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### W Mass From LEP

Fermilab Wine and Cheese Seminar

6th October, 2006

Ambreesh Gupta, University of Chicago

1. Introduction

- W Boson in the Standard Model of Particle Physics

2. W mass Measurement

- Identifying and reconstructing W’s.

- Mass extraction techniques used by LEP experiments

3. Systematic Uncertainties on W mass measurement

5. Summary

I will show results from all the four experiments with details on OPAL analyses.

Fermilab Wine & Cheese

Standard Model of Particle Physics

Our picture of the fundamental constituents of nature

There are about 19 (+10) free

parameters in the theory to be

determined experimentally

Standard Model predicts

relationship between

these parameters.

Fermilab Wine & Cheese

H

W

W

W

t

(running of a)

f

Standard Model Relations

- Standard Model predicts relation between the parameters; W boson mass(MW)
- and Fermi constant(GF), fine structure constant(), Z boson mass (MZ)

- : electron g-2 0.004 ppm

GF : muon life-time 9 ppm

MZ : LEP 1 lineshape 23 ppm

- Precision measurements require higher order terms in the theory and help
- constraint the unknown pieces.

Fermilab Wine & Cheese

top-quark mass “predicted” by electroweak corrections prior to direct discovery

- The measured W mass precision is such that Top and Higgs loops required

for consistency in the Standard Model (SM)

- This gives an indirect inference on the Higgs.
- Better precision on W mass constraints the Higgs
- Indirect measurement of W mass
- - W mass known to 20 MeV from indirect measurement (LEP1 + SLD +Tevatron).
- - A direct measurement of W mass with similar precision is of great interest.
- Measurement of the width of W boson can also be carried out at LEP providing

further checks on consistency of the SM.

Fermilab Wine & Cheese

Large Electron Positron Collider (LEP)

LEP I (1989-1993) : Z physics. 18 million Z bosons produced

LEP II (1996-2000) : W physics. 80,000 W’s produced. (Energies from 161 GeV

– 209 GeV) W’s produced in pairs.

Fermilab Wine & Cheese

WW Production and Decay at LEP

Backgrounds

BR ~ 10%

WW ll

- W’s produced in pairs at LEP
- - 700 pb-1/experiment; 40,000 WW

BR ~44%

WW qql

Efficiency Purity

l l70%90%

qql85% 90%

qqqq85% 80%

BR ~ 46%

WW qqqq

Fermilab Wine & Cheese

Event Selection

- Event selection primarily based on multivariate relative likelihood discriminants

OPAL

Very good agreement between expected and observed.

Fermilab Wine & Cheese

W Mass at LEP

- The WW cross section at s = 2Mw
- sensitive to W mass
- LEP experiments collected
- 10 pb-1 data at s = 161 GeV
- Combined Result :
- Mw = 80.40 0.21 GeV

- Most of LEP 2 data at higher energies - use direct reconstruction
- There are two main steps in measuring W mass and width

1. Reconstruct event-by-event mass of W’s

2. Fit mass distribution Extract MW and W.

- However, jet energies poorly measured ( /E ~ 12% ), neutrinos unobserved.

Kinematic fitting plays vital role

Fermilab Wine & Cheese

Kinematic Fitting

- Mass Reconstruction
- - Identify lepton and jets (DURHAM)
- -- Energy flow techniques
- - Kinematic fitting
- -- Use LEP beam energy as constraint
- -- Total Energy = s; Total Momem. = 0;
- -- Additionally, apply equal mass constraint
- mw+ - mw- = 0;
- Significantly improved mass resolution

- Caveat- Photon radiation will change

s s’ (photon energy)

Need good WW4f theory model (~0.5% theory error )

Fermilab Wine & Cheese

Mass Reconstruction

- qqqq channel
- - Well constrained events
- - But, ambiguity in assigning jets to
- W’sCombinatorial Background
- - 5-jet event: 10 comb., 4-jet: 3-comb.

- qql channel
- - 1 or 2 constraint kinematics fit
- - Golden channel

Fermilab Wine & Cheese

81.33

Fit Methods- LEP experiments used three likelihood methods to extract W mass and width

from the reconstructed mass spectrum.

1.Re-weighting

2. Breit-Wigner

3.Convolution

The primary difference between the methods is the amount of information

they try to use for the best measurement.

