# Presentation: 119865

## Precision Measurement of the 

*W* Boson Mass with CDF

*Chris Hays, *
*University of Oxford*

***Les Rencontres de Physique ***
***de la Vallee d'Aoste***
*March 7, 2007*

## W Boson Mass

- C. Hays, University of Oxford

- 2

***Given precise measurements of m******Z****** and ************EM******(m******Z******), we can predict m******W******:***

-  *m**W*2 =

- EM

- √2*G**F* (1 - *m**W*2/*m**Z*2)(1 - r)

- r:  O(3%) radiative corrections dominated by *tb* and Higgs loops

*********m******W****** ************  m******t******2***

- (“on-shell scheme”)

*********m******W****** ************ ln (m******H******/m******Z******)***

## W Mass Prediction and Measurement

- 3

***W mass uncertainty from input parameters:***

***Direct W mass measurement***

- C. Hays, University of Oxford

***W mass predicted much more precisely (13 MeV) than measured (29 MeV)***
-       Need to reduce *m**W* to further constrain *m**H* and other new physics

- Next talk

## Tevatron Run II

- C. Hays, University of Oxford

- Run II
**CDF**

**Year            2002             2003              2004              2005               2006**

- Each experiment has collected >**2 fb****-1** of 1.96 TeV √s pp collisions
- Current Run II:  >**15**x Run I data set

**  ****Month    1   4   7  10   1   4   7   10  1   4    7  10   1   4    7   10  1   4   7 10**

***First Run II W mass measurement***
*** ******uses 200 pb******-1****** of CDF data***

- 4

## W & Z Boson Production and Decay 

- 5

*********(W     l************) = *****2775 pb**
- After event selection
- (*l*,  *E**T* > 30 GeV):
- 51,128 *W*      candidates
- 63,964 *W*     *e* candidates

***Dominant production mechanism:  qq******(******'******)****** annihilation***

*********(Z     ll) = *****254.9 pb**
- After event selection
- (*l* *E**T* > 30 GeV):
- 4,960 *Z*      candidates
- 2,919 *Z*     *ee* candidates

*W* & *Z* Boson Production and Decay

## CDF Detector

- C. Hays, University of Oxford

***High-precision tracking drift chamber ***
***p**T**/p**T**= *0.05%* p**T** : *2% for 40 GeV 

***High-precision electromagnetic calorimeter***
***E**T**/E**T**= *13.5%/*√**E**T** ***** 1.7% :*	** *
*	**	**	**	**	**	*3% for 40 GeV* e*

- 6

## Measurement Strategy

- Calibrate *l*± track momentum with mass
- 	measurements of *J*/ and  decays to 
- Calibrate calorimeter energy using
- 	track momentum of *e* from *W* decays
***Cross-check with Z mass measurement, ***
***	******then add Z's as a calibration point ***

- Calibrate recoil measurement with
*	**Z* decays to *e*, 
***Cross-check with W recoil distributions***

- Combine information into transverse mass:
*m**T** = **√**E**T**E**T**(1 - *cos***)*
***Statistically most powerful quantity for m******W****** fit***

- C. Hays, University of Oxford

*W*     *e*

*Z*     

- 7

## Alignment and  Corrections

- C. Hays, University of Oxford

- Statistical uncertainty of track-level corrections leads to *******m******W***** = 6 MeV**

- L = 200 pb-1          CDF Run II Preliminary

- Align tracker using cosmic-ray data
- Determine track-level corrections from electron-positron differences
*	*Use ratio of calorimeter energy to track momentum
*	**Curvature biases affect e**+**, e**-** differently, but calorimeter measurement independent of charge *

- 8

## Mass Measurements 

- C. Hays, University of Oxford

**

- Template mass fits to *J/***, , *Z* resonances in muon decay channels
- Fast detector simulation models relevant physical processes
*	**internal bremstrahlung *
*	**ionization energy loss*
*	**multiple scattering*
- Simulation includes event reconstruction and selection
- Detector material model
*	**Map energy loss and radiation lengths in each *
*	**	**detector layer*
- One material parameter determined from data:
*	**Overall material scale*

**

- 9

## Momentum Scale Calibration

- Constrain tracks to originate from
- 	the beam line
*Improves resolution by a factor of ****3*

- 10

- 606,701 *J*/ candidates
- Fit mass as a function of mean inverse *p**T*
- Slope affected by energy loss modelling
*	**Scale detector material by 0.94 to remove slope*

