# Presentation: 279057

## Evidence forSingle Top Quark Production at DØ

**Evidence for****Single Top Quark Production at DØ**

**Ann Heinson**
**University of California, Riverside**
**for the DØ Collaboration**
**CERN Particle Physics Seminar**
**Tuesday January 30, 2007**

## Top Quarks

- Spin 1/2 fermion,   charge +2/3
- Weak-isospin partner of the bottom quark
- ~40x heavier than its partner
**M****top**** = 171.4 ± 2.1 GeV**
- Heaviest known fundamental particle

*t*

- top

- Produced mostly in *tt* pairs at the Tevatron
- 85% *qq,*   15% *gg*
- Cross section = 6.8 ± 0.6 pb at NNLO
- Measurements consistent with this value

- 200
- 150
- 100
- 50
- 0

- up
- down
- strange
- charm
- bottom
- top

- [GeV]

## The DØ Experiment

- Fermilab
- Tevatron

- Top quarks observed by DØ and CDF in 1995 with ~50 pb–1 of data

- Still the only place to see top
- Now have 40x more data  precision measurements

## Dataset

- DØ has 2 fb–1 on tape
- Many thanks to the Fermilab accelerator division!
- This analysis uses 0.9 fb–1 of data collected from 2002 to 2005

## Single Top Overview

**Single Top Overview**

- s-channel:   “*tb*”
- NLO = 0.88 ± 0.11 pb

- t-channel:   “*tqb*”
- NLO = 1.98 ± 0.25 pb

**Experimental results **(95% C.L.)
**DØ****	*****tb***** < 5.0 pb****	**(370 pb–1)
**CDF****	*****tb***** < 3.2 pb****	**(700 pb–1)

**DØ****	*****tqb***** < 4.4 pb****	**(370 pb–1)
**CDF****	*****tqb***** < 3.1 pb****	**(700 pb–1)

**CDF****	*****tb+tqb***** < 2.7 pb**	Likelihoods**	**(960 pb–1)
- 		***tb+tqb***** < 2.6 pb****	**Neural networks
- 		***tb+tqb***** = 2.7 ****+1.5**** pb****	**Matrix elements	(significance of 2.3 )

**–****1.3**

- “*tW* production”
- NLO = 0.21 pb
- (Too small to see at the Tevatron)

## Motivation

**Study *****Wtb***** coupling in top production**
- Measure |*V**tb*| directly  (more later)
- Test unitarity of CKM matrix
- Anomalous *Wtb* couplings
**Cross sections sensitive to new physics**
- s-channel: resonances (heavy *W**** *boson, charged Higgs boson, Kaluza-Klein excited *W**KK*, technipion, etc.)
- t-channel: flavor-changing neutral currents (*t – Z / **** / g – c / u* couplings)
- Fourth generation of quarks
**Polarized top quarks – spin correlations measurable in decay products**
**Measure top quark partial decay width and lifetime**
**CP violation (same rate for top and antitop?)**
**Similar (but easier) search than for *****WH***** associated Higgs production**
- Backgrounds the same – must be able to model them successfully
- Test of techniques to extract a small signal from a large background

## Event Selection

**Event Selection**

**One isolated electron or muon**
- Electron pT > 15 GeV, || < 1.1
- Muon pT > 18 GeV, || < 2.0
**Missing transverse energy**
- ET > 15 GeV
**One b-tagged jet and at least one more jet**
- 2–4 jets with pT > 15 GeV,   || < 3.4
- Leading jet pT > 25 GeV, || < 2.5
- Second leading jet pT > 20 GeV

## Signal and Background Models

**Single top quark signals modeled using SINGLETOP**
- By Moscow State University theorists, based on COMPHEP
- Reproduces NLO kinematic distributions
- PYTHIA for parton hadronization
***tt***** pair backgrounds modeled using ALPGEN**
- PYTHIA for parton hadronization
- Parton-jet matching algorithm used to avoid double-counting final states
- Normalized to NNLO cross section
- 18% uncertainty includes component for top mass
**Multijet background modeled using data with a non-isolated lepton and jets**
- Normalized to data before *b*-tagging (together with *W*+jets background)

