# Presentation: 371596

## The W Angular Decay Distribution

- G. Steinbrück	Columbia University
- For the DØ Collaboration
- Wine & Cheese Seminar Sept. 1, 2000
- Outline
- Introduction to QCD with W and Z Bosons
- Some Measurements:
- W/Z Cross Section, W width, Z p**T**
- W Angular Decay Distribution:
- Monte Carlo
- Data Selection
- Backgrounds
- Results

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##  Introduction to W & Z Production at the Tevatron 

-  Due to very large pp jj production, need to use leptonic decays
-  W  l (BR ~ 11% per mode)
-  Z  ll (BR ~ 3% per mode)
-  Distinctive event signatures
-  High PT isolated leptons (e or ******)**
-  One high PT lepton + Missing  E**T **(W)
-  Two high PT leptons (Z)
-  Low backgrounds
-  Large samples
-  Well understood EW vertex
-  Test QCD

-  Introduction to W & Z Production at the Tevatron* *

- O(as0)

- W Bosons Detected

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## QCD Corrections O(s) 

- QCD Corrections O(s)

**W**

*g*

*q*

*q’*

*q*

*q’*

*q’*

**W**

*g*

**Modifications**** ****due to QCD corrections:**

- O(s)

**Boson produced with transverse momentum  ( < P****T**** > ~ 10 GeV )**
**Boson + jet events possible  ( W + 1 jet ~ 7%, E****T****jet**** > 25 GeV )**
**Inclusive cross sections larger (K factor ~ 18%)**
**Boson decay angular distribution modified**

**W**

*q*

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##       Connections between W,Z Production, QCD and New Physics 

-       Connections between W,Z Production, QCD and New Physics* *

- W mass + top mass:  Constrain Higgs mass

- Need precise model of W production
- and decay for Monte Carlos

- NLO QCD

- W mass measurements require low PTW

- Resummation techniques

- Non-perturbative QCD

- Current DØ MW ~ 10 -25 MeV from PTW model
- MW = 10 MeV MH/MH = 14%

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## W Event 

- W Event

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##          Inclusive Cross Section

- L(D0) = 1.062 x L(CDF)
- D0 uses world avg. ppinel, CDF uses CDF measurement

**Measurement errors:**
- Stat  Sys ~ 2%,
-  Luminosity error ~ 4%

**Theory error:**
-  ~ 3%, NNLO, O(s2) Dominated by PDF’s at NLO...
- (need NNLO)

**         **Inclusive Cross Section

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##    W Width

-    W Width

**(SM:2.094 ********0.008)**

- Form ratio:

**LEP**

**W Width**

**Perturbative**
**QCD**

- e

**SM EW**

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## W, Z pT Theory

- W, Z pT Theory

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## Z pT

- Z pT

- Data corrected for resolution effects

**Less dominated by detector res. at low p****T**** **

**More sensitive to theory than W**

**PRD 61 (2000) + PRL 84 (2000)**

**W p****T**** in progress, results and W&C soon**

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## Z pT: Data-Theory/Theory

- Z pT: Data-Theory/Theory

- Compared to published parameters,        could be refitted

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## W Angular Decay Distribution

- V-A Theory: Angular Distribution in W Rest Frame:

- QCD effects alter the Angular Distribution.
- Calculation now done Collins-Soper-Frame.

**- Sign of Charge of W**

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## W Angular Decay Distribution

- Spin orientation altered by additional gluon.

- q

- q’

- s(q)

- s(q’)

- s(W)

- q

- q’

- s(q)

- s(q’)

- s(W)

- g

- O(s)

- O(s0)

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## Angular Distribution Theory

- Integration over ****yields:

- general

- QCD

- Eight helicity terms

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## W Angular Decay Distribution

- E. Mirkes.        Nucl. Phys., **B387** 3 (1992)

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## The  Collins-Soper Frame

- z

- y

- x

- p

- P

- p**T****W**

- Ambiguity in M**W** and sign

- Rotation around z, orienting p**T****W** along x
- Boost along z so that W is at rest wrt z
- Boost along x’ so that W is at rest

- From Lab Frame to CS Frame:

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## W Angular Decay Distribution

- Independent test of QCD corrections
- Spin Structure of W Production and Decay
- Correction to W Mass Measurement ~40 MeV

- We measure ******2**(p**T**)

- Previous Measurement of ******2**(p**T**) in Run 1a  by Manuel Martin, who developed many of the techniques used here.
- Limited by statistics and low p**T****W **=>
- No distinguishing power

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## W Mass Monte Carlo: Production

- Factorize:

- Parton Luminosity

- Width

- True Mass

- Polarization

**ß **from fits to Herwig + PDFLIB W mass spectrum

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## W Production cont.

- Sign of W charge is chosen randomly
- For valence quarks, this determines polarization
- For sea-sea interactions (20%), choose polarization randomly

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## W Transverse Momentum

- Perturbative part

- Ladinski-Yuan:

- cutoff

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##  W Decay

-  W Decay

- W Bosons are decayed in Collins-Soper Frame, using the QCD prediction for the angular distribution
- Generate Radiative Decays
- Boost to Lab Frame
- Calculate derived quantities
- Apply Detector Smearing

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##  Hadronic Scale 

-  Hadronic Scale

**Scale of hadronic recoil different from EM energy scale: Includes energy from had. Showers, energy loss in uninstrumented regions of calorimeter. **

**Determined from ****Z ********ee**** ****events: ****Z p****T**** either from two electron system (p****T****ee****) or from recoil activity (- p****T****rec****).**** **
**Project transverse momenta onto ********direction.**

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##  Hadronic Scale 

-  Hadronic Scale

**Linear scale for p****T ****> 10 GeV.**

**Log scale for p****T ****< 10 GeV.**

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## Hadronic Resolution

**Resolution for hard component of recoil, u****T****:**

**Soft component of recoil modeled by adding E****T**** from Minimum Bias events scaled by tunable factor ********mb****.**

**Plot ********balance resolution in bins of p****T********(ee) and calculate ********2****.**

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## Hadronic Resolution

- Plot ******2**+1 ellipse for ******mb** and S**rec**.

- Vary ******mb **and srec separately

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## Transverse Mass Distributions

- Data and Monte Carlo agree

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## The D0 detector

- This analysis uses the calorimeter and the central detector

**Tracking: **
******vertex********mm **
******r********) =****	****60********m (VTX)**
**       ****= 180 ********m (CDC)**
**       ****= 200 ********m (FDC)**

**Calorimeter: **
****** **
******x ********1x0******
******EM)=15%/E****1/2**
******had)=50%/E****1/2**

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## Data Selection

- Electron: ET>25 GeV, |****<1.1
- Missing ET>25 GeV
- Reject Events with a second electron and invariant mass close to Z mass: 75 GeV < Mee < 105 GeV.
- 41173 events
- This analysis uses 50 GeV <MT<90 GeV.

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## W Angular Decay Distribution

- angle cannot be measured directly
- use correlation with transverse mass

- M**W** sensitive to angular distribution

- From Monte Carlo

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## W Angular Method

- Use Bayesian approach:

**From Monte Carlo**

**Prior from V-A theory: 1+ cos****2**********.

- Multiply with M**T****W **distribution to obtain angular distribution:

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## W Angular Method

- Use same method to obtain cos ******* **distribution from data:

- Use this method to generate cos ******* **templates (from MC):

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## W Angular Method

- Compare measured angular distribution to templates using Log L method:

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## Monte Carlo Closure Test 

- Monte Carlo Closure Test

- Large Statistics

- Statistics Scaled to Data

- Method works!

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## Backgrounds

- QCD multijet: One jet looks like an electron + energy mismeasured  missing ET.
- Determined from data. Rate ~1%

- Z ee, one electron lost in uninstrumented or underinstrumented region of the calorimeter. Determined from Herwig Monte Carlo. Rate ~1%.

- ttbar  WWbb, WW  e****jj from Herwig Monte Carlo. Rate ~0.2%.

- W  ********e****Included in Monte Carlo. Rate ~2%.

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## QCD Multijet Background

**Matrix Method: Divide W sample M with looser cuts in P (pass) and F (fail). Can also divide in B  (background) and R (real W’s):**

**From Z ******** ee events**

**Efficiency for “fake” loose electrons to pass tight cuts **

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## QCD Multijet Background

- Jet efficiency ******j**** **calculated from data sample with anti-W cut: ET < 15 GeV.

**MC W’s**** **

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## Backgrounds

- Backgrounds small due to tight electron quality cuts

- Analysis done in 4 p**T****W **bins.

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## Log L Distributions

- Note that ******2** gets smaller for larger p**T.**

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## Angular Distributions

- Lower p**T****W**

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## Angular Distributions

- Higher p**T****W**

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## Result 

- Result

| pT (GeV) | 0-10 | 10-20 | 20-35 | 35-200 |
| --- | --- | --- | --- | --- |
| 2,measured | 1.09 | 0.84 | 0.52 | 0.13 |
| Stat. Errors | ±0.13 | ±0.25 | ±0.36 | ±0.38 |
| 2,predicted | 0.98 | 0.89 | 0.68 | 0.24 |
| Mean pTW | 5.3 | 13.3 | 25.7 | 52.9 |
| Combined Syst. | ±0.08 | ±0.09 | ±0.12 | ±0.12 |

- Dominated by Statistical Errors

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## Systematic Errors 

- Systematic Errors

| pT (GeV) | 0-10 | 10-20 | 20-35 | 35-200 |
| --- | --- | --- | --- | --- |
| QCD | ±0.04 | ±0.05 | ±0.09 | ±0.07 |
| Z ee | ±0.01 | ±0.01 | ±0.02 | ±0.04 |
| ttbar | ±0.00 | ±0.00 | ±0.00 | ±0.02 |
| EM scale | ±0.06 | ±0.05 | ±0.03 | ±0.04 |
| Had Scale | ±0.03 | ±0.01 | ±0.04 | ±0.04 |
| Had Resol | ±0.02 | ±0.02 | ±0.05 | ±0.06 |
| fixed 1 | ±0.01 | ±0.05 | ±0.03 | ±0.03 |
| Combined syst. | ±0.08 | ±0.09 | ±0.12 | ±0.12 |

**Estimated by generating cos ************* templates with varied parameters.**

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## W Angular Result

-  errors dominated by statistics

- QCD preferred:2.3 ****** **effect

- To be submitted to PRD very soon

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## Significance Calculation

-  Odds-Ratio Method

- Log R = 0.5 **** 1 ****
- We get 2.3****

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## Summary

- Measured the Angular Distribution in W Decays
- Angular Distribution Modified by QCD Corrections
- Important Effect in W mass measurement
- NLO QCD Calculation preferred by 2.3 ****
- Other Measurements probing QCD with W and Z Bosons include:
-  Inclusive W and Z Cross Sections and W Width
- The  Z p**T **Distribution
- Coming soon: W p**T**** **paper and W&C

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