- C. Hays, University of Oxford

- Use calibrated momentum scale to
- 	measure *Z* mass

## Full Electron Simulation

- C. Hays, University of Oxford

- EM Calorimeter

- Bremstrahlung and conversions in silicon

- Track reconstruction in outer tracker

- Energy loss in
- solenoid

- Energy loss into
- hadronic calorimeter

- Response and resolution in EM calorimeter

- 11

## Energy Scale Calibration

- C. Hays, University of Oxford

- Calibrate calorimeter energy with peak of *W* electron *E/p* distribution
- One free parameter for *X**0* scale (set with high *E/p* region)
- 	Material scale:  1.004 ± 0.009

- L = 200 pb-1          CDF Run II Preliminary

*Calorimeter Energy < *
*Track Momentum:*
- Energy loss in
- hadronic calorimeter

*Calorimeter Energy > *
*Track Momentum:*
- Energy loss in tracker

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**Energy scale uncertainty:  0.034%**

## Scale Energy Dependence

*W* data

- Energy Scale

- Energy Scale

*E**T* (*e*) (GeV)

*Z* data

*E**T* (*e*) (GeV)

- L = 200 pb-1          CDF Run II Preliminary

- L = 200 pb-1          CDF Run II Preliminary

- C. Hays, University of Oxford

- 13

- Apply energy-dependent scale to each simulated electron and photon
- Determine energy dependence from *E/p* fits as functions of electron *E**T*
- 	Scale:  1 + (**6 ****± ****7**)  10-5 [*E**T*/GeV - 39]
*Most energy dependence implicitly accounted for by detector model*

**(*********m******W***** = 23 MeV)**

## Z Mass Measurement

- C. Hays, University of Oxford

- 14

***Fit Z mass using scale from E/p calibration***

- L = 200 pb-1          CDF Run II Preliminary

- Measured value consistent with world average value (91188 MeV)
*Incorporate mass fit into calibration to reduce scale uncertainty*

*******m******W***** = 30 MeV**

## Boson pT Model

- Model boson *p**T* using RESBOS generator with tunable non-perturbative parameters
- 	“*g**2*” parameter determines position of peak in *p**T* distribution
- 	Measure *g**2* with *Z* boson data (other parameters have negligible effect on *W* mass)
*	**	**g**2** = 0.685 **± **0.048:  **********m******W****** = *****3 MeV**

- C. Hays, University of Oxford

***electron channel***

***muon channel***

- 15

## Recoil Measurement

- C. Hays, University of Oxford

- Electron:  Remove 7 towers (shower)
- Muon:  Remove 3 towers (MIP)
- Model tower removal in simulation
*********m******W****** = *****8 (5) MeV for***** e (************)***

- L = 200 pb-1          CDF Run II Preliminary

- 16

*e*

- Calculate recoil by summing over calorimeter towers, excluding:
- 	*Towers with lepton energy deposits *
*	**Towers near the beam line*

## Recoil Model

- C. Hays, University of Oxford

- L = 200 pb-1          CDF Run II Preliminary

- 17

- Components:
- 	*Recoil scale **(R = u**meas** / u**true**)*
*	**Recoil resolution*
*	**Spectator and additional interactions *
*	**	**(contribute to resolution)*
- Calibrate scale with momentum balance along bisector axis ()
*	*
- Calibrate models of recoil resolution and
- spectator interactions using momentum
- resolution along both axes
*********m******W****** = *****11 MeV**

## Recoil Model Checks

- C. Hays, University of Oxford

- Apply model to *W* boson sample, test consistency with data
- 	Recoil distribution
*	**	**Sensitive to scale, resolution, *
*	**	**boson p**T*
*	**u**||* distribution
*	**	**Sensitive to lepton removal, *
*	**	**efficiency model, scale, *
*	**	**resolution, W decay*
*	**	**Directly affects m**T** fit result*

- 18

## Production, Decay, Background

- C. Hays, University of Oxford

- Boson *p**z* determined by
-  parton distribution functions
- 	*Vary PDFs according to uncertainties*
*********m******W****** = *****11 MeV**

- Bremtrahlung reduces charged lepton *p**T*
-  	*Predict using NLO QED calculation, *
*	**	**apply NNLO correction*
*********m******W****** = *****11 (12) MeV for *****e***** (********)**

- Background affects fit distributions
-  	*QCD: Measure with data*
*	**Electroweak:  Predict with MC*
*********m******W****** = *****8 (9) MeV for *****e***** (********)**

- 19

## W Mass Fits

- C. Hays, University of Oxford

- Mass fit results blinded with [-100,100] MeV offset throughout analysis
- Upon completion, offset removed to determine final result
*Transverse mass fits:*

***muon***
***channel***

***electron***
***channel***

***m******W****** = *****80417 ****± ****48***** *****MeV****  (stat + sys)**
**for *****e***** + ******** combination (*****P*****(********2****) = 7%)**

- 20

## W Mass Fits

- Fit *E**T*, *E**T* distributions and combine with *m**T* to extract most precise result
*Electron E**T** fit:**	**	**	**	**	**	**	**	**Muon p**T** fit:*

***m******W****** = *****80388 ****± 59***** *****MeV**** (stat + sys)**
**for lepton *****p******T***** *****e***** + ********combination (*****P*****(********2****) = 18%)**

*W* Mass Fits

- 21

## W Mass Fits

*Electron E**T** fit:**	**	**	**	**	**	**	**	**Muon E**T** fit:*

***m******W****** = *****80413 ****± ****48***** *****MeV**** (stat + sys)**
**for six-fit combination (*****P*****(********2****) = 44%)**

- 22

***m******W****** = *****80434 ****± 65***** *****MeV**** (stat + sys)**
**for neutrino *****p******T***** *****e***** + ********combination (*****P*****(********2****) = 43%)**

*W* Mass Fits

## W Mass Uncertainties 

- C. Hays, University of Oxford

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## W Mass Result

- C. Hays, University of Oxford

- New CDF result is world's most precise single measurement
*Central value increases: 80392 to 80398 MeV*
*World average uncertainty reduced ~15% (29 to 25 MeV)*

- 24

## Previous Higgs Mass Prediction

- C. Hays, University of Oxford

- 25

***Predicted Higgs mass from global electroweak data: ***
*m**H* = 85+39-28 GeV  (< 166 GeV at 95% CL)
- Direct search from LEP II:  *m**H* > 114.4 GeV at 95% CL

## New Higgs Mass Prediction

- C. Hays, University of Oxford

- 26

***Predicted Higgs mass from global electroweak data:  ***
*m**H* = 80+36-26 GeV  (< 153 GeV at 95% CL)
- Direct search from LEP II:  *m**H* > 114.4 GeV at 95% CL

## Effect on New Physics Models

- Supersymmetry now preferred at 1 level...

***New world average:***

- 27

## New W Mass Projections

- C. Hays, University of Oxford

***New projection with 1.5 fb******-1****** of data:***
- *m**W* < 25 MeV with CDF

- New* W* Mass Projections

- New projected Tevatron precision as a function of luminosity:

- 28

## Summary

- C. Hays, University of Oxford

- 29

*W mass excellent probe for new particles coupling to the electroweak sector*
- CDF has made the single most precise *W* mass measurement
*	**	****m******W****** = *****80413 ****± 34***** *****MeV**** (stat) ****± 34***** *****MeV**** (sys)**
**	****	****	****= 80413 ****± ****48***** *****MeV**** (stat + sys)**
*New SM Higgs mass prediction:  ****m******H****** = ******80******+36******-26  ******GeV ***
***	******	******Mass has moved further into LEP-excluded region***
***Expect CDF ************m******W****** < 25 MeV with 1.5 fb******-1****** already collected***
***	******	******Will squeeze SM in conjunction with Tevatron Higgs results***
***Electroweak data will probe more new physics after the Higgs***

## Backup

- C. Hays, University of Oxford

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## Filling in the Pieces

- C. Hays, University of Oxford

- C. Hays, University of Oxford

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- Precision electroweak data will continue to guide us to the next physics
**Today:**  *m**W* = 25 MeV, *m**H* < 153 GeV at 95% CL
**After Higgs: ** *m**W* = 15 MeV, SUSY predicted at 95% CL?
**After SUSY:**  *m**W* = 10 MeV, more new physics?

