1

VIII.Experimental tests of the Standard Model

1. Discovery of W and Z boson

2. Precision tests of the Z sector

3. Precision test of the W sector

4. Radiative corrections and prediction of the Higgs mass

5. Higgs searches at the LHC

1. Discovery of the W and Z boson 1983 at CERN SppS accelerator, √s≈540 GeV, UA-1/2 experiments

1.1 Boson production in pp interactions

p

pu

d

Ws

q,−l

q,lν p

pu

u

Zs

q,−l

q,+l

XWpp +→→ llν XffZpp +→→

Similar to Drell-Yan: (photon instead of W)

10 1001 ZWMs ,ˆ

)( ZW σσ

nb1.0

nb1

nb10

12.0x mitˆ q ≈= sxxs qq

22q )GeV65(014.0xˆ =≈= sss

→ Cross section is small !

2

1.2 UA-1 Detector

1.3 Event signature:

p p

+l

−l

High-energy lepton pair:

222 )( ZMppm =+= −+ llll

XffZpp +→→

GeV91≈ZM

3

1.4 Event signature: XWpp +→→ llν

p p

ν

l

High-energy lepton:

Large transverse momentum pt

Undetected ν:

Missing momentum

Missing pT vector

How can the W mass be reconstructed ?

W mass measurement

In the W rest frame:

•

•

2WMpp == ν

rrl

2WT Mp ≤l

Tpl

TdpdN

2WM

In the lab system:

• W system boosted only along z axis

• pT distribution is conserved

Jacobian Peak:

• Trans. Movement of the W

• Finitte W decay width

• W decay not isotrop

GeV80≈WM

212

2

42~

−

⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅ T

W

W

T

T

pMM

ppdN

4

The Nobel Prize in Physics 1984

Simon van der MeerCarlo Rubbia

"for their decisive contributions to the large project, which led to the discovery of the field particles W and Z, communicators of weak interaction"

One of the achievements to allow high-intensity p ⎯p collisions, is stochastic cooling of the ⎯p beams before inserting them into SPS.

S. van der Meer

1.5 Production of Z and W bosons in e+e- annihilation

Precision tests of the Z sector Tests of the W sector

qqW →

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2. Precision tests of the Z sector (LEP and SLC)

2.1 Cross section for ffZee →→−+ /γ

+=2M

2

γ Z

⎥⎦⎤

⎢⎣⎡ −

Γ+−−

⎥⎦⎤

⎢⎣⎡ −−=

−=

eggeiMMqMqqg

gggM

eeq

eM

eA

eV

ZZZ

ZAV

W

)(21

)()(

21

cos

)(1)(

522

25

2

2

22

γγµγγµθ

γµγµ

ρρννρµµνγ

µµγ

−+−+ → µµee for

Z propagator considering a finite Z width

~4.5M Z decays / experiment

One finds for the differential cross section:

⎥⎦

⎤⎢⎣

⎡Γ+−

+Γ+−

−+= 2222

2

2222

22

)()(cos

)()()(cos)(cos

2cos ZZZZ

ZZZ

ZZ MMs

sFMMs

MssFFsd

d θθθπαθ

σγγ

γ γ/Z interference Z

)cos1()cos1()(cos 2222 θθθ µγ +=+= QQF e

[ ]θθθθ

θ µµµγ cos4)cos1(2

cossin4)(cos 2

22 AeAV

eV

WW

eZ gggg

QQF ++=

[ ]θθθθ

θ µµµµ cos8)cos1)()((cossin16

1)(cos 22222

44 AVeA

eVAV

eA

eV

WWZ ggggggggF ++++=

θθθ

σ cos38)cos1(~

cos2

FBAd

d++

BF

BFFBA

σσσσ

+−

=

Forward-backward asymmetry

with

Vanishes at √s≈MZ

6

At the Z-pole √s≈MZ → Z contribution is dominant → interference vanishes

[ ][ ] 222

22222

44

2

)()(cossin1634

ZZZAV

eA

eV

wwZtot MMs

sggggs Γ+−

⋅++⋅=≈ µν

θθαπσσ

“Massive propagator” → 1 for MZ→0

( ) 2212

Z

e

ZZZ M

MsΓΓΓ

== µπσ

[ ]22

22 cossin4fA

fV

ww

Zf ggM

+⋅=Γθθ

α

∑Γ=Γi

iZ

With partial and total widths:Cross sections and widths can be calculated within the Standard Model if all parameters are known

Resonance curve:

22012

Z

e

ZM ΓΓΓ

= µπσ

• Resonance position → MZ

• Height → Γe Γµ

• Width → ΓZ

Initial state Bremsstrahlung corrections

22222 )(12)(

ZZZZ

e

MMss

Ms

Γ+−⋅

ΓΓ= µπσ

sE

zdzzszGsm

fffff

γγ σσ

21)()(

1

/4

0)(

2−=∫=

Peak:

2.2 Measurement of the Z lineshape

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Resonance looks the same, independent of final state: Propagator the same

hadronsee →−+ −+−+ → µµee

−e −e

+e +e

k k ′

p p ′

−e

+e−e

+e

k

p p ′

k ′

+

channel schannel t

−+−+ → eeee t channel contribution → forward peak

8

MZ = 91.1876 ± 0.0021 GeV

ΓZ = 2.4952 ± 0.0023 GeVΓhad = 1.7458 ± 0.0027 GeVΓe = 0.08392 ± 0.00012 GeVΓµ = 0.08399 ± 0.00018 GeVΓτ = 0.08408 ± 0.00022 GeV