## W+jets Background

***W*****+jets Background**

*W*+jets background modeled using ALPGEN
- PYTHIA for parton hadronization
- Parton-jet matching algorithm used to avoid double-counting final states
*Wbb* and *Wcc* fractions from data to better represent higher-order effects
- 30% uncertainty for differences in event kinematics and assuming equal for *Wbb* and *Wcc*
*W*+jets normalized to data before *b*-tagging (with multijet background)
*Z*+jets, diboson backgrounds very small, included in *W*+jets via normalization

- Ann Heinson   (UC Riverside)

## Event Yields Before b-Tagging

**W Transverse Mass**

- 2 jets

- Electrons

- Muons

- 3 jets

- 4 jets

- Signal acceptances: *tb* = 5.1%, *tqb* = 4.5%
**S:B ratio for *****tb+tqb***** = 1:180**
- Need to improve S:B to have a hope of seeing a signal  select only events with *b*-jets in them

- Ann Heinson   (UC Riverside)

## b-Jet Identification

- Ann Heinson   (UC Riverside)

- Separate *b*-jets from light-quark and gluon jets to reject most *W*+jets background
**DØ uses a neural network algorithm**
- 7 input variables based on impact parameter and reconstructed vertex
**Operating point:**
*b*-jet efficiency  50%
*c*-jet efficiency  10%
- light-jet effic.    0.5%

## Event Yields after b-Tagging

- Signal acceptances: *tb* = (3.2 ± 0.4)%, *tqb* = (2.1 ± 0.3)%
**Signal:background ratios for *****tb+tqb***** are 1:10 to 1:50**
- Most sensitive channels have 2jets/1tag, S:B = 1:20
**Single top signal is smaller than total background uncertainty**
- counting events is not a sensitive enough method
- use a multivariate discriminant to separate signal from background

## Search Strategy Summary

**Search Strategy Summary**

**Maximize the signal acceptance**
- Particle ID definitions set as loose as possible (i.e., highest efficiency, separate signal from backgrounds with fake leptons later)
- Transverse momentum thresholds set low, pseudorapidities wide
- As many decay channels used as possible – this analysis shown in red box
- Channels analyzed separately since S:B and background compositions differ
**Separate signal from background using multivariate techniques**

## 12 Analysis Channels 

**W Transverse Mass**

- 2 jets

- Electrons

- 3 jets

- 4 jets

- 1 tag

- 2 tags

- Muons

- 1 tag

- 2 tags

## Systematic Uncertainties

- Uncertainties are assigned for each signal and background component in all analysis channels
- Most systematic uncertainties apply only to normalization
**Two sources of uncertainty also affect the shapes of distributions**
- jet energy scale
- tag-rate functions for *b*-tagging MC events
- Correlations between channels and sources are taken into account
**Cross section uncertainties are dominated by the statistical uncertainty,** the systematic contributions are all small

| Source of Uncertainty | Size |
| --- | --- |
| Top pairs normalization | 18% |
| W+jets & multijets normalization | 18–28% |
| Integrated luminosity | 6% |
| Trigger modeling | 3–6% |
| Lepton ID corrections | 2–7% |
| Jet modeling | 2–7% |
| Other small components | Few % |
| Jet energy scale | 1–20% |
| Tag rate functions | 2–16% |

## Final Analysis Steps

- We have selected 12 independent sets of data for final analysis
- Background model gives good representation of data in ~90 variables in every channel
**Calculate discriminants that separate signal from background**
- Boosted decision trees
- Matrix elements
- Bayesian neural networks
- Check discriminant performance using data control samples
- Use ensembles of pseudo-data to test validity of methods
**Calculate cross sections using binned likelihood fits of**
**	****(floating) signal + (fixed) background to data**

