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Electroweak Physics(from an experimentalist!)

Victoria MartinSUPA/University of Edinburgh

SUPA Graduate Lectures

Term 2 2005/06

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The Electroweak Lagrangian

Q: How do we relate this to observables that we can measure in experiments?

A: Take one piece at a time!

Often need to consider corrections from other terms

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Experimental Measurements • Look how well EW

theory explains our measurements!

• But what are these measurements!?

• How do we relate what the theory tells us and what experimentalists measure?

Experiment Theory

Observables & Pseudo-

Observables

Pull= [X(expt)-X(theory)] / σX

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The Blue Band Plot!

• Electroweak theory is so good, it predicts the Higgs mass

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Course Contents

• Measurements at the Z pole: LEP & SLD• LEP production of W+W-• Measurements at low energy: muon lifetime, g-2• Electroweak and top physics at the Tevatron• The search for the Higgs & BSM• What the future holds

• But first, back to the theory…

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Parameters of the Electroweak Sector

• Three key parameters:– The two gauge coupling constants: gW and g’W

– The vacuum expectation value of the Higgs field: v

• These can be obtained through 3 measurements.• Choose the 3 most precise:

– The electric charge, e-• measured by the electric dipole moment

– The Fermi Constant, GF (precision: 0.9x10-5)• measured by the muon lifetime

– The mass of the Z boson, MZ (precision: 2.3x10-5)

2 '212Z w wM v g g= +2 2

''

W W

W W

g geg g

=+ 2

12FG v

=

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Other Useful Combinations

• Mass of the W boson:

• Weak mixing angle

• Relationship between W and Z mass:

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2 2

'sin 0.23'

WW

W W

gg g

θ = ≈+

2W

WvgM =

cosW

ZW

MMθ

=

2

2 2

18 22

WF

W

gGM v

= =

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Other Parameters in the Model• The masses of the

fermions:– Most influential is

m(top) due to its huge size

• Mass of the Higgs, mH

• The EWK model tells us nothing about these values!

mH=(2λ)½v

λ is not specified

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First Topic: Physics at the Z Pole• What EWK theory

tells us about Z• How to make and

detect Zs

• Physics Topics:– Z mass– Partial and Total

Widths– Z couplings to

fermion pairs– Asymmetries

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Z in the Lagrangian

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Z boson-fermion interactions

Q: Charge

T: Weak Isospin

T3 :Third Component

• Piece of the Lagrangian that describes fermion – Z interactions:

• Vector coupling to Z: Vf = T3-2Q sin2θW

• Axial coupling to Z: Af = T3

5 5( )f f f fV A Zμψ γ γ ψ−

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A Z-boson factory• LEP=Large Electron Positron

Collider @ CERN

• 1989 to 1995: LEPI– CM energy: 88 to 94 GeV

• 7 energy points– 17,000,000 Zs produced– 1995: 1000 Z/h recorded by

each experiment

• 1996 to 2000: LEPII– CM energy 161 to 209 GeV

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LEP Experiments

• 4 experiments:– ALEPH– DELPHI– OPAL– L3

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The Aleph Experiment

y

z

x

θ φ

y

z

x

θ φ

y

z

x

θ φ

y

z

x

θ φ

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Z bosons at LEP

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SLC & Mark II• SLAC Linear Collider

– Only linear collider to date

• First detector: Mark II– 1989: First to publish

observation of e+e−→Z

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SLC & SLD• 1992: SLC polarised e+e− beams established!• Mark II replaced with SLD detector

• 1992 to 1998: 600,000 Z decays

• Complementary to LEP for some measurements

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Two Main Measurables

• What happens to the Z once produced?– It decays

• What into?– Any fermion: e, μ, τ, ν, quarks

• What can we measure?– Two main quantities to measure:

• Cross sections to fermion final states, σ(e+e−→ff)• Decay Asymmetries eg, Afb and ALR

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Z Boson Decay→e+e−

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Z Boson Decay→ μ+μ-

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Z Boson Decay→ τ+τ− (e− + jet)

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Z Boson Decay→ Hadrons (qq jets)

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Decay into Fermion anti-Fermion Pairs

• At tree level not too hard to calculate!• Vertex strength:

• Summing over the possible electron polarisations:

• Integrate over available phase space (p, p’) to get:

( ) ( ')Z f p f p→

5( ) ( ) ( ')2cos

Wf f

W

ig u p V A v pμγ γθ

− −

( )4

2 28 | | | |3 2

ZFf f

G MV A+

( )3 2 2( )

6 2F Z

C f fG MZ f f N V A

πΓ → = +

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In reality…• Need to include:

– Interference from the γ– QED corrections due to

gamma radiation– For quarks: QCD corrections

due to gluon radiation– Fermion masses

• Correction factors:~1

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Total Cross Section

• The total cross section to a given fermion depends on:– The rate for e+e− to make Zs: Γ(e+e−)– The rate for the Z to decay to a given fermion type: Γff

– The rate for the Z to decay to anything, ΓZ

• We can parameterise this for different centre of mass energies, s:

Parameterises final state QED corrections in Γ(e+e−)

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Widths

• Total width of the Z is sum of widths of everything it can decay into:

• Hadronic modes due to quarks:– (top is too heavy for Z to decay into)

• Invisible modes due to neutrinos:

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Observables extracted from σ• Many parameters can be extracted from the

measurement of σ(e+e−→hadrons)• Highly correlated! Choose to use just six:

– If we assume the three lepton types have the same interactions (lepton universality), last three measurements are the same. (Small correction to required for lepton mass difference).

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More Ratios: R0q and R0

inv

• When the type of quark can be identified, we can define:

• Define ratio of invisible width and charged leptonic width:

• Related to number of neutrinos, Nν: