W Boson mass and width

W mass and width Emily Nurse 1


Overview

• Standard Model Precision Measurements– Motivation for W mass and width measurements

• The Tevatron and CDF– W and Z production– W and Z reconstruction at CDF

• Analysis Strategy and Measurement steps• Results and implications


Standard Model

The Standard Model (SM) describes the Universe’s fundamental building blocks and their interactions.

Comparisons of predictions with experimental data have successfully tested the theory to a high precision but some questions remain un-answered.

What’s the origin of particle mass? (SM Higgs?)

Is the SM the full story? (SUSY?, extra-dimensions?, …??)


Discovering new physics

Direct Discovery of New Particles

Precision Measurementsof SM Parameters

80 180 280

Reconstructed Mass (GeV)


Testing the SM - W and Z bosons

• The W and Z bosons were predicted by Glashow, Salam and Weinberg’s electroweak theory in the 1960s discovered by the UA1/UA2 experiments in 1983, with masses (MW

and MZ) consistent with the tree level predictions. • Current SM calculations make very accurate predictions of

MW and MZ and the widths (W and Z) including higher order radiative corrections (i.e. through remormalisation of SM parameters). LEP experiments measure MZ=91187.6 2.1 MeV (0.002%) and

Z=2495.2 2.3 MeV (0.09%). LEP2 and Tevatron experiments measure MW=80403 29 MeV

(0.04%) and W=2141 41 MeV (1.9%).

prior to these results


Testing the SM - W mass

rW: radiative corrections dominated by tb and Higgs loops

we can constrain MH by precisely measuring MW and Mt

known to 0.015%

known to 0.0009% MZ known to 0.002%

MW known to 0.036%

GF is found from muon lifetime measurements and can be predicted in terms of MW

(tree level)

Write g in terms of and cosw=MW / MZ and rearrange:

rW could also have contributions from new particle loops

+e+e

W+

g

g


Testing the SM - W width

Within the SM W is predicted by summing leptonic and hadronic partial widths:

(Note: Most higher order corrections are absorbed in the experimental values of MW and GF.)

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W = 3ΓW0 + 3KQCD Vqq '

2

|no top|

∑ ΓW0

W0 = (We) is precisely predicted in terms of MW and GF :

PDG: J. Phys. G 33, 1

• Measuring W tests this accurate SM prediction (deviations of which suggest

non-SM decay modes).

• W is an input to the MW measurement: MW~W / 7.

W = 2091 2 MeV

predominantly from MW


The Tevatron

The Tevatron currently has ~2.5 fb-1 on tape (6-8fb-1 expected by the end of Run II).The Tevatron is a W/Z factory (as well

as many other things!) : (Wl) ~ 2700 pb (currently ~7 million created, ~0.9 million to analyse). (Zll ) ~ 250 pb (currently 0.7 million created, ~40 thousand to analyse).

But : precision measurements are hard! We need a “precision level” calibration of our detector to keep systematics low. These analyses are based on 200/350pb-1 of CDF data.


W and Z production at the Tevatron

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

LEADING ORDER

Similar for Z production (decays into two charged leptons)

W events: Charged lepton is detected and momentum directly measured. Neutrino cannot be detected! Transverse momentum (pT) is inferred by a vector sum of the total “transverse energy (Esin)” in the detector. The “missing ET

(ETmiss)” is found by constraining the sum to zero interpreted as the neutrino pT.

Z events: Both charged leptons are detected and their momenta measured.


W and Z production at the Tevatron

Initial state gluon radiation from incoming quarks gives the W a boost in the transverse direction W pT

The recoiling gluons form hadrons that are detected in the calorimeter Hadronic recoil

HIGHER ORDER CORRECTIONS

Final state radiation affects the kinematics of the charged lepton

Goes into ETmiss = pT

measurement!


e

Detecting particles at CDF

SILICON

DRIFT CHAMBER SOLENOID

EM HADRONIC MUONCHAMBERS

Electrons: detected in central trackers (drift chamber provides p measurement) and EM calorimeter (provides energy measurement).

Muons: detected in central trackers (drift chamber provides p measurement), calorimeter (MIP signal) and muon chambers.

ETmiss : Hadronic recoil found by summing the EM

and HADRONIC calorimeter energy.

TRACKERS CALORIMETERS

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δpT / pT ≈ 0.0005 × pT [GeV/c; beam constrained]; η <1

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δET / ET ≈ 13.5%/ ET ⊕ 1% η <1.1


Analysis strategy: measuring MW and W

• Ideal world: MW and W would be reconstructed from from the invariant mass of the W decay products (Breit-Wigner lineshape of propagator peaks at the mass and has an intrinsic width).• Reality: The neutrino is not detected thus the invariant mass cannot be reconstructed. Instead we reconstruct the transverse mass.

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mT = 2pTl pT

ν (1− cosφlν )

-channel: central trackere-channel: EM calorimeter

inferred from missingtransverse energy

MW

W

Breit-Wigner:


Analysis strategy: measuring MW and W

• MW/W found from MT MC template fits data.

• Simulate MT distribution with a dedicated fast parameterised MC.• Utilise well understood data samples (Z events used extensively) to calibrate detector simulation to high precision - we need an excellent description of the lineshape! - W fit range: 90 -200 GeV

- MW fit range:65 - 90 GeV

W templates

MW templates


MW vs W

• The MW and W analyses are very similar - with different

dominant uncertainties.• They are performed independently using 200(350)pb-1 of

data for the MW (W) analyses .

• As I describe the the measurement steps I will discuss the method used in the analysis for which the effect is more important:

MW =

W =


Measurement Steps

Muon momentum measurement:

Electron energy measurement: ppTT

= E = ETTmissmiss = -(U + p = -(U + pTT

leplep))

Hadronic recoil measurement:

Generator effects:PDFs, QCD, QED corrections.

Backgrounds:

€

mT = 2pTl pT

ν (1− cosφlν )


Measurement Steps : 1




leplep))



Backgrounds:

€

mT = 2pTl pT

ν (1− cosφlν )


Generator effects : PDFs

€

x p

€

x p

€

l

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Parton Distribution Functions (PDFs) are parameterised functions that

describe the momentum distribution of quarks in the (anti)proton.

Different PDFs result in different acceptance and spectra:

Use CTEQ6M and the CTEQ6 ensemble of

2x20 error PDFs (20 orthogonal

parameters varied up and down within

their errors).

MW = 11 MeV, W = 17 MeV


Generator effects : QCD/QED corrections

• Simulate QCD corrections (initial state gluon radiation) using RESBOS [Balazs et.al.

PRD56, 5558]: NLO QCD + resummation + non-perturabtive.

• Constrain non-perturbative parameter using our own Z data :

• QED bremsstrahlung reduces l pT

• Simulated at NLO (one-) using Berends&Kleiss [Berends et.al. ZPhys. C27,

155] / WGRAD [Baur et.al. PRD59, 013002].• PHOTOS [Barberio et.al. Comput. Phys. Comm., 66, 115] used to establish systematic due to neglecting NNLO (two-) terms.

MW = 3 MeV, W = 7 MeV

MW () = 12 MeV, W () = 1 MeV MW (e) = 11 MeV, W (e) = 8 MeV






leplep))



Backgrounds:

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mT = 2pTl pT

ν (1− cosφlν )


Momentum scale set with di-muon

resonance

peaks in data, using well known particle

masses: J/ ; 1S Z

Lepton momentum calibration (pT)

M (GeV)

M (GeV)

DataMC

DataMC

MW () = 17 MeV, W () = 17 MeV

p scale known to 0.021%

1/<pT>(GeV-1)


Lepton momentum resolution (pT)

fullMC = (q/pT)meas - (q/pT )gen taken from full GEANT MC.

• Sample this histogram and multiply by a constant parameter: fastMC = SresfullMC

• Sres found by tuning to M in

Z data.

MW () = 3 MeV, W () = 26 MeV






leplep))



Backgrounds:

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mT = 2pTl pT

ν (1− cosφlν )


The electron’s journey through CDF

energy leakage “out the back” of the EM calorimeter

energy loss in solenoid

bremsstrahlung in silicon

track momentum measurement in COT

energy measurement in EM calorimeter


Scale and found in two independent ways:

1) Fit to Mee peak in Zee data using well known Z mass/width.

2) Fit to E/p in We data (since p has already been well

calibrated.)

Electron energy calibration/resolution (pTe)

electron energy measured in EM calorimeter

electron momentum measured in central tracker

Fundamentally E = p (electron mass is negligible).

Photons are emitted from electron (bremsstrahlung) which reduces p.

The photons usually end up in the same calorimeter tower as theelectron thus E doesn’t decrease.

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E

€

p

Calorimeter scale: Emeas = scale Etrue

Calorimeter resolution: (E) / E = 13.5% / √ET


Bremsstrahlung in

tracker

E

p

MW (e) = 30 MeV, W (e) = 17 MeV scale: resolution:

Mee (GeV) E/p

DataMC

DataMC

E scale known to 0.034%

Leakage “out the

back” of the EM

calorimeter

MW (e) = 11 MeV, W (e) = 31 MeV

Electron energy calibration/resolution (pTe)






leplep))



Backgrounds:

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mT = 2pTl pT

ν (1− cosφlν )


Hadronic Recoil: U

• To get pT we need a good model of the total

energy in W events.• U=(Ux, Uy)=towersEsin (cos, sin)• Vector sum over calorimeter towers

Excluding those surrounding lepton

• Recoil has 3 components:

ppTT = E = ETT

missmiss = -(U + p = -(U + pTTleplep))

(3) Underlying energy Multiple interactions and remnants from collision.

(2) Bremsstrahlung Photons emitted by lepton that do not end up in the excluded region

(1) QCD Gluons recoiling off

the boson


Hadronic Recoil: U

U1U2

• Accurate predictions of U is difficult (and slow) from first principles.

• U simulated with ad-hoc parameterised model, tuned on Zll data.

• U split into components parallel (U1) and

perpendicular (U2) to Z pT

• 7 parameter model describes the response and resolution in the U1 and U2 directions as a function of the Z pT.

• Systematic comes from parameter uncertainties (limited Z stats).

Zee Zee

response resolution

DataMC

MW () = 12 MeV

W () = 49 MeV

MW (e) = 14 MeV

W (e) = 54 MeV






leplep))



Backgrounds:

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mT = 2pTl pT

ν (1− cosφlν )


multijet

muon channel only:

• Jet fakes/contains a lepton• ET

miss from misconstruction

electron and muon channel:

Backgrounds

Zll• One lepton lost• ET

miss from missing lepton

W• decays to e/• intrinsic ET

miss

Decay In-Flight

xxx

x

xx

x

x

K,fake

high-pT track

• Kaon/pion decays “In-Flight” to a .• Kink in track gives high-pT measurement. • ET

miss from mis-measured track pT.

Need the mT distributions and the

normalisations!


• Dominant background is Z (it’s easy to lose a muon leg!) - but we can estimate this background very reliably (using full MC).

• Decay In-Flight (DIF) has large mT

tails: problematic for the width!

Backgrounds: Muon channel

fin

al

cu

t v

alu

e

/NDF

The handles we have on DIF are track quality 2

track and impact parameter.

Fractional background found from a template fit to the 2

track distribution. Z provides the signal template

High impact parameter cuts provide the DIF templateMW () = 9 MeV, W () = 33 MeV


Backgrounds: Electron channel

fin

al

cu

t v

alu

e

• Multijet has large mT tails: problematic for

the width!

MW (e) = 8 MeV, W (e) = 32 MeV

Fractional multijet background found from a template fit to the ET

miss distribution.

“Anti-electron” sample provides the mulitjet template


Measurement Steps




leplep))



Backgrounds:

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mT = 2pTl pT

ν (1− cosφlν )


Results: MW fits

DataMC

DataMC

Also includes fits to pTl and pT

:

MW = 80413 48 (stat + syst) MeV

MT() (GeV) MT(e) (GeV)


MW systematic uncertainties


MW : world average

Central value increases by 6 MeV:

80392 80398 MeV

Uncertainty reduced by 15%:

29 25 MeV

World’s most precise single measurement!


MW : Implications

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mH = 85−28+39 GeV

mH <166 GeV @ 95% C.L.