*m**W*

*SM*

*measurement*

*m**W*

*SM*

*measurement*

*m**W*

*MSSM*

*measurement*

## Electron mT Signed 

- C. Hays, University of Oxford

- Electron *m**T* Signed 

- C. Hays, University of Oxford

- High 2 dominated by a few bins with large fluctuations

- 33

## Tevatron Run I Uncertainties

- C. Hays, University of Oxford

- 34

## Tracker Alignment

- Determine individual cell tilts & shifts using
- 	cosmic-ray data
*	**Fit a single 'dicosmic' to track segments on *
*	**	**opposite sides of the chamber *
*	**Measure cell displacement*

- Central Outer Tracker: Open-cell drift chamber
- 	*Wires strung under tension between two endplates*
- 	  *Model endplate distortions and constructional *
*	**  **variations using a cell-to-cell endplate alignment *

- C. Hays, University of Oxford

*NIM A 506, 110 (2003)) *

*(Kotwal, Gerberich, Hays,*

- 8

## Weak Boson Physics

- C. Hays, University of Oxford

*Z* boson parameters measured precisely by LEP:
- 	* **17** million measured *Z* candidates:  *m**Z* = **2.1** MeV, *Z* = **2.3** MeV

***WWZ coupling**** *

***xf******a******(x******p******,Q)***

***m******W**** *

***V******tb***

- Tevatron goal:
- 	* World's most precise *W* boson measurements
- 	* Expect **15** million measured *W* candidates

*********W**** *

- 35

## Alignment Example

- 36

- C. Hays, University of Oxford

- Cell number ()

- Cell number ()

- Before alignment

- After alignment

- CDF Run II preliminary

- Cell Shift (microns)

*Inner 'Superlayer:'*

## Wire Alignment

- C. Hays, University of Oxford

- Wire shape along z-axis determined by:
*	**Gravitational sag*
*	**Electrostatic effects *

- Apply additional correction based on
- 	cosmic ray study
*	**Compare parameters of incoming and *
*	**outgoing tracks from a cosmic ray muon*

- Final correction removes *z*-dependent
- 	curvature biases

- *c* (cm-1)

*z* (cm)

## Electron Track Model Validation

- C. Hays, University of Oxford

***Fit Z mass reconstructed from electron track momenta***

- Measured value consistent with world average value (91188 MeV)

- L = 200 pb-1          CDF Run II Preliminary

- 38

## Calorimeter Energy Calibration

- C. Hays, University of Oxford

***Calibrate electron energy using electron track momentum***
- 	First step:  validate model of electrons in tracker
- 	Additional physical effects beyond those associated with muons:** **
*	**	**Photon radiation and conversion in tracker*

*e**-*

**

*e**-*

*e**+*

*e**-*

- 39

## Combined Momentum Scale

- C. Hays, University of Oxford

*******p/p***** = (1.50 ****± ****0.19) ******** ****10****-3**

***Systematic uncertainties:***

- 40

## Transverse Mass Distribution 

- C. Hays, University of Oxford

- Distribution peaks just below *m**W* and falls sharply just above *m**W*

*m**W** = *80 GeV

*m**W** = *81 GeV

- 41

## Energy Loss Model

- C. Hays, University of Oxford

***Use GEANT to parametrize energy loss in solenoid and hadronic calorimeter***
- Energy loss in hadronic calorimeter:

- 42

## Previous W Mass Projections

- C. Hays, University of Oxford

***Projection with 2 fb******-1****** of data:***
- *m**W* = 40 MeV per experiment

- Previous *W* Mass Projections

- Previously projected Tevatron precision as a function of luminosity:

- 43

## Higgs Mass Prediction

- C. Hays, University of Oxford

***Predicted Higgs mass from global electroweak data: ***
*m**H* = 85+39-28 GeV  (< 166 GeV at 95% CL)
- Direct search from LEP II:  *m**H* > 114.4 GeV at 95% CL

- 44

##  Mass Measurement

- 34,618  candidates
- Short lifetime allows a track constraint to the
- 	beam line
*Improves resolution by a factor of ****3*

- Test beam constraint by measuring mass using unconstrained tracks
- Correct by half the difference between fits
- Take correction as a systematic uncertainty

- C. Hays, University of Oxford

- 45

- L = 200 pb-1          CDF Run II Preliminary

- L = 200 pb-1          CDF Run II Preliminary

## Momentum Scale Calibration

- C. Hays, University of Oxford

- Magnetic field along z-axis causes
- curvature in transverse plane:
*mv**2**/R = evB*,
*p**T** = eBR*
- CDF:  Insufficient precision on *B * and *R* for* W* mass measurement
***In-situ calibration:***
- (1) Apply relative alignment of
- 	drift chamber wires
- (2)  Determine momentum scales
- 	such that *J/*, , and *Z* mass
- 	measurements result in the
- 	world-average values

- Combine results to obtain scale for *m**W* measurement

- 46

## Effect on New Physics Models

- Additional space-time symmetry
- (Supersymmetry) would affect the *W* mass

***Previous world average:***

- 47

## Effect on New Physics Models

- Supersymmetry now preferred at 1 level...

***New world average:***

- 48