1 / 33

Exploring Electroweak Physics through Z Boson Measurements

This lecture covers using the Electroweak Lagrangian to predict Z boson widths and relating them to measurable events in labs like LEP and SLC. Topics include total cross section measurements, neutrino counts, various asymmetries, and techniques for measuring cross sections experimentally. The lecture also delves into angular cross sections and extracting values crucial to understanding the Standard Model.

buchanon
Download Presentation

Exploring Electroweak Physics through Z Boson Measurements

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related