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mH = 80−26+36 GeV

mH <153 GeV @ 95% C.L.

Previous World Data :

Including New MW :

Direct search from LEP II :

mH > 114.4 GeV @ 95% C.L.

Including New Mt :


Results: W fits

W = 2032 71 (stat + syst) MeV


W systematic uncertainties


W : world average

Central value decreases by 44 MeV:

2139 2095 MeV

Uncertainty reduced by 22%:

60 47 MeV

World’s most precise single measurement!


Indirect Width Measurement

R = W

Z (Zll)

(Wl)

(W)

(Z) X X

Rexp = BR (Wl)

BR (Zll) Precision LEP Measurements

SM CalculationNNLO Calculation

CDF Run II INDIRECT width :

2092 ± 42 MeVPRL 94, 091803

CDF Run II DIRECT width :

2032 ± 71 MeVpreliminary


Projections

20 MeV syst limit

2.5fb-1 : ~25 MeV ~35 MeV

Naïve statistical scaling, 20 MeV syst. limit


Summary• Two new measurements from CDF:

– W mass : 80413 ± 48 MeV (stat + syst)

– W width : 2032 ± 71 MeV (stat + syst)• Both are the world’s most precise single measurements!!

• Getting to this point requires a “precision” level calibration of the detector.

• Together with direct Higgs searches we will continue to squeeze the phase space available to the SM Higgs.

• Analyses utilised 200 pb-1 and 350 pb-1 respectively, both CDF and DØ already have ~2.5 fb-1 on tape.

• Working on improved mass/width measurements to further test the SM and constrain mH


Back-up slides…


W mass

€

MW ∝ M top2

€

MW ∝ ln M H

e

e

GF (fermi-coupling constant) can be predicted in terms of MW

W width: W’ analysis excludes W’ < 788 GeV


Generator effects : PDFs

9 - highx valence quarks.

∆XW = 0.5*√ (∑i ([∆i

up-∆idown) 2 ))/1.6


Generator effects : QCD corrections

RESBOS: NLO QCD + resummation + non-perturbative.

Collins-Soper-Sterman (CSS) resummation formalism.Sums LL terms + sub-logs

Brock-Landry-Nadolsky-Yuan (BLNY) form:

exp [-g1 - g2ln(Q/2Q0) - g1g3ln(100x1x2)]b2

g1 =0.210.01; g1 =0.68+0.01-0.02; g3 =-0.6+0.05

-0.04; From fits to R209, E288, E605 fixed target Drell-Yan data (5< shat <18 GeV) + CDF RunI

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g2 = 0.64 ± 0.05

b = −0.0014 ± 0.0010 GeV -1

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dσ

dpTZ

~ (1+ B ⋅ pTZ ) × f (g1,g2,g3)RESBOS


Simulated effects

• Bremsstrahlung in si (Bethe-Heitler equation)

– Migdal suppression

• Conversions (Bethe-Heitler equation)

• Compton scattering (for low energy photons: scattering off e ~ conversions)

• Ionisation energy loss

• Energy loss in coil

• Leakge into HAD calorimeter

• Acceptance

• Ionisation energy loss

• Multiple scattering

• Acceptance

Electrons Muons


log10(incident electron energy)

visible EM energy fraction

Simulating Electrons () : CAL

superconducting coil

electromagnetic cal.

hadronic calorimeter

Soft electrons suffer absorption

in the coil

Energetic electrons leak into the

hadronic compartment

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Ee ~ 100 MeV

€

Ee ~ 100 GeV


We

Hadronic Recoil: U (pT)

U||

U • U split into components parallel (U||) and

perpendicular (U) to charged lepton.

• Many distributions used to cross check the model in Wl data:

DataMC

We

€

< u1

>= (P1

+ P2p

T) ∗(1 − e (−P3 ×pT ))

€

(u1) = (P

4+ P

5pT) ∗M

1∑E

T

M2


Electron mT signed plot


pT and ETmiss fits


pT and ETmiss fits


MSSM parameter range

Decoupling limit with SUSYmasses of order 2 TeV.

Moderate splitting between stop andsbottom doublets (m2/m2 <2.5)

Documents

W Boson mass and width