2.0
**Missing E****T **(MET)** **> 25 GeV
**2 Jets, **ET > 15 GeV, ||< 2.8
**Veto** Fake W, Z, Dileptons, 		Conversions, Cosmics
**At least one b-tagged jet**, 			(secondary vertex tag)

- CDF W+2jet Candidate Event:
- Close-up View of Layer 00 Silicon Detector

- Run: 205964,  Event: 337705
- Electron ET= 39.6 GeV, MET = 37.1 GeV
- Jet 1: ET = 62.8 GeV,  Lxy = 2.9mm
- Jet 2: ET = 42.7 GeV,  Lxy = 3.9mm

- 12mm

| Number of Events / 955 pb-1 | Single Top | Background |   S/B  |   S/B  |
| --- | --- | --- | --- | --- |
| W(l) + 2 jets | 74 | 15500 | ~1/210 | ~ 0.6 |
| W(l) + 2 jets + b-tag | 38 | 540 | ~1/15 | ~ 1.6 |

## Background Estimate

- Falsely tagged light quark or gluon jets
- Mistag probability parameterization obtained from inclusive jet data

*Background Estimate*

_**W+HF jets (Wbb/Wcc/Wc)**_
- W+jets normalization from data and
- heavy flavor (HF) fraction from MC

- _Top/EWK (WW/WZ/Z__→__ττ, ttbar__)_
- MC normalized to theoretical cross-section

- _Non-__*W (QCD)*_
- Multijet events and jets with semileptonic *b*-decay
- Fit low MET data and extrapolate into signal region

**Wbb**

**Wcc**

**Wc**

**non-*****W***

**Z/Dib**

**Mistags**

**tt**

- _W+HF jets (Wbb/Wcc/Wc)_
- W+jets normalization from data and heavy flavor (HF) fractions from ALPGEN Monte Carlo

## Signal and Background Event Yield

*Signal and Background Event Yield*

- CDF Run II Preliminary, L=955 pb-1 Event yield in W+2jets

| s-channel | 15.4 ± 2.2 |
| --- | --- |
| t-channel | 22.4 ± 3.6 |
| tt | 58.4 ±13.5 |
| Diboson | 13.7 ± 1.9 |
| Z + jets | 11.9 ± 4.4 |
| Wbb | 170.9 ± 50.7 |
| Wcc | 63.5 ± 19.9 |
| Wc | 68.6 ± 19.0 |
| Non-W | 26.2 ± 15.9 |
| Mistags | 136.1 ± 19.7 |
| Single top | 37.8 ± 5.9 |
| Total background | 549.3 ± 95.2 |
| Total prediction | 587.1 ± 96.6 |
| Observed | 644 |

## Jet Flavor Separation

- Distinguish *b*-quark jets from charm / light jets using a Neural Network trained with secondary vertex information
- Applied to b-tagged jets with secondary vertex
- 25 input variables:                           Lxy, vertex mass, track multiplicity, impact parameter, semilepton decay information, etc...
- Good jet-flavor separation!
- Independent of b-jet source
- Used in all three single top analyses

## Jet Flavor Separation II

- Fit to W+jets data shows good shape agreement
- Fit result consistent with background estimate

*W* + 2 jet events with ≥1 *b*-tag

|  | Background Estimate | Neural Network Fit |
| --- | --- | --- |
| W+bottom | 299.0  56.8 | 292.8  26.3 |
| W+charm | 148.1  39.4 | 171.6  53.8 |
| Mistags | 140.0  19.8 | 179.5  42.5 |
| Sum | 587.1  96.6 | 644.0 |

**Analysis **
**Techniques**

## Analysis Flow Chart

- Analysis Event Selection

- CDF Data

- Monte Carlo
- Signal/Background

- Apply MC
- Corrections

- 3 Analysis Techniques

- Template
- Fit to Data

- Discriminant

- Signal
- Background

- Cross Section

## Analysis Techniques

- Likelihood Analysis
- Neural Network Analysis
- Matrix Element Analysis

## The Likelihood Function Analysis

*The Likelihood Function Analysis*

- t-channel LF Input Variables:
- total transverse energy: HT
- Mlb (neutrino pz from kin. fitter)
- Cos(lepton,light jet) in top decay frame
- Qlepton*untagged jet aka QxEta
- mj1j2
- log(MEtchan) from MADGRAPH
- Neural Network b-tagger
- LF=0.01 for double tagged events

