precise measurements of the w mass at the tevatron and...

Precise measurements of the W mass at the Tevatronand indirect constraints on the Higgs mass

Rafael Lopes de Safor the CDF and DØ Collaborations

March 11, 2012

Rencontres de MoriondQCD and High Energy Interactions

Precise measurement of the W-boson mass with the CDF II detector arXiv:1203.0275

Measurement of the W Boson Mass with the D0 Detector arXiv:1203.0293

R. Lopes de Sa (Stony Brook University) W Mass at the Tevatron March 2012 1

Motivation

Electroweak theory

The W boson mass is not an input parameter, but can be calculated

MW

(1− M2

W

M2Z

)=

πα√2Gµ

(1 + ∆r)

Loop Corrections

∆r(MZ ,MH ,mt, αs, . . .) W+

t

W+

b

W W

H

Indirect dependence δMW

δMH = 13GeV [114→ 127] −6.2MeV

δmt = 1.8GeV [172.4→ 174.1] 10.8MeV

δ(∆α(5)HAD) = 0.0002 −3.6MeV

Current theoretical uncertainty 4MeV

SM prediction known to complete2-loop order (and some 3-loopparts)Phys.Rev.D69:053006,2004


Motivation

Direct Measurements (before February 2012)

(GeV)Wm80 80.2 80.4 80.6

LEP2 average 0.033±80.376

Tevatron 2009 0.031±80.420

D0 Run II 0.043±80.402

D0 Run I 0.083±80.478

Tevatron 2007 0.039±80.432

CDF Run II 0.048±80.413

CDF Run 0/I 0.081±80.436

World average 0.023±80.399

July 09

Top quark mass (GeV)165 170 175 180 185

W b

os

on

ma

ss

(G

eV

)

80.3

80.32

80.34

80.36

80.38

80.4

80.42

CMS excl.

Atlas excl.

Tevatron excl.

LEP excl.

References:

SM prediction: Phys.Rev.D69:053006,2004

0.9 GeV (arXiv:1107.5255)±Top Mass: 173.2

= 122.5HM

= 127.0HM

68%


Motivation

Global Electroweak Fit (before February 2012)

(TEV EWWG and LEP EWWG – July, 2011)

Does not include LHC direct exclusion.

Precision EW Measurements(Tevatron, LEP and SLD data)

W boson mass and width

Z boson mass, total and partial width

Z pole asymmetries and sin θW

Indirect measurementof the Higgs boson mass

MH = 92+34−26GeV


CDF Detector

General purpose detector. For thisanalysis, the important subdetectorsare:

Central Drift Chamber immersed ina 1.4T solenoid. Provides accuratelepton momentum measurementand position measurement.

Electromagnetic Calorimeter.Lead-aluminium-scintillatorcalorimeter. Provides showerenergy measurement as well asposition measurement via wirechamber embedded at the EMshower maximum.

Central tracker single muon resolution: 3.2% (for pT = 45GeV )


DØ detector

General purpose detector. For thisanalysis, the important subdetectorsare:

Central Tracker. Silicon andscintillating fiber trackers immersedin a 2T solenoid provide accurateposition measurement.

Electromagnetic Calorimeter.Highly segmented uranium-liquidargon calorimeter with good energyresolution and coverage.

Electromagnetic calorimeter single electron energy resolution (with E = 45GeV ): 3.33%at η = 0. Average over central cryostat with W → eν angular spectrum: 4.16%.


Measurement Strategy

The Tevatron was a pp collider with 1.96TeV of energy. In a hadron collision, it isimpossible to know the parton system initial longitudinal momentum and, therefore,to measure the longitudinal momentum of the neutrino from the W boson decay.

