# Presentation: 202734

## Measurements of the W Helicity in Top Quark Decays

**Kenneth Johns**
- University of Arizona
- for the
- DØ and CDF Collaborations

## W Helicity

- The heavy mass of the top quark makes it a prime target for searches of physics beyond the Standard Model
- Measurement of the W helicity is a measurement of the tbW vertex
- Top quark lifetime < hadronization time
- V-A weak interaction determines the top quark decay in SM

- b

- b

## W Helicity

- In the mb=0 limit,
- Finite mb and O(αs) corrections change the above values by < 2%
- We look for new physics by searching
- for F0 ≠ 0.7 (assuming F+=0)
- for F+ > 0 (assuming F0=0.7 )
- F+ is indirectly constrained to a few percent by b→sγ data (e.g. Fujikawa&Yamada, PRD 49 (1994) 5890)

## W Helicity

- The angular decay distribution for unpolarized top
*w(cosθ) = 3/8(1+cosθ)**2**F**+** + 3/8(1-cosθ)**2**F**-** + 3/4(sin**2**θ)F**0*

## W Helicity

- The angular factors are also reflected in the shape of the lepton PT distribution
- The lepton PT spectrum for F+ will be harder than that for F0
- The lepton PT spectrum for F- will be softer than that for F0

## W Helicity Measurements

| Expt | Published? |  | Method |
| --- | --- | --- | --- |
| CDF Run I | PRL 2000 | 106 pb-1 | PTlepton |
| CDF Run I | PRD 2005 | 109 pb-1 | Mlb2 |
| DØ Run I | N | 125 pb-1 | Matrix Element |
| CDF Run II | N | 162 pb-1 | PTlepton |
| CDF Run II | N | 162 pb-1 | Mlb2 |
| DØ Run II | N | 163 pb-1 | cos(θ*)
 |

## W Helicity Measurements

| Expt | Method | Samples | Notes |
| --- | --- | --- | --- |
| CDF Run I | PTlepton | LJ (w/wo b-tag)
LL (eμ) | SVT, SLT |
| CDF Run I | Mlb2 | LJ (w b-tags)
LL (eμ) | SVT |
| DØ Run I | ME | LJ | 4 jets only |
| CDF Run II | PTlepton | LJ w b-tags
LL | SVT 
3, 4 jets |
| CDF Run II | Mlb2 | LJ w b-tag  | SVT |
| DØ Run II | cos(θ*)
 | LJ w/wo b-tag | SVT |

**SVT = Secondary Vertex Tag**
**SLT = Soft Lepton Tag**

## Matrix Element Method

- ME method offers the possibility of increased statistical precision by using all measured quantities in an event
- Write the probability density
- Include background
- Form a likelihood

## Matrix Element Details

- Mttbar
- qqbar only (no gg)
- 4 jets only (no NLO)
- Mbkg
- W+jets only
- Selection cut on Pbkg used to reduce background
- Ensemble tests are used to estimate bias

## Matrix Element Results

- Assuming mt =175 GeV, F0 = 0.60 ± 0.30 (stat)
- Uncertainty in mt is accounted for by integrating L(F0,mt) over mt
- Including the remaining systematic errors gives
- F0 = 0.56 ± 0.31 (stat+mt) ± 0.07 (sys)

**m****t**

**F****0**

## PTlepton Method

- PTlepton is sensitive to the W helicity
- Charged leptons tend to be emitted opposite to WL direction
- Charged leptons tend to be emitted transverse to W0 direction
- F+ = 0 (hence measure F0)
- Select LJ b-tag and LL events
- Determine backgrounds ala cross section analyses
- Construct PTlepton PDF’s for signal and background
- Construct unbinned
- Including bias correction
- Estimate systematic uncertainties using ensemble testing
- Method of Feldman-Cousins is used to make a coherent statement about the true F0 given an estimated F0

## PTlepton Details

- Signal and background composition

**LJ**

**LL**

## PTlepton Combined Results

## PTlepton LL Results

## Mlb2 Method

- This method exploits the approximation
- A kinematic χ2 is used to match a reconstructed jet with the b parton
- Top-specific corrections derived from Monte Carlo are used to convert jet energies into parton energies
- F0 is extracted using a binned maximum likelihood fit
- Again, the results are interpreted using Feldman-Cousins confidence belts

## Mlb2 Details

- Systematic errors for the LJ data (CDF)

| Source | ΔF0 |
| --- | --- |
| Background shape | 0.12 |
| Top mass uncertainty | 0.09 |
| Jet energy scale | 0.06 |
| PDF uncertainty | 0.04 |
| MC modeling | 0.03 |
| ISR/FSR | 0.02 |
| SVT b-tagging | 0.01 |
| MC statistics | 0.01 |
| Total | 0.17 |

## Mlb2 Results

## Mlb2 Run I Results

- Similar to the Run II analysis
- b-tagged jets are chosen to form Mlb2
- Neyman construction for upper limit

## Cos(θ*) Method

- Use topological likelihood to determine signal and background contributions
- Use kinematic fit (assuming mt=175 GeV) to select b-jet associated with leptonically decaying W
- Selects correct b-jet ~57% of the time
- Produce cos(θ*) templates using Monte Carlo
- Perform binned likelihood fit to data
- Use Bayesian approach to set a confidence interval
- Use ensemble tests for systematic errors

## Cos(θ*) Details

- Cos(θ*) for ttbar signal (b-tag, e+jets channel)

**F****-****=0.3**
**F****+****=0.3**

## Cos(θ*) Results

- Topological analysis (no explicit b-tag)