ΓZ = 2.4952 ± 0.0023 GeVΓhad = 1.7444 ± 0.0022 GeVΓe = 0.083985 ± 0.000086 GeV

Z line shape parameters (LEP average)

Assuming lepton universality: Γe = Γµ=Γτ

3 leptons are treated independently

±23 ppm (*)

±0.09 %

*) error of the LEP energy determination: ±1.7 MeV (19 ppm)

http://lepewwg.web.cern.ch/ (Summer 2005)

test of lepton universality

LEP energy calibration: Hunting for ppm effects

Changes of the circumference of the LEP ring changes the energy of the electrons:

• tide effects

• water level in lake Geneva

1992 1993

Changes of LEP circumference ∆C=1…2 mm/27km (4…8x10-8)

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Effect of the French “Train a Grande Vitesse” (TGV)

In conclusion: Measurements at the ppm level are difficult to perform. Many effects must be considered!

Vagabonding currents (~1A) from trains

2.3 Number of light neutrino generationsIn the Standard Model:

νν Γ⋅+Γ⋅+Γ=Γ NZZ l3

invΓ :invisible

eeZee νν→→−+

µµνν→→−+ Zee

ττνν→→−+ Zee

To determine the number of light neutrino generations:

SM

invN ⎟⎟⎠

⎞⎜⎜⎝

⎛ΓΓ

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛ΓΓ

=ν

νl

l exp

GeV0015.04990.0 ±=Γinv

=1.991±0.001 (small theo. uncertainties from mtop MH)

5.9431±0.0163

Nν = 2.9840 ± 0.0082

No room for new physics: Z→new

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2.4 Forward-backward asymmetry and fermion couplings to Z

−+−+ →→ µµZee θθθ

σ cos38)cos1(~

cos2

FBAd

d++

BF

BFFBA

σσσσ

+−

=with

θθ

σσ coscos

)0(1

)1(0)( d

dd

BF ∫−

=

FσFσ

Fermion couplings

-0.041

-0.038

-0.035

-0.032

-0.503 -0.502 -0.501 -0.5

gAl

g Vl

68% CL

l+l−

e+e−

µ+µ−

τ+τ−

mt

mH

mt= 178.0 ± 4.3 GeVmH= 114...1000 GeV

∆α

Forward-backward asymmetry

• Away from the resonance AFB large → interference term dominates

• At the Z pole: Interference = 0

→ very small because gVl small in SM

2222

2

)()(~

ZZZ

ZfA

eAFB MMs

MssggAΓ+−

−⋅

fV

fA

eV

eAFB ggggA ~

Asymmetries together with cross sections allow the determination of the fermioncouplings gA and gV

Confirms lepton universality

Higher order corrections seen

Lowest order SM prediction:

32

3 sin2 TgqTg AWV =−= θ

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3. Precision tests of the W sector (LEP and Tevatron)

ffffWWee →→−+

Threshold behavior of the cross section (phase space) for ee→WW production:

Phase space factor = f(MW, √s):

→ Allows determination of MW

~10K WW events / experiment

W decays

Lepton Neutrino

Jet

Jet

12

W branching ratios

Lepton universality tested to 2%

)%28.077.67()( ±=→ qqWBr

Invariant W mass recontructionin

dire

ct

More difficult: pairing ambiguities

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Effect of triple gauge coupling

Data confirms the existence of the γ/ZWW triple gauge boson vertex

4. Higher order corrections and the Higgs mass

Lowest order SM predictions

Including radiativecorrections

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Top-Quark Mass [GeV]

mt [GeV]125 150 175 200

χ2/DoF: 2.6 / 4

CDF 176.1 ± 6.6

D∅ 179.0 ± 5.1

Average 178.0 ± 4.3

LEP1/SLD 172.6 + 13.2172.6 − 10.2

LEP1/SLD/mW/ΓW 181.1 + 12.3181.1 − 9.5

The measurement of the radiative corrections:

weff

AVeff gg

θκθ

θ

22

2

sin)1(sin

)1(41sin

∆+=

−≡

Allows the indirect determi-nation of the unknown parameters mt and MH.

Direct measurement of mt

Top mass prediction from radiative corrections

Good agreement between the indirect prediction of mt and the value obtained in direct measurements confirm the radiative corrections of the SM

Prediction of mt by LEP before the discovery of the top at TEVATRON.

Observation of the top quark at TEVATRON (1995)

q

Top decay

q

l

lν

Channel used for mass reconstruction:),( jetjetWjetbmm invt +→−=

TeV2@pp

q

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Higgs mass prediction from radiative corrections

MH > 114 GeV (from direct searches)

MH < 300 GeV @ 95 % C.L.Awaiting the discovery of the Higss at LHC

Status Summer 2005

5. Higgs searches at the LHC (pp collider @ 14 TeV) Only missing ingredient of the Standard Model: Higgs-Boson

Huge effort to find itHiggs Production mechanism:

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Higgs decay channels

At LEP: Searches were done using

bbH →(“golden” Higgs decay channel at LEP energies because of large b mass →too much background at LHC)

At LHC:

• mH< 150 GeV:

• 150 GeV < mH < 1 TeV

γγ→H

(*)ZZH →−+→ WWH

MH > 114 GeV

Simulated H→ZZ→4µ event at LHC

• 20 pp interaction / event

• Large number of particles

To trigger and to reconstruct these events is an exp. challenge.

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The ATLAS Experiment at LHC

ATLAS Construction

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Higgs discovery potential (ATLAS experiment)

If the Higgs Boson exists, it will be found at LHC

LHC start is foresenfor the end of 2007.