- s-channel LF Input Variables:
- Mlb
- log(HT* Mlb )
- ET(jet1)
- log(MEtchan)
- HT
- Neural Network b-tagger

*N**sig*

*N**bkg*

*i, indexes input variable*

## Likelihood Function Analysis

*Likelihood Function Analysis*

- Background

- Background

- Signal

- Signal

- Background

- Signal

- Unit area

- Wbb
- ttbar

- Wbb
- ttbar

- Wbb
- ttbar

- tchan
- schan

- tchan
- schan

- tchan
- schan

## Likelihood Function Discriminants

*Likelihood Function Discriminants*

- t-channel

- s-channel

- Background

- Signal

- Background

- Signal

- Unit Area

- Wbb
- ttbar

- tchan
- schan

- tchan
- schan

- Wbb
- ttbar

- Templates normalized
- to prediction

- Templates normalized
- to prediction

## Analysis Techniques

- Likelihood Analysis
- Neural Network Analysis
- Matrix Element Analysis

## Neural Network Analysis - Combined Search

- Single Neural Network trained with SM combination of s- and t-channel as signal
- 14 Variables: top and dijet invariant masses, Qlxq, angles, jet ET1/2 and j1+ j2, W-boson , lepton pT, kinematic top mass fitter quantities, Neural Network b-tag output etc..

- Current result using 695/pb (update with 955/pb expected shortly!)
- Yield Estimate [695/pb]: Single-Top: 28±3 events, Total Background: 646±96 events

## Neural Network Analysis - Separate Search

*Neural Network Analysis - Separate Search*

- Two NN’s trained separately for s-channel and t-channel (similar variables)

- t-channel

*W*+heavy flavor

- ttbar

- s-channel

## Analysis Techniques

- Likelihood Analysis
- Neural Network Analysis
- Matrix Element Analysis

## Matrix Element Approach

- Inspired by D0/CDF Matrix Element top mass analyses
- Here, we apply the method to a search!
- Attempt to include all available kinematic information:
- Calculate an event-by-event probability (based on fully differential cross-section calculation) for signal and background hypothesis

## Matrix Element Method

*Matrix Element Method*

- Parton distribution function (CTEQ5)

- Leading Order matrix element (MadEvent)

***W(E******jet******,E******part******)*** is the probability of measuring a jet energy Ejet when Epart was produced

- Integration over part of the phase space *Φ**4*

- Event probability for signal and background hypothesis:

- Input only lepton
- and 2 jets 4-vectors!

## Event Probability Discriminant (EPD)

*Event Probability Discriminant (EPD)*

*;b* = Neural Network *b*-tagger output

- We compute probabilities for signal and background hypothesis per event
- Use full kinematic correlation between signal and background events
- Define ratio of probabilities as event probability discriminant (EPD):

## Event Probabilty Discriminant

*Event Probabilty Discriminant*

- S/B~1/3
- S/B~2.5
- In most sensitive bins!
- (EPD>0.8)

- S/B~1/15, S/B~1.6

- All events

- Templates normalized
- to prediction

**Cross-Checks**

## Cross-Checks in Data Control Samples

- Validate method using data without looking at single top candidates
- Compare the Monte Carlo prediction of the discriminant shape to
- various control samples in data
- W+2 jets data (veto *b*-jets, orthogonal to our candidate sample)

## Cross-Checks in Data Control Samples

*Cross-Checks in Data Control Samples*

- CDF Run II Preliminary

- CDF Run II Preliminary

- b-tagged dilepton + 2 jets sample
- Purity: 99% ttbar
- Discard lepton with lower pT

- b-tagged lepton + 4 jets sample
- Purity: 85% ttbar
- Discard 2jets with lowest pT

**Template Fit**
**to the data**

## Analysis Flow Chart

- Analysis Event Selection

- CDF Data

- Monte Carlo
- Signal/Background

- Apply MC
- Corrections

- Likelihood
- Fit to Data

- Discriminant

- Signal
- Background

- Cross Section

- Multivariate
- Analysis
- Technique

## Likelihood Fit to Data

- The distribution of the discriminant in data is a superposition
- of the single top and several background template distributions
- Obtain most probable single top content in data by performing a
- binned maximum likelihood fit
- Background templates are allowed to float in the fit within
- their rate uncertainties (Gaussian constrained)
- Other sources of systematic uncertainty (rate and shape) are
- included as nuisance parameters in the likelihood function and
- are also allowed to float within their uncertainties

