# Presentation: 103214

## W mass and width at CDF

- Emily Nurse
- University of Manchester Seminar
- 30th March 2006

## Outline

- EWK precision measurements
- Unstable particles: mass and width
- The W mass and width:
- Motivation
- Current status
- CDF width measurement
- CDF mass measurement (brief summary)
- Summary and projections

## Introduction: EWK measurements

- The Standard Model contains free parameters that must be found from experiment.
- Relationships between these parameters are given in the theory.
- Measuring the parameters to a high precision is a stringent test of the theory and deviations from expected values indicate physics Beyond The Standard Model.

## Introduction : unstable particles mass and width

- The properties of short lived particles can be measured by reconstructing the *invariant mass* of their decay products.
- This distribution peaks at the particle *mass* and
-       has a finite intrinsic *width*.
- The width is due to the Heisenberg uncertainty
-      principle: Et ≥ ћ
- The shorter the lifetime the larger the width.

##  Z bosons decaying to neutrinos cannot be detected. 
 This decay mode will, however, contribute to the  width. 

The LEP experiment measurements of the Z width gives the number of neutrino species.

-  This decay mode will, however, contribute to the  width.
- The LEP experiment measurements of the Z width gives the number of neutrino species.

## W mass and width: motivation

- _W mass and width: __motivation_

- r~Mt2

- r~ln MH

- Plot from LEP EWK working group web page

- Measured to 0.0009%

- Measured to 0.004%

- Measured to 0.014%

- “on-shell” mass scheme

## W mass and width: current status

- _W mass and width: __current status_

- Plots from LEP EWK working group web page

- direct

- indirect

- cf/ Z-Boson: mass = 91.1876 ± 0.0021 GeV
-                     width  =  2.4952 ± 0.0023 GeV

## The Tevatron

- The highest energy accelerator in the world, collides protons with antiprotons at a centre of mass energy of 1.96 TeV.

- Each experiment currently has ~1.2 fb-1 on tape.
- Aim to have ~8 fb-1 by 2009.

## Collider Detector at Fermilab 

## W and Z production

- W

- e ,  ,  , q

- e  ,  , , q’

- P

- P

-  q’

-  q

- The large masses (~100 GeV ) of W and Z bosons means their decay products will have large pT.
- The electron and muon channels are used to measure W properties, due to their clean experimental signature.

## CDF W width analysis

- note: this analysis is work in progress!

- current analysis based on 350 pb-1

## Analysis strategy

- Ideally, the mass and width of the W would be found from the invariant mass distribution of its decay products (line-shape).
- We cannot reconstruct the W invariant mass distribution since the neutrino escapes detection.
- Instead we reconstruct the transverse mass:
-                MT = 2 pT**l** pT (1 - cos∆****)
- pT found by summing total “transverse” energy in detector ( calorimeter towers) + lepton to give the “missing ET”.

- 

- l

-  l 

## Analysis strategy

- Width and mass found by fitting MT in data to that in Monte Carlo.
- The line-shape of the W is described by a Breit-Wigner distribution with a scale dependent width:

- x1x2s

## Analysis strategy

- Same principle for W mass, with fit region 50 - 100 GeV

-  Simulate MT distributions using Monte Carlo event generator with various “blinded” input width values.
-   Normalise to data in the low MT region.
-   Fit to data in the high MT region (exactly where is a trade off between systematics and statistics).
-  A *fast* simulation is required (rather than full detector simulation).
-  Z events used to tune the detector response to particles.

## The data

- Select 4 data samples:
-      Z and  Zee (control samples).
-      W and We

- Muons identified in COT, calorimeters (MIP signature) and muon detectors.

- Electrons identified in COT and
- EM calorimeter.

## 2 electrons, 

- 2 electrons,
- ET > 25 GeV

- 2 muons,
-    pT > 25 GeV

- 1 electron,
- ET > 25 GeV
- ETmiss > 25 GeV

- 1 muon,
- pT > 25 GeV
- ETmiss > 25 GeV

- |e| < 1

- || < 1

## The simulation

- Toygen event generator produces Z, W, Zee and We samples.
- Purely electroweak (no gluon radiation, i.e. pT(boson) = 0 GeV).
-      pT(Z) is added from a functional form (fit to pT(Z) data). A theoretical calculation converts pT(Z)pT(W).
- QED radiation - Toygen is interfaced with Berends and Kleiss program: one photon FSR correction.