The transverse momenta carry part of the mass information. Both CDF and DØmeasurements use binned likelihood fits to extract the value of the W boson massfrom the following kinematical distributions:

Transverse mass mT =√

2 (pT (`)pT (ν)− ~pT (`) · ~pT (ν))

Lepton transverse momentum pT (`)

Neutrino transverse momentum pT (ν)

peT

electron

uT

/ET

pWT

Hadronic Recoil

UnderlyingEvent

peT

electron

peT

posit

ron

uT

pZT

Hadronic Recoil

UnderlyingEvent

1


Event Selection

CDF analysis

Analyzed 2.2 fb−1.

Uses W → eν and W → µν decaychannels.

Central leptons |η| < 1 with30 < pT < 55GeV

Missing transverse energy30 < /ET < 55GeV

Transverse mass60 < mT < 100GeV

Hadronic recoil momentumuT < 15GeV

DØ analysis

Analyzed 4.3 fb−1 (1 fb−1

analyzed before)

Uses W → eν decay channel.

Central electrons |η| < 1.05 withpT > 25GeV

Missing transverse energy/ET > 25GeV

Transverse mass50 < mT < 200GeV

Hadronic recoil momentumuT < 15GeV

W → eν candidates W → µν candidates Total

CDF 2.2 fb−1 470, 126 624, 708 1, 094, 834

DØ 4.3 fb−1 1, 677, 394 – 1, 677, 394(+1 fb−1) 2, 177, 224


Calibration Strategies

Full GEANT detector simulations are not fast nor accurate enough to describe thekinematical distributions used to measure the W boson mass.

Both CDF and DØ develop parametrized fast simulations of the detector response toW → `ν events. The parametrizations are calibrated with data, using very differentstrategies.

CDF strategy

Detailed model of leptoninteractions at the central tracker.

Precise alignment using cosmicrays.

Momentum scale calibrated usingJ/ψ → µµ, Υ→ µµ and Z → µµmass fits.

Use calibrated momentum scaleand E/p distribution in W → eνevents to calibrate the calorimeterenergy scale.

DØ strategy

Detailed model of the calorimeterresponse to electrons and photons.

Detailed model of the underlyingenergy flow.

Detailed model of efficiencies.

Calibrate the calorimeter energyscale using the dielectron invariantmass and angular distribution inZ → ee decays (electron energyscale α and energy offset β).


Calibration Results

)-1> (GeVµ

T<1/p

0 0.2 0.4 0.6

p/p

∆

-0.002

-0.0015

-0.001

-1 2.2 fb≈ L dt ∫CDF II

data (stat. only) µµ→ψJ/

data (stat. only) µµ→Υ

data (stat. only) µµ→Z

eventsνµ→ syst.) for W⊕ p/p (stat. ∆combined

)νe→E/p (W1 1.2 1.4 1.6

ev

en

ts /

0.0

1

0

10000

20000

/dof = 18 / 222χ

-1 2.2 fb≈ L dt ∫CDF II

αScale, 1 1.01 1.02 1.03 1.04 1.05

(G

eV

)β

Off

se

t,

0

0.075

0.15

0.225

0.31D0 Run II, 4.3 fb

L<0.72

0.72<L<1.4

1.4<L<2.2

L>2.2

(L in 1032 cm−2 s−1)

DØ tests the calibration method doing a closure testwith GEANT simulation treated as data. Theresults are consistent with the input value of MW

within statistical uncertainty (≈ 6MeV ) for a sampleequivalent to 24 fb−1!

CDF momentum scale and DØ energy scaleprecision: ≈ 0.01% (!!!)


Z Mass Fits

A very strict test of the calibration procedure

(GeV)µµm70 80 90 100 110

ev

en

ts /

0.5

Ge

V

0

2000

4000) MeVstat 12± = (91180 ZM

/dof = 30 / 302χ

-1 2.2 fb≈ L dt ∫CDF II preliminary

MZ(µµ) = 91180±12(stat)±10(syst)MeV

(GeV)eem70 80 90 100 110

ev

en

ts /

0.5

Ge

V

0

500

1000

) MeVstat 30± = (91230 ZM

/dof = 42 / 382χ


MZ(ee) = 91230± 30(stat)± 14(syst)MeV

All values consistent with theprecisely measured value at LEP.

