# Presentation: 053487

## Measurement of the W-Boson Helicity Fractions in Top-Quark Decays at CDF

- Measurement of the W-Boson Helicity Fractions in Top-Quark Decays at CDF

**Thorsten Chwalek, Dominic Hirschb****ühl, Thomas Müller, Jeannine Wagner-Kuhr, Wolfgang Wagner**
**Karlsruhe Institute of Technology**

## Top-quark lifetime is shorter than hadronization time  
Decay products preserve the helicity content of the underlying weak interaction
Chance to probe the V-A structure of the weak interaction in the top-quark decay

- W-Boson Helicity in Top-Quark Decays

- Top-quark lifetime is shorter than hadronization time
- Decay products preserve the helicity content of the underlying weak interaction
- Chance to probe the V-A structure of the weak interaction in the top-quark decay

**SM prediction for m****t****=175 GeV/c****2****, m****b****=0**

**t**

**W****+**

**b**

- Sb=1/2            St=1/2              SW=1

- longitudinal
- left-handed
- right-handed

- Helicity fractions that differ from the SM predictions indicate new physics
- For example: V+A component in weak interaction, anomalous couplings in top-decay.

## Angle between the direction of the charged lepton in the W-boson rest frame and the direction of the W-boson in the top-quark rest frame
Characteristic angular distribution depending on the polarization of the W-boson

To calculate * we have to reconstruct the four-vectors of top-quark, W-boson, and charged lepton 

- Sensitive Observable: cos*

- Angle between the direction of the charged lepton in the W-boson rest frame and the direction of the W-boson in the top-quark rest frame
- Characteristic angular distribution depending on the polarization of the W-boson
- To calculate * we have to reconstruct the four-vectors of top-quark, W-boson, and charged lepton

- l

- l

- W+

- b

- *

## Neutrino four-vector is obtained from MET and W-boson mass-constraint
All possibilities to assign the jets to the 2 b-quarks and 2 light quarks are considered
  Leads to a multiplicity of possibilities to reconstruct the event 
The challenge is to find the right hypothesis for each event using constraints on:	
mass of reconstructed W-boson
mass difference of the two top-quarks
transverse energy of the two top-quarks
b-likeness of the jets assigned to the b-quarks (NN b-tagger)

- Full Reconstruction

- _Lepton+Jets:_
- one charged lepton, missing trans-verse energy, four or more jets (one with a secondary vertex tag)

- Neutrino four-vector is obtained from MET and W-boson mass-constraint
- All possibilities to assign the jets to the 2 b-quarks and 2 light quarks are considered
-   Leads to a multiplicity of possibilities to reconstruct the event
- The challenge is to find the right hypothesis for each event using constraints on:
- mass of reconstructed W-boson
- mass difference of the two top-quarks
- transverse energy of the two top-quarks
- b-likeness of the jets assigned to the b-quarks (NN b-tagger)

- Number of possibilities to reconstruct one event:

## Calculate expected number of events in each bin of the cos* distribution
Consider effects due to event-selection and event-reconstruction
by applying efficiency and migration matrix
Two separate measurements:
measure F0, fix F+ = 0.0 (SM)
measure F+, fix F0 = 0.7 (SM)
 One free parameter
Combined measurement:
F0 and F+ are both free parameters 
Perform binned likelihood fit

- Calculate expected number of events in each bin of the cos* distribution
- Consider effects due to event-selection and event-reconstruction
- by applying efficiency and migration matrix
- Two separate measurements:
- measure F0, fix F+ = 0.0 (SM)
- measure F+, fix F0 = 0.7 (SM)
-  One free parameter
- Combined measurement:
- F0 and F+ are both free parameters
- Perform binned likelihood fit

## Results (1 parameter fit)

**   ****Measurement of F****+****(F****0****=0.7):**

- Correct distribution for event-selection and reconstruction effects

-  448 candidates in Lint=1.7fb-1

## Results (2 parameter fit)

- 448 candidates in Lint=1.7fb-1

## Results are within the uncertainties in agreement with the standard model prediction.
Analysis is still statistically limited.

- Conclusion

- Results are within the uncertainties in agreement with the standard model prediction.
- Analysis is still statistically limited.