- Re-weighting

- Weight fully simulated events to create

sample with new W mass and width

parameter

- No external bias correction needed

- Need large event sample to derive stable

weights

Fermilab Wine & Cheese

Fit Methods (continued)

Fitted Function (70-88) GeV mass

- Breit-Wigner
- - Fit to W mass spectrum with Breit-Wigner function
- - Width adjusted to account for resolution and ISR effects.
- - Bias corrected by comparing to fully simulated MC.

- Convolution

- P(m1,m2|Mw,Gw)R(m1,m2)

- Build event-by-event Likelihood

- Maximize statistical sensitivity

- Need bias correction as in BW

Fermilab Wine & Cheese

- - Likelihood built using three variables -- both in qqlv, qqqq channels
- ~ 400 events per bin for stable fit
- Fit for eight energy point, four channels, then combine => lots of MC needed.

- OPAL variables
- ALEPH also
- 3-d fit

5C fit mass error

Hadronic 4C mass

5C fit mass

4C fit mass

difference

5C fit mass error

5C fit mass

Fermilab Wine & Cheese

Performance of Likelihood Fucntion

- Check bias and pulls distributions. . .below a typical example

OPAL

- Test the central value modeling with bias plot
- Test the uncertainty on central value with pull distribution.

Fermilab Wine & Cheese

CV 80.416 0.053

RW 80.405 0.052

BW 80.390 0.058

OPAL W mass- Very good agreement between three methods in

channel and year

- Strong correlation between methods

=> Combining them had only small stat. gain

- CV, which has the smallest expected statistical

uncertainty is used as the main method.

- Use ofmomentum cut analysismakes

significant reductionin FSI uncertainty.

- Final W mass and total uncertainty from

the three methods on OPAL -

Fermilab Wine & Cheese

combined

qql

Source

19

5

8

35

79

11

Hadronisation

QED(ISR/FSR)

Detector

Colour Reconnection

Bose-Einstein Correlation

LEP Beam Energy

Other

14

7

10

9

2

10

4

13

8

10

0

0

9

3

44

40

59

Total Systematics

Statistical

Total

21

30

36

22

25

33

LEP W Mass

Channel weights

qqlv : 76%

qqqq : 22%

xs : 2%

- The combined preliminary LEP W mass
- MW = 80.376 0.025 (stat) 0.022 (syst) GeV
- Systematics on W mass

(MeV)

Fermilab Wine & Cheese

- The combined preliminary LEP W width
- W = 2.196 0.063(stat) 0.055(syst) GeV
- Systematics on W width

qql + qqqq

(MeV)

Source

Hadronisation

QED(ISR/FSR)

Detector

Colour Reconnection

Bose-Einstein Correlation

LEP Beam Energy

Other

40

6

22

27

3

5

19

Total Systematics

Statistical

Total

55

63

84

Fermilab Wine & Cheese

- LEP beam energy used in event kinematics fit DMW/MW DELEP/ELEP

- Beam energy calibrated using
- - Resonant De-Polarization (41- 60 GeV.)
- - Extrapolated to LEP II energies NMR probes
- - Main systematic error due toextrapolation
- Extrapolation checked with
- 1. Flux Loop
- 2. Spectrometer
- 3. Synchrotron Oscillation

- Final results on LEP beam energy ( Eur. Phys. J., C 39 (2005), 253 )
- - Reduction of beam energy uncertainty used in earlier W mass combination
- - old : DEbeam= 20-25 MeV DMW = 17 Mev
- - new : DEbeam = 10-20 MeV DMW ~ 10 Mev
- -- OPAL Final 9 MeV

Fermilab Wine & Cheese

LEP Beam Energy Cross Check with Data

- LEP beam energy can be estimated using radiavtive return events

- Z mass precisely known

- Measured mass in radiative events sensitive to beam energy

- Result consistent with zero within experimental errors

Fermilab Wine & Cheese

Systematics from MC Modeling

- Main Sources
- - QED/EW radiative effects
- - Detector Modeling
- Hadronisation Modeling
- - Background Modeling
- - Final State Interaction

MC modeled to represent data;

Disagreements Systematic error

Fermilab Wine & Cheese

- KoralW’s O(3) implementation adequate,
- but misses
- - WSR
- - interference between ISR,WSR & FSR
- KandY includes
- - O() corrections
- - Screened Coulomb Correction