## Cos(θ*) Results

- b-tag analysis

## Measurement Summary

| Expt | Method |  | Result |
| --- | --- | --- | --- |
| CDF Run I | PTlepton | 106 pb-1 | F0 = 0.91 ± 0.37 ± 0.13
F+ < 0.28 (95%CL) |
| CDF Run I | Mlb2 | 109 pb-1 | F+ < 0.24 (95%CL) |
| DØ Run I | ME | 125 pb-1 | F0 = 0.56 ± 0.31 |
| CDF Run II | PTlepton | 162 pb-1 | F0 < 0.88 (95% CL)
F0 = 0.27 + 0.31 -0.21 |
| CDF Run II | Mlb2 | 162 pb-1 | F0 > 0.25 (95% CL) 
F0 = 0.89 ± 0.32 ± 0.17 |
| DØ Run II | cos(θ*)
 | 163 pb-1 | F+ < 0.24 (90%CL)
F+ < 0.24 (90%CL) |

## Conclusions

- Good effort in measuring the W helicity in top decay
- Variety of methods, variety of data samples
- All measurements are consistent with the SM
- CDF PTlepton spectrum in the LL sample is interesting
- Presently statistical errors are x2 systematic errors
- Very useful to combine results from DØ and CDF
- Dominant systematic errors arise from uncertainties in top quark mass, backgrounds, and jet energy scale
- Look forward to exploiting the full statistical power of Run II data
- Look forward to exploiting the top quark factory at the LHC

## W Helicity

- Top decays

## Matrix Element Details

- Systematic errors

| Source | σ(F0) |
| --- | --- |
| Acceptance | 0.05 |
| Jet energy scale | 0.01 |
| Spin correlations | 0.01 |
| PDF | 0.01 |
| Signal model | 0.02 |
| Multiple interactions | 0.006 |
| QCD background | 0.02 |
| Subtotal | 0.07 |
| Statistical + mass | 0.31 |
| Total | 0.314 |

## PTlepton Method

##  PTlepton LJ Results

## PTlepton Details

- Systematic errors

| Source | σsys (LJ+LL) |
| --- | --- |
| Background normalization | 0.10 |
| Top mass uncertainty | 0.11 |
| ISR/FSR | 0.05 |
| PDF uncertainty | 0.03 |
| PTlepton shape uncertainty | 0.02 |
| Monte Carlo statistics | 0.01 |
| Acceptance correction | 0.02 |
| Trigger correction | 0.02 |
| Total | 0.17 |

## Feldman-Cousins

- The result of the maximum likelihood fit for F0 can be outside the physical region
- The procedure of Feldman-Cousins can be used to construct a confidence interval in the physical region
- Ensemble tests are used to map true F0’s to a distribution of estimated F0’s using the Feldman-Cousins ordering principle
- Systematic errors can be included by adding in quadrature σ(F0est) and σ(sys)
- The resulting 2D figure then gives the confidence interval on true F0 for a measured (estimated) F0

## Mlb2 Details

- Systematic errors

| Source | ΔF0 |
| --- | --- |
| Bkg shape | 0.12 |
| Top mass uncertainty | 0.09 |
| Jet energy scale | 0.06 |
| PDF uncertainty | 0.04 |
| MC modeling | 0.03 |
| ISR/FSR | 0.02 |
| SVT b-tagging | 0.01 |
| MC statistics | 0.01 |
| Total | 0.17 |

## Mlb2 Details

- Backgrounds
- 31 events observed

| Background | Total |
| --- | --- |
| QCD | 3.4±1.0 |
| W+jets (mistags) | 2.8±0.6 |
| Wbb | 1.6±0.7 |
| Wcc | 0.6±0.3 |
| Wc | 0.7±0.3 |
| WW/WZ | 0.29±0.05 |
| Single top | 0.49±0.07 |
| Total | 9.9±1.7 |
| Total * χ2 acceptance | 6.4±1.1 |

## Cos(θ*) Details

- Systematic errors (topological)

- Systematic errors        (b-tag)

| Source | σ (F+) |
| --- | --- |
| Top mass | 0.11 |
| Jet energy scale | 0.04 |
| Background model | 0.08 |
| Signal model | 0.05 |
| Total | 0.15 |

| Source | σ (F+) |
| --- | --- |
| Top mass | 0.06 |
| Jet energy scale | 0.06 |
| Likelihood fit | 0.02 |
| Background model | 0.01 |
| Underlying event | 0.06 |
| MC statistics | 0.01 |
| Total | 0.11 |

## Cos(θ*) Details

- Cos(θ*) for tt signal (b-tag, e+jets channel)

## Cos (θ*) Details

- Signal and background are determined using a topological likelihood

- b-tag (μ+jets)** **

| Channel | tt | W+jets | QCD |
| --- | --- | --- | --- |
| μ+jets | 9.6 ± 2.7 | 2.0 ± 1.4 | 0.7 ± 0.4 |
| e+jets | 14.2 ± 3.4 | 6.6 ± 1.8 | 0.6 ± 0.3 |

| Channel | tt | W+jets | QCD |
| --- | --- | --- | --- |
| μ+jets | 11.3 ± 1.3 | 17.6 ± 1.2 | 2.1 ± 0.5 |
| e+jets | 25.9 ± 1.5 | 20.3 ± 1.5 | 2.7 ± 0.5 |

- b-tag

- topological

## Bayesian Limit

- DØ uses a Bayesian technique to set a confidence interval in the physical region of F+
- Let xML be the result of the maximum likelihood fit
- If xML is outside the physical range (or close to the physical