- UA2 program

- Simulation of detector:
- Simple tracking: helix extrapolation through detector with calorimeter and muon geometry simulated.
- The ionisation energy loss of muon tracks in central trackers taken from the Bethe-Bloch equation.
- Electron bremsstrahlung and photon conversion within central trackers simulated.
- Clustering of electrons/photons in calorimeter simulated.

**nIter = 0**

**1**

**2**

**3  ... etc.**

## Recoil ( non-lepton calorimeter towers) distribution modeled by tuning to Z and Zee data.

- Lepton id and trigger efficiencies input from data.
- COT momentum scale and resolution found by fitting to M in Z events.
- Calorimeter energy scale and resolution found by fitting to Mee in Zee events.
- Calorimeter energy scale and resolution also found from     E/P    in We events.
- Recoil ( non-lepton calorimeter towers) distribution modeled by tuning to Z and Zee data.

- E: energy of electron measured in calorimeter.
- P:  momentum of electron measured in central tracker.

## Sources of systematic uncertainty(anything affecting the MT distribution)

- PDFs and W pT distribution
- QED corrections
- Lepton energy scales and resolutions
- ETmiss distribution (recoil model)
- Backgrounds in W samples

## Parton Distribution Functions 

- PDFs are used as inputs to the MC to give the momentum distributions of partons within the incoming protons.
- The PDFs have an uncertainty associated with them due to the uncertainty in the many datasets used to fit them.
- This uncertainty gives an uncertainty on the MT distribution and hence the width determination.
- Use the CTEQ6 and MRST PDF error sets to obtain the uncertainty on the W width:
- CTEQ6:  +25 MeV, -25 MeV
- MRST:   +14 MeV,  -10 MeV

## Z and W pT 

- The Z pT is parameterised by an ad-hoc functional form:
- The parameters are found by fitting
-       to the Z data.
- A theoretical calculation
-      converts this to a W pT distribution.
- The  bosons (generated with 0 pT)
-      obtain a pT from this functional form.

- P1 = 0.564716 ± 0.0235054
- P2 = 5.04421 ± 0.247411
- P3 = 16.1793 ± 1.00640
- P4 = 0.921681 ± 0.0616547

## Lepton momentum/energy scales and resolutions

-    Since we do not model the complete CDF detector and event reconstruction we must smear the “true” lepton momentum (as measured in the COT) and energy (as measured in calorimeter). The smearing parameters are found by tuning to the data.

## Tuning method (e.g. track resolution)

-       82 <  M  < 100 GeV.
- Simulate 100 million Z-> events. Make many M  templates with different values for momentum resolution constant.
- Plot 2 vs resolution. Fit to a polynomial and minimise!

- 2 - 2min

- 1

- resolution

- _Tuning method __(e.g. track resolution)_

## Track momentum 

- scale:                  pTmeas    = 0.9986  pT
- resolution:        (1/pT)  = 0.00055    0.006 / pT

- curvature term

- multiple scattering term

## Calorimeter energy 

- scale:                  Emeas     = 1.0030  E
- resolution:        (E) / E = 13.5% / ET   2.2%

- stochastic term

- constant term

**scale = 1.0030 ******** 0.0006**
**kappa = 2.22  ******** 0.14 %**
******2**** = 18.5 / 18**

## Calorimeter energy: E/P 

- Momentum loss in
- trackers through
- bremsstrahlung

- Energy leakage
- from electron
- calorimeter
- tower (not yet
- simulated)

- Calorimeter energy and track momentum resolutions

- scales consistent; resolutions have ~4 different!

**scale = 1.0030 ******** 0.0006**
**kappa = (2.22  ******** 0.14) %**

- e  energy in calorimeter

- e  mom in COT

## Recoil (U) comes from multiple interactions, underlying event and initial state gluon radiation.
Defined as the sum of all non-lepton calorimeter towers.
Measured and modeled in Z events and applied to W events.