Error ~ 7 MeV

Fermilab Wine & Cheese

Detector Systematics

Jet energy resolution

- Z0 calibration data recorded annually provides
- a control sample of leptons and jets (~ 45 GeV).
- Data/Mc comparison used to estimate corrections for
- - Jet/Lepton energy scale/resolution
- - Jet/Lepton energy linearity
- - Jet/Lepton angular resolution/biases
- - Jet mass
- Error is assigned from the error on correction

Jet energy scale

LEP Combined:

qqlv qqqq Combined

10 MeV 8 MeV 10 MeV

Fermilab Wine & Cheese

- MC programs (JETSET,HERWIG,ARIADNE) model production of hadrons

but difference in particles and their distributions

- The difference interplays with detector response

- particle assignment to jets

- cuts applied to low momentum particles

- low resolution for neutral particles

- assumptions made on particle masses at reco.

- JETSET used by all LEP experiment with parameters tuned with

Z peak data

systematic shift estimated from shift with other hadronization models.

LEP Combined:

qqlv qqqq Combined

13 MeV 19 MeV 14 MeV

Fermilab Wine & Cheese

Final State Interactions

The Basic Problem: If products of hadronically decaying W’s (~0.1 fm)

interact before hadronization (~1.0 fm) Can create a mass bias.

Two known sources that could potentially bias W mass

and width measurement

1.ColorReconnection

- color flow between W’s could bias their masses

- only phenomenological models exist.

- Most sensitive variable to CR is W mass itself

2. Bose-Einstein Correlation.

- coherently produced identical pions are closer in

phase space.

- BE correlation between decay products of same

W established

- Does the effect exist between W’s?

Fermilab Wine & Cheese

Color reconnection

- Only phenomenological models exist.

- SK1 model produces largest shift CR strength

parameter (ki)

- LEP experiments estimate effect of color reconnection
- Measure particle flow in the inter-jet regions of the
- W’s
- - Extreme values of CR disfavored by data
- but it does not rule out CR
- - A 68% upper limit on ki is used to set a data driven
- uncertainty on W mass.
- - Combined LEP value of ki = 2.13
- For this Reco. Prob., CR error ~ 120 MeV (OPAL)

Fermilab Wine & Cheese

Cuts and Cones: Reducing CR effect

- CR affects mostly soft particles between

jetschanges jet direction

- Re-calculate Jet direction

1.Within cone of radius R

2.Cut on particle momentum P

3.Weighted particle momentum |P|

- A,D,L,O use varations of below

- OPAL Uses P-cut2.5 GeVfor

qqqq

- ~18% loss in statistics.

- - Much reduced CR systematics
- 125 41 MeV (ki =2.3) OPAL
- - A worthwhile tradeoff!
- - ALEPH28 MeV, L338 MeV

Final CR error in qqqq 35 MeV

Fermilab Wine & Cheese

- 2.5 GeV P-cut to redefine jet direction also

reduces BEC W mass bias

- OPAL (default) 46 MeV (P-cut) 24 MeV.

- LEP experiments have measured BEC between

W’s

- Using “mixing method”

- A,D,L,O: only a fraction of Full BEC seen in

data (0.1713)

- A 68% upper limit on BEC fraction seen in data

(OPAL), used to set W mass systematics

MW = ( 0.33 + 044) MW (Full BEC) = 19 MeV

- L3 18 MeV, ALEPH 2 MeV

Final BEC error in qqqq 7 MeV

Fermilab Wine & Cheese

Results: qqqq and qqlv channels

Fermilab Wine & Cheese

mW (LEP) = 80.376 ± 0.033 GeV

GW (LEP) = 2.196 ± 0.083 GeV

Fermilab Wine & Cheese

W’s as Calibration Sample at LHC

“Yesterdays sensation is today’s calibration

and tomorrows background” - Telegdi

- W’s from top decay are foreseen to provide the
- absolute jet scale.
- - Fast simulation studies in the past showed feasibility

- Select samples with a four jets and lepton
- (electron,muon) with two jets b-tagged.
- estimated 45K events from 10 fb-1
- Cross check with Z/ +Jet sample
- Sattistics not the issue but understanding
- the physics of the events.

Fermilab Wine & Cheese

- Final results from all the four LEP experiments
- Final LEP combination will use combined FSI error
- Much reduced FSI error in final results
- A new preliminary LEP combination
- Total LEP W mass uncertainty decreased to 33 MeV
- It took about five years after LEP shut down to get final W mass
- results from all the four experiment. Now it is up to Tevatron to
- better the W mass precision before LHC turns on.

Fermilab Wine & Cheese

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