MZ = 91188± 2MeV

, GeVeem70 75 80 85 90 95 100 105 110

Ev

en

ts

/0

.2

5 G

eV

0

425

850

1275

1700Data

Fast MC

-1D0 Run II, 4.3 fb

Fit Region/d.o.f. = 153/1592!

, GeVeem70 75 80 85 90 95 100 105 110

!

-4

-2

0

2

4-1D0 Run II, 4.3 fbMZ(ee) = 91193± 17(stat)MeV


Systematic uncertainties

Comparison of systematic uncertainties in the mT (`, ν) measurement(values in MeV)

Source CDF mT (µ, ν) CDF mT (e, ν) DØ mT (e, ν)

Experimental – Statistical power of the calibration sample.

Lepton Energy Scale 7 10 16Lepton Energy Resolution 1 4 2

Lepton Energy Non-Linearity 4Lepton Energy Loss 4Recoil Energy Scale 5 5

Recoil Energy Resolution 7 7Lepton Removal 2 3

Recoil Model 5Efficiency Model 1

Background 3 4 2

W production and decay model – Not statistically driven.

PDF 10 10 11QED 4 4 7

Boson pT 3 3 2


CDF Results

Method (2.2 fb−1) MW (MeV) Method (2.2 fb−1) MW (MeV)

mT (µ, ν) 80379± 16(stat) mT (e, ν) 80408± 19(stat)pT (µ) 80348± 18(stat) pT (e) 80393± 21(stat)/ET (µ, ν) 80406± 22(stat) /ET (e, ν) 80431± 25(stat)

Combination (2.2 fb−1) 80387± 19MeV (syst + stat)


DØ Results

, GeVTm50 60 70 80 90 100

Ev

en

ts/0

.5 G

eV

0

5000

10000

15000

20000

25000

30000

35000

DATA

FAST MC

ντW>

Z>ee

MJ

1D0 Run II, 4.3 fb

Fit Region/dof = 37.4/492χ

, GeVTm50 60 70 80 90 100

χ

4

3

2

1

0

1

2

3

41D0 Run II, 4.3 fb

, GeVe

Tp

25 30 35 40 45 50 55 60

Ev

en

ts/0

.5 G

eV

0

10000

20000

30000

40000

50000

60000

70000

DATA

FAST MC

ντW>

Z>ee

MJ

1D0 Run II, 4.3 fb

Fit Region/dof = 26.7/312χ

, GeVe

Tp

25 30 35 40 45 50 55 60

χ

4

3

2

1

0

1

2

3

41D0 Run II, 4.3 fb

Method (4.3 fb−1) MW (MeV)

mT (e, ν) 80371± 13(stat)pT (e) 80343± 14(stat)/ET (e, ν) 80355± 15(stat)

Combination mT ⊕ pT (4.3 fb−1) 80367± 26(syst + stat)

Combination (5.3 fb−1) 80375± 23(syst + stat)


Comparing Results

Fitted W boson mass (MeV)80250 80300 80350 80400 80450

0

1

2

3

4

5

6

7

8

9

10

D0 (4.3/fb) mT(e,nu)

D0 (4.3/fb) pT(e)

D0 (4.3/fb) MET(e,nu)

CDF (2.2/fb) mT(mu,nu)

CDF (2.2/fb) pT(mu)

CDF (2.2/fb) MET(mu,nu)

CDF (2.2/fb) mT(e,nu)

CDF (2.2/fb) pT(e)

CDF (2.2/fb) MET(e,nu)

CDF 2.2/fb combination (stat+syts)

D0 4.3/fb combination (stat+syts)

D0 MET not included

in the combination

Very consistent results obtained with completely different calibration strategies!(uncertainties from individual measurements are only statistical)


Single Experiment Uncertainty

)-1Integrated Luminosity (pb210 310 410

W M

ass

un

cert

ain

ty (

MeV

)

50

100

150

200

250

300

350

400

Tevatron Single Experiment Uncertainties

)-1Integrated Luminosity (pb210 310 410

W M

ass

un

cert

ain

ty (

MeV

)

50

100

150

200

250

300

350

400

DZero (e)

CDF (e + mu)

Both experiments are getting close to the model and theoretical plateau.