- Defined as the sum of all non-lepton calorimeter towers.
- Measured and modeled in Z events and applied to W events.

- _Recoil Model _

## U in Z events resolved into 2 directions:
U1 : anti-parallel to the Z pT  
U2 : perpendicular to Z pT
U1  and U2 are gaussian in bins of Z pT.
<U1> = a +bpT +cpT2
<U2> = 0
(U1) = d + epT + f(ET)g
(U2) =h(ET)i

- U1 : anti-parallel to the Z pT
- U2 : perpendicular to Z pT
- U1  and U2 are gaussian in bins of Z pT.
- <U1> = **a** +**b**pT +**c**pT2
- <U2> = 0
- (U1) = **d** + **e**pT + **f**(ET)**g**
- (U2) =**h**(ET)**i**

- Zee events:

- The recoil is then added in this way to the simulation for both Z and W events.
- Note: this is ongoing work, the simulation currently uses a Run I model.

## Efficiencies

- ...measured in the data and applied to MC as a function of 

## Potential backgrounds to W events

- _Potential backgrounds to W events_

-  One lepton lost
-  ETmiss due to
- missing lepton

-   decays to e/
-  intrinsic ETmiss

- We need to know MT distribution of backgrounds as well as overall normalisation!!

- _Residual background_: run full event selections on signal and background MC samples passed through simulation of CDF detector to get fractional background.
- muon channel: Z  : 4.7%
-                         W ** : 1.9%

- _Background suppression_: veto on additional high pT, isolated track

- electroweak

- W **

## .

-  ETmiss from
- misconstruction

- _Residual background_: Found from difference in isolation distributions in W and Z events.
- muon channel: 0.5%,
- electron channel: 1.4%

- _Background suppression_: total recoil in event < 20 GeV

- _Background suppression_: Cosmic tagger takes a seed track and searches for additional track hits on the other side of the interaction point.

- _Residual background_:
- muon channel: negligible
- electron channel: N/A

- di-jet

- cosmic muons

##  Kaon decays to a  pair when passing through COT.

- _Residual background_: Found by fitting the d0 distribution in W  events to that in Z  + W  + kaon  (with fraction of kaon varying).
-             muon channel:        1.00  0.19 %
-             electron channel:   N/A

-  Kaon decays to a  pair when passing through COT.
-  kink in track can give a *fake* high pT and ETmiss.

- _Background suppression_: Cut on track 2 and d0 (impact parameter).

- kaon decay

- Tracks with no silicon hits

## Muon channel backgrounds:

- 1% kaon background is probably too much for us!

- Muon channel transverse mass distributions:

## Width measurement: summary

- Fast simulation modeling the detector reasonably well.
- Work still required to ensure a good understanding of some effects:
- electron energy resolution
- recoil model
- Need to determine systematic uncertainties for all the effects discussed.
- When this is done fits for the width will be “un-blinded”.

## Width measurement: estimated uncertainties

- Run I analysis achieved 130 MeV with 110 pb-1 (one third of our luminosity).
- A naïve estimate of most systematics can be obtained by scaling Run I numbers by increased statistics (since they are controlled by Z statistics).
- Some systematics are *not* determined by Z statistics (e.g. QED corrections).
- Estimate ~80 MeV with this dataset with dominant errors from statistics, recoil and backgrounds.
- In reality may be higher...

## W mass status

- Current analysis uses 200 pb-1.
- Very similar to the width analysis, but with 50 - 100 GeV fit region.
- Some effects are more important and must be better understood (e.g. track momentum scale determined using J/ and  decays to muons, with Z events as a cross check). Therefore their simulation is more sophisticated than ours.
- Use Resbos Monte Carlo event generator interfaced with Wgrad for QED corrections.

## W mass status

- current work

- Total uncertainty 76 MeV (Run 1b: 79 MeV)

- Fits blinded with additive offsets

- 110 pb-1

## Projections

- _Projections_

- W width to a similar level of precision

## Outlook

- Hope to have these first round measurements out by the summer(?)
- After that the plan is join forces on the “W mass 1 fb-1 challenge”.
- Watch this space....

## Back-up slides

## Slide 42