V. Electroweak Precision Observables

• What radiative corrections can teach us

• Basic formalism

Weak Decays: GF encodes information on the spectrum via radiative corrections

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+L

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μ−€

ν μ

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ν e€

e−

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W −

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μ−€

ν μ

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ν μ

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ν e€

e−

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e−

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W −

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Z 0

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+

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+

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μ−€

ν μ

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ν e€

e−

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W −

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W −

gg

Muon Decay

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GFμ

2=

g2

8MW21+ Δrμ( )

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1

τ μ

=GF2mμ

5

192π 3+L rμ depends on parameters

of particles inside loops

Comparing radiative corrections in different processes can probe particle spectrum

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+L

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ν μ

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e−

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Z 0

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+

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+

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Z 0

gg

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ν μ

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Z 0

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e−

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Z 0

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Z 0

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ν μ

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e−

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e−

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e−

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e−

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e−

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ν μ

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ν μ

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ν μ

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ν μ

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GFZ

2=

g2

8MW21+ ΔrZ( )

rμ differs from rZ

Comparing radiative corrections in different processes can probe particle spectrum

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t

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t

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Z 0

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Z 0

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t

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b

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W +

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W +

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GFZ

GFμ≈ 1+ ΔrZ −Δrμ( )

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rZ ~α

πln

mt2

MW2

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rμ ~α

π

mt2

MW2

Charged Current Interactions I

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G.B. Propagator

Fermion Propagator

Vertex Correction

Box (finite)

Charged Current Interactions II

Muon decay at one loop:

Muon lifetime:

Fermi constant & rμ : Tree level

Vertex, box, fermion prop

Neutral Current Interactions I

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G.B. Propagator

Fermion Propagator

Vertex Correction

Box (finite)

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Complication: Z mixing

Neutral Current Interactions II

Neutral current l+f --> l+f at one loop:

Normalization:

Vector & axial vector couplings:

Normalize to Gμ: Remove rμ

Weak mixing:

Vertex & ext leg

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Oblique Parameters I

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The parameter:

Weak mixing:

Can impose constraints from global fits to EWPO via S,T,U-dependence of these quantities

Oblique Parameters II

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Fit to electroweak precision observables:

Plus low-energy observables: atomic PV, PV electron scattering, ν scattering…

mH = 114.4 GeV