Some work need to be done in this front as well!


Theoretical and modeling issues

Ideas and developments to improve the modeland theoretical uncertainties in the W mass measurement

Use a wider lepton η–acceptance to be lesssensitive to PDF uncertainties. It has been donebefore at the Tevatron (DØ RunI).Phys.Rev.D62:092006,2000

Use Tevatron W lepton charge asymmetry toconstrain the u/d PDF instead of low energyexperiments. Available: CT10W PDF set.Phys.Rev.D82:074024,2010

Explore lepton longitudinal momentum toextract the W mass. Concrete example:JHEP 1108:023,2011

Study QED uncertianties in the measurementusing NLO QCD ⊕ EW generators. Two recentimplementations in the POWHEG framework.arXiv:1202.0465, arXiv:1201.4804

|eη|0 0.5 1 1.5 2 2.5 3

Asy

mm

etry

-0.6

-0.4

-0.2

-0

0.2

-1DØ, L=0.75 fb

>25 GeVT

eE

>25 GeVT

νE

CTEQ6.6 central value

MRST04NLO central value

CTEQ6.6 uncertainty band

|eη|0 0.5 1 1.5 2 2.5 3

Asy

mm

etry

-0.8

-0.6

-0.4

-0.2

-0

0.2

-1(a) DØ, L=0.75 fb

<35 GeVT

e25<E

>25 GeVTν

E

CTEQ6.6 central value

MRST04NLO central value

CTEQ6.6 uncertainty band


Higgs Constraints

(Preliminary) New World Average

(GeV)Wm80 80.2 80.4 80.6

LEP2 average 0.033±80.376

Tevatron 2012 (prel.) 0.017±80.387

CDF II (prel.) 0.019±80.387

D0 Run II (prel.) 0.023±80.376

D0 Run I 0.083±80.478

CDF Run I 0.081±80.436

World average (prel.) 0.015±80.385

Winter 2012

Top quark mass (GeV)165 170 175 180 185

W b

os

on

ma

ss

(G

eV

)

80.3

80.32

80.34

80.36

80.38

80.4

80.42

CMS excl.

Atlas excl.

Tevatron excl.

LEP excl.

References:

SM prediction: Phys.Rev.D69:053006,2004

0.9 GeV (arXiv:1107.5255)±Top Mass: 173.2

= 122.5HM

= 127.0HM68%


(Preliminary) Global Electroweak Fit

0

1

2

3

4

5

6

10040 200

mH [GeV]

∆χ

2

LEPexcluded

LHCexcluded

∆αhad

=∆α(5)

0.02750±0.00033

0.02749±0.00010

incl. low Q2 data

Theory uncertainty

March 2012 mLimit

= 152 GeV

New (preliminary) indirect Higgs mass determination

MH = 94+29−24GeV (was MH = 92+34

−26GeV before)


Conclusions

CDF and DØ measured the W mass with precision at least as good as theworld average before.

The CDF measurement is now the single most precise measurement of the Wmass.

CDF and DØ measurements in excellent agreement.

Model and theory uncertainties begin to play an important role.

CDF analyzed 2.2 fb−1. DØ analyzed 4.3 fb−1 of integrated luminositycollected at high instantaneous luminosity runs of the Tevatron.

The measurements at CDF and DØ can reduce the world average uncertaintydown to 10MeV when all the rest of the data is analyzed.

The W mass will play an ever increasing role in the determination of theconsistency of the Standard Model.