## Measuring a Cross Section

**Measuring a Cross Section**

- Nbkgds = 6   (*ttll, ttlj, Wbb, Wcc, Wjj, *multijets),    Nbins = 12 chans x 100 bins = 1,200
- Cross section obtained from peak position of Bayesian posterior probability density
- Shape and normalization systematic uncertainties treated as nuisance parameters
- Correlations between uncertainties are properly accounted for
- Signal cross section prior is non-negative and flat

- Ann Heinson   (UC Riverside)

## Testing with Pseudo-Data

- To verify that the calculation methods work as expected, we test them using several sets (“ensembles”) of pseudo-data
- Wonderful tool to test the analyses!  Like running DØ many 1,000’s of times
**Select subsets of events from total pool of MC events**
- Randomly sample a Poisson distribution to simulate statistical fluctuations
- Background yields fluctuated according to uncertainties to reproduce correlations between components from normalization
**Ensembles we used:**
- Zero-signal ensemble, (*tb+tqb*) = 0 pb
- SM ensemble, (*tb+tqb*) = 2.9 pb
- “Mystery” ensembles, (*tb+tqb*) = ? pb
- Measured Xsec ensemble, (*tb+tqb*) = meas
- Each pseudo-dataset is like one DØ experiment with 0.9 fb–1 of “data”,
- 	up to 68,000 pseudo-datasets per ensemble

- Ann Heinson   (UC Riverside)

## Signal-Background Separationusing Decision Trees

**Signal-Background Separation****using Decision Trees**

- Machine-learning technique, widely used in social sciences, some use in HEP
- Idea: recover events that fail criteria in cut-based analyses
- Start at first “node          ”  with “training sample” of 1/3 of all signal and background events
- For each variable, find splitting value with best separation between two children (mostly signal in one, mostly background in the other)
- Select variable and splitting value with best separation to produce two “branches          ” with corresponding events, (F)ailed and (P)assed cut

- Repeat recursively on each node
- Stop when improvement stops or when too few events are left (100)
- Terminal node is called a “leaf          ” with purity = Nsignal/(Nsignal+Nbackground)
- Run remaining 2/3 events and data through tree to derive results
- Decision tree output for each event = leaf purity
- 	(closer to 0 for background, nearer 1 for signal)

- Ann Heinson   (UC Riverside)

## Boosting the Decision Trees

- Boosting is a recently developed technique that improves any weak classifier (decision tree, neural network, etc)
- Recently used with decision trees by GLAST and MiniBooNE
- Boosting averages the results of many trees, dilutes the discrete nature of the output, improves the performance
**This analysis:**
- Uses the “adaptive boosting algorithm”:
- Train a tree *T**k*
- Check which events are misclassified by *T**k*
- Derive tree weight *w**k*
- Increase weight of misclassified events
- Train again to build *T**k+*1
- Boosted result of event *i *:
- 20 boosting cycles
- Trained 36 sets of trees: (*tb+tqb, tb, tqb*) x (*e,***) x (2,3,4 jets) x (1,2 *b*-tags)
- Separate analyses for *tb* and *tqb *allow access to different types of new physics
- Search for *tb+tqb* has best sensitivity to see a signal – results presented here

- Before boosting

- After boosting

- Ann Heinson   (UC Riverside)

## Decision Tree Variables

**Decision Tree Variables**

- 49 input variables
- Adding more variables does not degrade the performance
- Reducing the number of variables always reduces sensitivity of the analysis
- Same list of variables used for all analysis channels

- Ann Heinson   (UC Riverside)

- cos(leptonbesttop,besttopCofM)
- cos(leptonbtaggedtop,btaggedtopCofM)

**Most discrimination power:**
- M(alljets)
- M(*W*,tag1)
- cos(tag1,lepton)btaggedtop
- Q(lepton) x (untag1)

## Decision Tree Cross Checks

- Select two background-dominated samples:
- “*W*+jets”:   = 2 jets, HT(lepton, ET, alljets) < 175 GeV, =1 tag
- “*tt*”:   = 4 jets, HT (lepton, ET, alljets) > 300 GeV , =1 tag
- Observe good data-background agreement

