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Electroweak Physics (from an experimentalist!) SUPA Graduate Lectures Term 2 2005/06 Victoria Martin SUPA/University of Edinburgh 1 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 2 Pull= [X(expt)-X(theory)] / X 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 & PseudoObservables 3 The Blue Band Plot! • Electroweak theory is so good, it predicts the Higgs mass 4 Course Contents • • • • • • Measurements at the Z pole: LEP & SLD LEP production of W+WMeasurements 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… 5 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) e gW g 'W g g' 2 W 2 W MZ v g g 1 2 2 w '2 w 1 GF 2v 2 6 Other Useful Combinations vgW • Mass of the W boson: M W 2 2 g ' • Weak mixing angle sin 2 W 2 W 2 0.23 g 'W gW • Relationship between W and Z mass: MW MZ cos W gW2 GF 1 2 2 2 8M W 2v 7 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 8 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 9 Z in the Lagrangian 10 Z boson-fermion interactions T: Weak Isospin T3 :Third Component Q: Charge • Piece of the Lagrangian that describes fermion – Z interactions: f 5 (V f Af 5 ) f Z • Vector coupling to Z: Vf = T3-2Q sin2θW • Axial coupling to Z: Af = T3 11 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 12 LEP Experiments • 4 experiments: – – – – ALEPH DELPHI OPAL L3 13 The Aleph Experiment y z θ φ x 14 Z bosons at LEP 15 SLC & Mark II • SLAC Linear Collider – Only linear collider to date • First detector: Mark II – 1989: First to publish observation of e+e−→Z 16 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 17 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 18 Z Boson Decaye+e− 19 Z Boson Decay +- 20 Z Boson Decay +− (e− + jet) 21 Z Boson Decay Hadrons (qq jets) 22 Decay into Fermion anti-Fermion Pairs Z f ( p ) f ( p ') • At tree level not too hard to calculate! • Vertex strength: ig W u ( p) (V f Af 5 )v( p ') 2 cos W • Summing over the possible electron polarisations: 4 8 GF M Z | V f |2 | Af |2 3 2 • Integrate over available phase space (p, p’) to get: 2 GF M Z3 ( Z f f ) N C V f Af 6 2 2 23 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 24 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−) 25 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: 26 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). 27 More Ratios: R0q and R0inv • 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: 28