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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)] / X
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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 ge
g g
2
1
2FG
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
'W
WW W
g
g g
2W
W
vgM
cosW
ZW
MM
2
2 2
1
8 22WF
W
gG
M 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)½vλ 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 Z
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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 Decaye+e−
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Z Boson Decay +-
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Z Boson Decay +− (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
igu p V A v p
4
2 28| | | |
3 2
ZFf f
G MV A
32 2
( )6 2F Z
C f f
G MZ f f N V A
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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: