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Electroweak Physics Lecture 2

Electroweak Physics Lecture 2. Last Lecture. Use EW Lagrangian to make predictions for width of Z boson: Relate this to what we can measure: σ (e+e − → ff ) Lots of extracted quantities m Z , Γ Z Today look at the experimental results from LEP&SLC. Review of our Aim.

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Electroweak Physics Lecture 2

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  1. Electroweak PhysicsLecture 2

  2. Last Lecture • Use EW Lagrangian to make predictions for width of Z boson: • Relate this to what we can measure: σ(e+e−→ff) • Lots of extracted quantities • mZ, ΓZ • Today look at the experimental results from LEP&SLC

  3. Review of our Aim • Aim: to explain as many of these measurements as possible Z pole measurements from LEP and SLC!

  4. Physics Topics • Total cross section to quarks and leptons • Number of neutrinos • Angular cross sections • Asymmetries • Between forward and backward going particles • Between events produced by left and right electrons • e+e−e+e− • τ-polarisation • Quark final states

  5. Measuring a Cross Section • Experimentalists’ formula: • Nsel, number of signal events • Choose selection criteria, count the number that agree • Nbg, number of background events • Events that aren’t the type you want, but agree with criteria • εsel, efficiency of selection criteria to find signal events • use a detailed Monte Carlo simulation of physics+detector to determine • L, luminosity: measure of e+e− pairs delivered

  6. An example: σ(e+e−→quarks) • Select events where the final state is two quarks • In detector quarks appears as jets • Simple selection criteria: • Number of charged tracks, Nch • Sum of track momenta, Ech • Efficiency,ε~ 99% • Background ~ 0.5% • mainly from τ+τ−

  7. Measured Cross Sections • as function of CM energy

  8. Use Fit to Extract Parameters • Fit σ(e+e−→hadrons) as function of s with to find best value for parameters: • mZ • ΓZ • σ0had

  9. Energy of the Beam • Critical to measurement: • How well do you know the energy of the beam, s? • At LEP, it was required to take into account: • The gravitational effect of the moon on tides • The height of the water in Lake Geneva • Leakage Currents from the TGV to Paris

  10. Leptonic Cross Sections • Leptonic cross sections measured in a similar way: • σ(e+e−→e+e−) • σ(e+e−→μ+μ−) • σ(e+e−→τ+τ−) • Use to extract values for Equal up to QED, QCD corrections

  11. Values Extracted from Total Cross Section

  12. Number of Neutrinos • Use σhad to extract number of neutrinos • N(ν)=2.999  0.011 • Only three light (mν~<mZ/2) neutrinos interact with Z

  13. Cross Section Asymmetries • Results so far only use the total number of events produced • Events also contain angular information • Cross section asymmetries can be used to exploit the angular information • Forward Backward Asymmetry, Afb • Left-Right Asymmetry, ALR

  14. y θ φ z x Angular Cross Section

  15. Angular Cross Section II • Simplifies to: • Pe is the polarisation of the electron • Pe=+1 for right-handed helicity • Pe=−1 for left-handed helicity • For partial polarisation: • and: • depends on axial and vector couplings to the Z • SM:

  16. Asymmetries • Can measure the asymmetries for all types of fermion • axial & vector couplings depend on the value of sin2θW Asymmetries measure Vf, Af and sin2θW

  17. Forward-Backward Asymmetry I • At Z energies the basic Feynman diagrams are: • Z exchange (dominant, due to resonance effect) •  exchange (becomes more important ‘off-peak’) •  exchange is a pure vector: parity conserving process • the angular distribution of the final state fermions only involves even powers of cos •  is the angle between the outgoing fermion direction and the incoming electron • for spin 1   spin 1/2 e+e- (cos) ~ 1 + cos²

  18. Forward-Backward Asymmetry II • Z exchange is a V-A parity violating interaction • the angular distribution of the final state fermions can involve odd and even powers of cos  • (cos) ~| AZ +A |²~ AZ²+2A AZ +A² • ~ 1 + g(E) cos + cos²-1 < g(E) < 1 • Away from resonance: E >> MZ or E << MZ • Can neglect |AZ|² contribution • cos term due to /Z interference; g(E) increases as |E-MZ| increases • Near resonance: E  MZ • neglect |A|² and 2A AZ contributions • small cos term due to V-A structure of AZ

  19. Forward-Backward Asymmetry III • Asymmetry between fermions that go in the same direction as electron and those that go in the opposite direction. • At the Z pole (no γinterference): • SM values for full acceptance • Afb(ℓ)=0.029 • Afb(up-type)=0.103 • Afb(down-type)=0.140

  20. NB: Number of fermions produced in backward region, θ>π/2 NF: Number of fermions produced in forward region, θ<π/2 Forward Backward Asymmetry Experimentally • Careful to distinguish here between fermions and anti-fermions • Experimentalists’ formula: • Ratio is very nice to measure, things cancel: • Luminosity • Backgrounds + efficiencies are similar for Nf Nb • Expression only valid for full (4π) acceptance

  21. AfbExperimental Results • P: E = MZ • P 2: E = MZ  2 GeV

  22. Measured Value of Afb • Combining all charged lepton types:

  23. Extracting Vf and Af • Large off-peak AFB are interesting to observe but not very sensitive to V-A couplings of the Z boson … • … whereas AFB(E=MZ) is very sensitive to the couplings • by selecting different final states (f = e, , , u, d, s, c, b) possible to measure the Vf/Afratios for all fermion types • Use Vf/Af ratios to extract sin²W =1 - MW²/MZ² • Vu/Au= [ 1 - (4Qu/e) sin²W ] • Vd/Ad= - [ 1 + (4Qd/e) sin²W] • charged leptons (e, , ) V/A = − (1− 4 sin²W )

  24. Extracting Vf and Af II • σ(e+e−Z ff) also sensitive to Vfand Af • decay widths f ~ Vf² + Af² • combining Afb(E=MZ) and f:determination of Vf and Afseparately

  25. An aside: e+e−e+e− • Complication for e+e−e+e− channel… • Initial and final state are the same • Two contributions: s-channel, t-channel • … and interference

  26. Angular Measurements of e+e−e+e−

  27. Measured: Z+γ Z only contribution Correction for γinteraction Left-Right Asymmetry • Measures asymmetry between Zs produced with different helicites: • Need to know beam energy precisely for γcorrection

  28. <Pe>: polarisation correction factor. (bunches are not 100% polarised) NL: Number of Zs produced by LH polarised bunches NR: Number of Zs produced by RH polarised bunches Left Right Asymmetry II • Measurement only possible at SLC, where beams are polarised. • Experimentalists’ Formula: • Valid independent of acceptance • Even nicer to measure than Afb, more things cancel!

  29. Beam Polarisation at SLC • Polarised beams means that the beam are composed of more eL than eR, or vice versa |<Pe>|: (0.244 ±0.006 ) in 1992 (0.7616±0.0040) in 1996 • |<Pe>| = 100% for fully polarised beams

  30. SLC: ALRResults A0LR = 0.1514±0.0022 sin2θW=0.23097±0.00027

  31. One more asymmetry: ALRfb • Results: • Combined result: • Equivalent to:

  32. Extracted from σ(e+e−→ff) Afb (e+e−→ℓℓ) ALR Status so far… • 6 parameters out of 18

  33. The Grand Reckoning • Correlations of the Z peak parameters for each of the LEP experiments

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