## Rate vs Shape Systematic Uncertainty

- Discriminant

- Rate systematics give fit templates freedom to move vertically only
- Shape systematics allow templates to ‘slide horizontally’ (bin by bin)

- Rate systematics

- Shape systematics

- Systematic uncertainties can affect rate and template shape

## Binned Likelihood Fit

- Binned Likelihood Function:
- Expected mean in bin k:
- All sources of systematic uncertainty included as nuisance parameters
- Correlation between Shape/Normalization uncertainty considered (δi)

*β**j* = *σ**j**/**σ**SM* parameter
- single top (j=1)
- W+bottom (j=2)
*W+charm *(j=3)
- Mistags (j=4)
- ttbar (j=5)
*k* = Bin index
*i* = Systematic effect
*δ**i* = Strength of effect
*ε**ji±   **= *±1σ norm. shifts
*κ**jik**±** = *±1σ shift in bin k

## Sources of Systematic Uncertainty

| Single Top | Rate Variations | Shape Variations |
| --- | --- | --- |
| Jet Energy Scale |  |  |
| Initial State Radiation |  |  |
| Final State Radiation |  |  |
| Parton Dist. Function |  |  |
| Monte Carlo Generator |  |  |
| Efficiencies / b-tagging SF |  |  |
| Luminosity |  |  |
| Total Rate Uncertainty | 10.5% | N/A |

- CDF RunII Preliminary, L=955pb-1

| Background | Rate Unertainty |
| --- | --- |
| W+bottom | 25% |
| W+charm | 28% |
| Mistag | 15% |
| ttbar | 23% |

| Backgrounds | Rate Variations | Shape Variations |
| --- | --- | --- |
| Jet Energy Scale |  |  |
| Neural Net b-tagger |  |  |
| Mistag Model |  |  |
| Non-W Model |  |  |
| Q2 Scale in Alpgen MC |  |  |

**Discovery **
**Potential**

## Signal Sensitivity

*Signal Sensitivity*

- We use the CLs Method developed at LEP
*L. Read*, J. Phys. G **28**, 2693 (2002)
*T. Junk*, Nucl. Instrum. Meth. A 434, 435 (1999)
- http://www.hep.uiuc.edu/home/trj/cdfstats/mclimit_csm1/
- Compare two models at a time
- Define Likelihood ratio test statistic:
- Systematic uncertainties included		            in pseudo-experiments
- Use median p-value as expected sensitivity

| Likelihood Function Analysis: | Median p-value = 2.3%  (2.0) |
| --- | --- |
| Matrix Element Analysis: | Median p-value = 0.6%  (2.5) |

- Median

- More signal like

- Less signal like

**Results**

## Neural Network Results

- Best fit Separate Search:

- Best fit Combined Search:

- Analysis very correlated with Likelihood
- Function analysis
- Expected sensitivity similar to Matrix Element

## Likelihood Function Results

*Likelihood Function Results*

- Best fit Separate Search:

- Best fit Combined Search:

| 95 | s+t channel |
| --- | --- |
| Expected | 2.9 pb |
| Observed | 2.7 pb |

- 95% upper limit on combined
- single top cross section

*Note: Expected limit assumes no single top*

- Current result excludes models
- beyond the Standard Model

## Matrix Element Technique - Result

- Matrix Element analysis observes excess over background expectation
- Likelihood fit result for combined search:

## Observed p-value

*Observed p-value*

| Observed p-value = 1.0%  (2.3) |
| --- |

- b

- s+b

- CDF RunII Preliminary, L=955pb-1

| Observed p-value = 51.3% |
| --- |

- CDF RunII Preliminary, L=955pb-1

- -2lnQ

## Single Top Candidate Event

**Central Electron Candidate**
- Charge: -1, Eta=-0.72
- MET=41.85, MetPhi=-0.83
- Jet1: Et=46.7    Eta=-0.61    b-tag=1
- Jet2: Et=16.6    Eta=-2.91    b-tag=0
**QxEta = 2.91 (t-channel signature)**
- EPD=0.95