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Backup Slides


CDF Systematic Uncertainties

Source Uncertainty (MeV)

Experimental – Statistical power of the calibration sample.Lepton Energy Scale 7

Lepton Energy Resolution 2Recoil Energy Scale 4

Recoil Energy Resolution 4Lepton Removal 2

Background 3Experimental Total 10

W production and decay model – Not statistically driven.PDF 10QED 4

Boson pT 5W model Total 12

Total Systematic Uncertainty 15W Statistics 12

Total Uncertainty 19


DØ Systematic Uncertainties

Source mT MeV peT MeV /ET MeV

Experimental – Z statistics driven!Electron Energy Scale 16 17 16Electron Energy Resolution 2 2 3Electron Energy Nonlinearity 4 6 7W and Z Electron energy 4 4 4

loss differencesRecoil Model 5 6 14Electron Efficiencies 1 3 5Backgrounds 2 2 2Experimental Total 18 20 24W production and decay model – Not dependent on Z statistics!PDF 11 11 14QED 7 7 9Boson pT 2 5 2W model Total 13 14 17Total Systematic Uncertainty 22 24 29W Statistics 13 14 15

Total Uncertainty 26 28 33


Recoil Model

Hard recoil: Parametrized from

Z → `` events.

Soft recoil: Data min-bias (CDF)

or min-bias + zero-bias (DØ)

events.

Lepton removal: Hadronic

energy reconstructed as lepton.

Out-of-cone FSR: Photons

reconstructed as recoil.

CDF and DØ: Final tune with Z → ``

momentum imbalance.

(GeV)ee

Tp

0 5 10 15 20 25

Mean

(G

eV

)im

bη

0

1

2

3

4

5

6

7

8

9

10

Data

PMCS

1D0 Run II, 4.3 fb

(GeV)ee

Tp

0 5 10 15 20 25

χ

3

2

1

0

1

2

31D0 Run II, 4.3 fb

(GeV)ee

Tp

0 5 10 15 20 25 W

idth

(G

eV

)im

bη

3

3.5

4

4.5

5

5.5

6

Data

PMCS

1D0 Run II, 4.3 fb

(GeV)ee

Tp

0 5 10 15 20 25

χ

4

3

2

1

0

1

2

3

41D0 Run II, 4.3 fb

5

4

e−

e+

η

peeT · η

ξ

peeT

uTuT · η

x

y

FIG. 2. Graphical representation of η axis and observables used to fit the recoil model smearing parameters

the difference in the zero supression between the top and bottom parts of the DØ calorimeter is needed to the Full38

GEANT Monte Carlo closure part of this analysis III. The components uMBT and uZB

T are randomly selected from39

the minimum bias and zero bias libraries. The smearing is applied only on uMBT to cancel double counting that is40

unavoidable in the preparation of the minimum bias library.41

usoftT,smear =

√αMBuMB

T + uZBT + uTB

T (qT ,∆φ, SET ) (3)

where ∆φ is the angle between the uhadT and qT .42

To determine the smearing parameters, we split the set of parameters in two sets:43

(RelScaleA, RelScaleB, τHAD) which controls the relative response and (RelSampA,αMB) which controls the relative44

resolution.45

Both sets are determined from Z → ee events using a method first used by the UA2 collaboration [4]. The idea is46

to avoid introducing an explicit dependence on the electron energy scale by using an observable which depends only47

on the angular quantities. The observable used is the momentum imbalance in the direction of the bisector of the48

electron-positron system, which is labeled η, namely (peeT + uT ) · η 2.49

The imbalance is measured in 10 bins of reconstructed peeT = (pe

T + peT ) momentum with boundaries:50

(0, 1, 2, 3, 4, 5, 7, 10, 15, 20, 30) GeV . Following the UA2 method, only the mean and RMS of the eta imbalance distri-51

bution are used to determine the response and resolution parameters respectively.52

B. Fitting method53

The parameters are determined by a straightforward χ2 comparison between the parameterized model and either54

data or Monte Carlo. The W Mass analysis parameterized model is not always well suited to models such as the55

gradient method implemented in MINUIT, since discontinuities exist and, unless we are in a region very close to56

the minimum of the χ2 surface, it is safer, though much more time consuming, to determine the parameters by57

constructing the whole χ2 grid spanning a range around a physically well motivated set of values for the parameters.58