- “*W*+jets”

- Electrons

- “*tt*”

- Muons

**Decision Tree**
**Outputs**

- Ann Heinson   (UC Riverside)

## Decision Tree Verification

**Decision Tree Verification**

- Use “mystery” ensembles with many different signal assumptions
- Measure signal cross section using decision tree outputs
- Compare measured cross sections to input ones
**Observe linear relation close to unit slope**

- Input xsec

- Ann Heinson   (UC Riverside)

## Signal-Background Separationusing Matrix Elements

- Method pioneered by DØ for top quark mass measurement
- Use the 4-vectors of all reconstructed leptons and jets
- Use matrix elements of main signal and background Feynman diagrams to compute an event probability density for signal and background hypotheses
- Goal: calculate a discriminant:
- Define *P**Signal* as a normalized differential cross section:
- Performed in 2-jets and 3-jets channels only
- No matrix element for *tt* so no discrimination between signal and top pairs yet
- Matrix element verification with ensembles shows good linearity, unit slope, near-zero intercept

- Ann Heinson   (UC Riverside)

## Matrix Element MethodFeynman Diagrams

- Ann Heinson   (UC Riverside)

*tb*

*tq*

- 2-jet channels

*Wbb*

*Wcg*

*Wgg*

- 3-jet channels

*tbg*

*tdb*

*Wbbg*

## Matrix Element S:B Separation

**Matrix Element S:B Separation**

- Ann Heinson   (UC Riverside)

*tb *discriminant

*tq* discriminant

- 2-jet channels

## Matrix Element Cross Checks

- Select two background-dominated samples:
- “Soft *W*+jets”:   = 2 jets, HT(lepton, ET, alljets) < 175 GeV, =1 tag
- “Hard *W*+jets”:  = 2 jets, HT(lepton, ET, alljets) > 300 GeV, =1 tag
- Observe good data-background agreement

- “Soft *W*+jets”

**Matrix Element**
**Outputs**

- Ann Heinson   (UC Riverside)

- “Hard *W*+jets”

- Full range

- High end

- Full range

- High end

*tb*

*tq*

## Signal-Background Separationusing Bayesian Neural Networks

- Ann Heinson   (UC Riverside)

**Bayesian neural networks improve on this technique:**
- Average over many networks weighted by the probability of each network given the training samples
- Less prone to over-training
- Network structure is less important – can use larger numbers of variables and hidden nodes
**For this analysis:**
- 24 input variables (subset of 49 used by decision trees)
- 40 hidden nodes, 800 training iterations
- Each iteration is the average of 20 training cycles
- One network for each signal (*tb+tqb, tb, tqb*) in each of the 12 analysis channels
- Bayesian neural network verification with ensembles shows good linearity, unit slope, near-zero intercept

- Neural networks use many input variables, train on signal and background samples, produce one output discriminant

## Statistical Analysis

**Before looking at the data, we want to know two things:**
**By how much can we expect to rule out a background-only hypothesis?**
- Find what fraction of the ensemble of zero-signal pseudo-datasets give a cross section at least as large as the SM value, the “expected p-value”
- For a Gaussian distribution, convert p-value to give “expected signficance”
**What precision should we expect for a measurement?**
- Set value for “data” = SM signal + background in each discriminant bin (non-integer) and measure central value and uncertainty on the “expected cross section”
**With the data, we want to know:**
**How well do we rule out the background-only hypothesis?**
- Use the ensemble of zero-signal pseudo-datasets and find what fraction give a cross section at least as large as the measured value, the “measured p-value”
- Convert p-value to give “measured signficance”
**What cross section do we measure?**
- Use (integer) number of data events in each bin to obtain “measured cross section”
**How consistent is the measured cross section with the SM value?**
- Find what fraction of the ensemble of SM-signal pseudo-datasets give a cross section at least as large as the measured value to get “consistency with SM”