*Single Top Candidate Event*

**Jet1**

**Jet2**

**Lepton**

**Run: 211883, Event: 1911511**

## QxEta for Candidate Events in Signal Region

- 1) EPD>0.60

- 2) EPD>0.80

- 3) EPD>0.90

- 4) EPD>0.95

- Look for signal features
- (QxEta) in signal region

## QxEta Distributions in Signal Region

- 1)

- 2)

- 3)

- 4)

## Compatibility of the New Results

- Performed common pseudo-experiments
- Use identical events
- ME uses only 4-vectors of lepton, Jet1/Jet2
- LF uses sensitive event variables
- Correlation among fit results: ~53%
- 6% of the pseudo-experiments had a difference in fit results at least as large as the difference observed in data

- CDF II data

*The result we observe in the data is *
*compatible at the ~6% level*

## Candidate Events in 2D LF and ME Discriminant Space

- Divide the 2D discriminant space of the Matrix Element
- and Likelihood Function analysis into 4 regions
- Define combined background region (1) and combined signal
- region (1)
- Look also at mixed regions (2,3)

- LF

- Signal Hypothesis Preferred

******2**** prob 33.7%**

******2**** prob 49.8%**

- 1

- 2

- 3

- 4

- 1

- 2

- 3

- 4

- Null hypothesis

- Signal hypothesis

## Conclusions

*Conclusions*

- Single top production probes Vtb and is sensitive new physics
- We improved sensitivity by a factor of 3-4 compared to published results
- We now have 2 - 2.5  sensitivity to single top per analysis!
- Presented three analyses using different techniques to separate signal from huge background
- Results consistent at 6% level but it's interesting that they show differences
- With more data and further improvements we learn what the data is telling us
- Exciting times! Back to work!

| Technique | s+t cross-section | Expected p-value | Observed p-value |
| --- | --- | --- | --- |
| Likelihood Function (955/pb) | 0.3(+1.2/-0.3)pb | 2.3% | 51.3% |
| Neural Network (695/pb) | 0.8(+1.3/-0.8)pb | coming soon | coming soon |
| Matrix Element (955/pb) | 2.7(+1.5/-1.3)pb | 0.6% | 1.0% |
| Combined Analysis (955/pb) | coming soon | coming soon | coming soon |

## Backup Slides

- Backup

## Non-W Estimate

- Build non-W model from anti-electron selection
- Require at least two non-kinematic lepton ID variables to fail:
- Ehad/Eem, EM Shower Profile 2, shower maximum matching (dX and dZ)
- Data is superposition of non-W and W+jets contribution -> Likelihood Fit

- Signal Region

- Before b-tagging:

- After b-tagging:

- Signal Region

## Mistag Estimate

- Mistag Events arise due to limited detector resolution
- Parameterize Mistag probability in control data (generic jet sample)
- Apply Mistag Matrix (MM) to W+jets events in data:

- Account for material interaction, long lived light particles

## W + Heavy Flavor Estimate

*W + Heavy Flavor Estimate*

- Method inherited from CDF Run I (G. Unal et. al.)
- Measure fraction of W+jets events with heavy flavor (b,c) in Monte Carlo
- Normalize fractions to W+jets events found in data

- Heavy flavor fractions
- and b-tagging efficiencies
- from LO ALPGEN Monte Carlo

- Calibrate ALPGEN heavy flavor
- fractions inclusive jet data and
- Inclusive ALPGEN jet Monte Carlo

*Note: Similar for W+charm background*

- Large uncertainties from Monte Carlo estimate and heavy flavor calibration (~25-30%)

- CDF RunII Reference:
- PhysRevD.71,052003

## Heavy Flavor Fraction Calibration

- 1) Estimate generic jet heavy flavor fraction in ALPGEN Monte Carlo
- 2) Fit for bottom and charm fraction in generic jet data
- Difference between the two outcomes suggests K=1.5±0.4
- Result supported by study using MCFM:

- J. M. Campbell, J. Houston,
- Method 2 at NLO, hep-ph/0405276

## Input Variables to Matrix Element Analysis

- Lepton

- Jet1

- Jet2

- Input to the Matrix Element Analysis are the measured four-vectors
- of the Lepton, Jet1 and Jet2 in the W+2jets data (>=1 b-tagged jet)