The χ2 grid, when sufficiently close to the minimum can be well fitted to a generic quadratic polynomial in either59

three dimensions (for the response parameters) or two dimensions (for the resolution parameters).60

From the fitted quadratic surface, the point of minimum and the hessian matrix at this point are calculated61

algebraically and interpreted as the best values and covariances matrix for the parameters. To improve the numerical62

stability of the algebraic manipulation, the parameters are rescaled to have all the principal curvatures in the same63

order of magnitude.64

This procedure is applied individually for the response and resolution parameters. Although the correlations65

between the two sets are small, they are not zero. Instead of dealing with a five-dimensional problem, which would66

FIG. 2. Graphical representation of η axis and observables used to fit the recoil model smearing

parameters.

in the preparation of the minimum bias library.50

usoftT,smear =

√αMBuMB

T + uZBT + uTB

T (uT , φ, SET ) (3)

where (uT , φ) are, respectively, the length and direction of the hadronic recoil vector in51

the transverse plane before the top-bottom asymmetry correction is applied and uT is top-52

bottom correction mentioned above and fully described later in this note.53

To determine the smearing parameters applied to both hard recoil and soft recoil, we split54

the set of parameters in two sets: (RelScaleA, RelScaleB, τHAD) which controls the relative55

response and (RelSampA,αMB) which controls the relative resolution.56

Both sets are determined from Z → ee events using a method first used by the UA257

collaboration [4]. The idea is to avoid introducing an explicit dependence on the electron58

energy scale by using an observable which depends only on the angular quantities. The59

observable used is the momentum imbalance in the direction of the bisector of the electron-60

positron system, which is labeled η, namely (peeT + uT ) · η (see Figure 2).61

The imbalance is measured in 10 bins of reconstructed peeT = (pe

T + peT ) momentum with62

boundaries: (0, 1, 2, 3, 4, 5, 7, 10, 15, 20, 30) GeV . Following the UA2 method, only the mean63

ee) (GeV)→(ZT

p0 5 10 15 20 25 30

(G

eV

)η

+ u

Z η0

.65

p

-3

-2

-1

0

1

2

3

/ DoF = 15.6 / 92χ


ee) (GeV)→(ZT

p0 5 10 15 20 25 30

) (

Ge

V)

η +

uZ η

( 0

.65

pσ

3.5

4

4.5

5

5.5

6

/ DoF = 15.9 / 92χ



DØ Consistency CheckInstantaneous Luminosity

Blinded W mass (GeV)

81.6 81.7 81.8 81.9 82 82.1

L > 6

4 < L < 6

2 < L < 4

L < 2

Tm

Tp

MET

Z mass (GeV)

91 91.05 91.1 91.15 91.2 91.25 91.3 91.35 91.4

(Blinded W mass) / (Z mass)

0.895 0.896 0.897 0.898 0.899 0.9 0.901


DØ Consistency Check – Time


81.6 81.7 81.8 81.9 82 82.1

Early Run IIb1

Late Run IIb1

Early Run IIb2

Late Run IIb2

Tm

Tp

MET

Z mass (GeV)

91 91.05 91.1 91.15 91.2 91.25 91.3 91.35 91.4


0.895 0.896 0.897 0.898 0.899 0.9 0.901


DØ Consistency Check – u‖

Blinded W mass (GeV)81.6 81.7 81.8 81.9 82 82.1

< 0 GeV||u

> 0 GeV||u

Tm

Tp

MET


DØ Consistency Check – Recoil uT


81.6 81.7 81.8 81.9 82 82.1

< 10 GeVTu

< 20 GeVTu

Tm

Tp

MET

Z mass (GeV)

91 91.05 91.1 91.15 91.2 91.25 91.3 91.35 91.4


0.895 0.896 0.897 0.898 0.899 0.9 0.901


precise measurements of the w mass at the tevatron and...

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