## Expected Results

**Expected Results**

**Decision Trees**
- 		1.9 %
- 		2.1 
- 		2.7       pb

- Expected p-value
- Expected significance
- Expected cross section

- +1.6
- –1.4

**Matrix Elements**
- 	3.7 %
- 	1.8 
- 	3.0       pb

- +1.8
- –1.5

**Bayesian NNs**
- 	9.7 %
- 	1.3 
- 	3.2      pb

- +2.0
- –1.8

**Decision Trees**
- Probability to rule out
- background-only hypothesis
- Zero-signal ensemble

**Matrix**
**Elements**
- Zero-signal
- ensemble

**Bayesian**
**Neural**
**Networks**
- Zero-signal
- ensemble

**Bayesian**
**Neural Networks**
- Expected
- result

**Matrix Elements**
- Expected
- result

**Decision Trees**
- “Data” =
- SM signal +
- background
- Expected
- result

- SM =
- 2.9 pb

- SM =
- 2.9 pb

- SM =
- 2.9 pb

## Bayesian NN Results

**Bayesian NN Results**

- (*tb+tqb*) = 5.0 ± 1.9 pb
- Measured p-value = 0.89 %
- Measured significance = 2.4 
- Compatibility with SM = 18%

**Bayesian**
**Neural**
**Networks**
- Measured
- result

- 5.0 pb

**Bayesian**
**Neural**
**Networks**
- Zero-signal
- ensemble

- Probability
- to rule out
- background-only
- hypothesis

**Bayesian**
**Neural**
**Networks**
- SM-signal
- ensemble
- Compatibility
- With SM

- 5.0 pb

## Matrix Element Results

**Matrix Element Results**

- (*tb+tqb*) = 4.6        pb
- Measured p-value = 0.21 %
- Measured significance = 2.9 
- Compatibility with SM = 21%

**Matrix**
**Elements**
- Measured
- result

- 4.6 pb

**Matrix**
**Elements**
- Zero-
- signal
- ensemble

- +1.8
- –1.5

**Matrix**
**Elements**
- SM-signal
- ensemble
- Compatibility
- With SM

- 4.6 pb

- Probability
- to rule out
- background-only
- hypothesis

## Matrix Element Results

**Matrix Element Results**

- Discriminant output without and with signal component
- (all channels combined to “visualize” excess)

## Decision Tree Results

**Decision Tree Results**

- (*tb+tqb*) = 4.9 ± 1.4 pb
- Measured p-value = 0.035 %
- Measured significance = 3.4 
- Compatibility with SM = 11%

**Decision**
**Trees**
- Measured
- result

- 4.9 pb

**Decision**
**Trees**
- Zero-
- signal
- ensemble

**Decision**
**Trees**
- SM-signal
- ensemble
- Compatibility
- With SM

- 4.9 pb

- Probability
- to rule out
- background-only
- hypothesis

## Decision Tree Results

**Decision Tree Results**

- Discriminant output (all channels combined) over the full range and a close-up on the high end

## ME Event Characteristics

**ME Event Characteristics**

- Mass (lepton,ET,btagged-jet)   [GeV]

- Q(lepton) x (untagged-jet)

- ME Discriminant < 0.4

- Mass (lepton,ET,btagged-jet)   [GeV]

- ME Discriminant > 0.7

- Q(lepton) x (untagged-jet)

## DT Event Characteristics

**DT Event Characteristics**

- Mass (lepton,ET,btagged-jet)   [GeV]

- W Transverse Mass   [GeV]

- DT Discriminant < 0.3

- Mass (lepton,ET,btagged-jet)   [GeV]

- DT Discriminant > 0.65

- W Transverse Mass   [GeV]

