# Presentation: 580521

## W Mass From LEP

-  Fermilab Wine and Cheese Seminar
- 6th October, 2006
- Ambreesh Gupta, University of Chicago

## Outline 

-  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.*

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## Standard Model of Particle Physics 

- _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. **

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## 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.

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## Precision EW

- 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.

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## 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.

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## The Four LEP Experiments 

- _The Four LEP Experiments _

**ALEPH**

**L3**

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## WW Production and Decay at LEP

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

- BR ~ 44%

- BR ~ 46%

- BR ~ 10%

- WW ll

- WW qql

- WW qqqq

**            **Efficiency    Purity
- l l        70%          90%
- qql         85%         90%
- qqqq        85%         80%** **

**Backgrounds**

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## Event Selection

-  Very good agreement between expected and observed.

-  Event selection primarily based on multivariate relative likelihood discriminants

- OPAL

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## 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_

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## 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 WW4f  theory model  (~0.5% theory error )

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## Mass Reconstruction 

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

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

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## Fit Methods

-   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

-   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.

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## Fit Methods (continued)

-  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.

- Fitted Function (70-88) GeV mass

-  Convolution
-      -  P(m1,m2|Mw,Gw)R(m1,m2)
-      -  Build event-by-event Likelihood
-      -  Maximize statistical sensitivity
-      -  Need bias correction as in BW

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## Likelihood Variables 

- - 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.

**5C fit mass error**

**5C fit mass**

**Hadronic 4C mass**

**5C fit mass error**

**5C fit mass**

**4C fit mass **
**difference**

-  OPAL variables
-  ALEPH also
-   3-d fit

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## Performance of Likelihood Fucntion 

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

- OPAL

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

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## 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 of momentum cut analysis makes
-      significant reduction in FSI uncertainty.
-  Final W mass and total uncertainty from
-      the three  methods on OPAL -

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## LEP W Mass 

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

- _Channel weights_
- qqlv    : 76%
- qqqq  : 22%
- xs       : 2%

- (MeV)

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## LEP W Width

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

- Source

- Hadronisation
- QED(ISR/FSR)
- Detector
- Colour Reconnection
- Bose-Einstein Correlation
- LEP Beam Energy
- Other

- Total Systematics
- Statistical
- Total

-   qql + qqqq
- (MeV)

- 40
- 6
- 22
- 27
- 3
- 5
- 19

- 55
- 63
- 84

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## LEP Beam Energy

-  LEP beam energy used in event kinematics fit          MW/MW ELEP/ELEP

-  Beam energy calibrated using
-    - Resonant De-Polarization  (41- 60 GeV.)
-    - Extrapolated to LEP II energies NMR probes
-    - Main systematic error due to extrapolation
-  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Ebeam= 20-25 MeV  MW = 17 Mev
-        -   new : Ebeam = 10-20 MeV  MW ~ 10 Mev
-     -- OPAL Final  9 MeV

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## 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

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## Systematics from MC Modeling

- MC modeled to represent data;
- Disagreements  Systematic error

- _Systematics from MC Modeling_

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

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

- Error ~ 7 MeV

- _Photon Radiation_

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## Detector Systematics

-    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

- qqlv            qqqq      Combined
- 10 MeV     8 MeV     10 MeV

- _Detector Systematics_

- _LEP Combined:_

**Jet energy scale**

**Jet energy resolution**

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## Detector Systematics: Breakdown

- _Detector Systematics: _*Breakdown*

- OPAL

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## Hadronization Modeling

-        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.

- qqlv            qqqq      Combined
- 13 MeV     19 MeV     14 MeV

- _LEP Combined:_

- _Hadronization Modeling_

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## Final State Interactions 

-  Two known sources that could potentially bias W mass
-   and width measurement
-   1. Color Reconnection
-       - 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?

- _The Basic Problem_:  If products of hadronically decaying W’s (~0.1 fm)
- interact before hadronization (~1.0 fm)      **Can create a mass bias.**

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## Color reconnection 

-  Only phenomenological models exist.
-     - SK1 model produces largest shift  CR strength
-       parameter (*k**i*)
-   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 *k**i* is used to set a data driven
-         uncertainty on W mass.
-      -  Combined LEP value of *k**i* = 2.13
-       For this Reco. Prob., CR error ~ 120 MeV (OPAL)

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## Cuts and Cones: Reducing CR effect

-       -  OPAL Uses P-cut 2.5 GeV for
-          qqqq
-       -  ~18% loss in statistics.
-       -  Much reduced CR systematics
-       125  41 MeV (*k**i* =2.3) OPAL
-       -  *A worthwhile tradeoff!*
-       - ALEPH 28 MeV, L3 38 MeV

- _Cuts and Cones: Reducing CR effect_

-  CR affects mostly soft particles between
-      jets   changes jet direction
-  Re-calculate Jet direction
-      1. Within cone of radius R
-      2. Cut on particle momentum P
-      3. Weighted particle momentum |P|

- Final CR error in qqqq    35 MeV

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## BEC in WW events 

-      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 (0.1713)

- _BEC in WW events _

-  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

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## Results: qqqq and qqlv channels

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## Results: LEP W mass and Width

**m****W**** (LEP) = 80.376 ****± 0.033 GeV**

******W**** (LEP) = 2.196 ****± 0.083 GeV**

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## 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.

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## Summary

-  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.*

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