## Correlation Between Methods

**Correlation Between Methods**

- Choose the 50 highest events in each discriminant and count overlapping events

- Measure cross section in 400 pseudo-datasets of SM-signal ensemble and calculate linear correlation between each pair of results

| Correlation between measured cross sections |  |  |  |
| --- | --- | --- | --- |
|  | DT | ME | BNN |
| DT | 100 % | 39 % | 57 % |
| ME |  | 100 % | 29 % |
| BNN |  |  | 100 % |

- Results from the three methods are consistent with each other

| Overlap of signal-like events |  |  |  |  |
| --- | --- | --- | --- | --- |
|  |  | DT | ME | BNN |
|  | DT | 100 % | 52 % | 56 % |
|  | ME |  | 100 % | 46 % |
|  | BNN |  |  | 100 % |
|  | DT | 100 % | 58 % | 48 % |
|  | ME |  | 100 % | 52 % |
|  | BNN |  |  | 100 % |

- Electrons

- Muons

## CKM Matrix Element Vtb

**CKM Matrix Element *****V******tb***

- Weak interaction eigenstates and mass eigenstates are not the same: there is mixing between quarks, described by CKM matrix
**In the SM, top must decay to *****W***** and *****d, s, *****or *****b***** quark**
- Constraints on *V**td** *and *V**ts* give
**If there is new physics, then**
- No constraint on *V**tb*
- Interactions between top quark and gauge bosons are very interesting

- Ann Heinson   (UC Riverside)

## Measuring |Vtb|

**Measuring |*****V******tb******|***

- Ann Heinson   (UC Riverside)

**Assume**
- SM top quark decay :
-  Pure *V–A *:        = 0
- CP conservation :        =       = 0
**No need to assume only three quark families or CKM matrix unitarity**
- 	(unlike for previous measurements using *tt* decays)
- Measure the strength of the *V–A* coupling, |*V**tb**     *|, which can be > 1

| Additional theoretical uncertainties |  |  |
| --- | --- | --- |
|  | tb | tqb |
| Top mass | 13 % | 8.5 % |
| Scale | 5.4 % | 4.0 % |
| PDF | 4.3 % | 10 % |
| s | 1.4 % | 0.01 % |

- Use the measurement of the single top cross section to make the first direct measurement of |*V**tb*|
- Calculate a posterior in |*V**tb*|2     ((*tb*, *tqb*)  |*V**tb*|2)
**General form of *****Wtb***** vertex:**

## First Direct Measurement of |Vtb|

- +0.6
- –0.5

**First Direct Measurement of |*****V******tb******|***

- |*V**tb**f**1**L*| = 1.3 ± 0.2

- Ann Heinson   (UC Riverside)

- 0.68 < |*V**tb*| ≤ 1 at 95% C.L.
- (assuming *f**1**L* = 1)

- |*V**tb**f**1**L*|2
- = 1.7

- +0.0
- –0.2

- |*V**tb*|2 = 1.0

## Challenging measurement – small signal hidden in huge complex background
	Much time spent on tool development (b-tagging) and background modeling

Three multivariate techniques applied to separate signal from background

Boosted decision trees give result with 3.4  significance

First direct measurement of |Vtb|

Result submitted to Physical Review Letters

Door is now open for studies of Wtb coupling and searches for new physics

- 	Much time spent on tool development (*b*-tagging) and background modeling
- Three multivariate techniques applied to separate signal from background
- Boosted decision trees give result with 3.4  significance
- First direct measurement of |*V**tb*|
- Result submitted to *Physical Review Letters*
- Door is now open for studies of *Wtb* coupling and searches for new physics

**Summary:   Evidence for****Single Top Quark Production at DØ**

## Additional Material

## Results for tb and tqb Separately

**Results for *****tb***** and *****tqb***** Separately**

**Decision**
**Trees**
- Measured
- result for
**s-channel  *****tb***

**Decision**
**Trees**
- Measured
- result for
**t-channel  *****tqb***

- (*tqb*) = 4.2        pb
- (*tb*) = 1.0 ± 0.9 pb

- +1.8
- –1.4